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I want to reduce memory storage of chars using Bitwise Operations,
for Example
input: {"ACGT"}
output: {"0xE4"}
where we represtnt the number in binary then into Hexadecimal
if A=00, C=01, G=10, T=11
so ACGT = 0xE4 = 11100100b
I cant Figure the whole way so here is what I did So Far
enum NucleicAc {
A = 0,
C = 1,
G = 2,
T = 3,
} ;
struct _DNA {
char * seq ;
};
DNAString DSCreate(char * mseq) {
DNAString dna = malloc(sizeof(struct _DNA));
if (!dna){
exit(-1);
}
const int length = strlen(mseq);
// left shift will create the base , in the case of ACGT --> 0000,0000
int base = 0 << length * 2;
//loop and set bits
int i = 0 ;
int k = 0 ; // the counter where i want to modify the current bit
//simple looping gor the string
for ( ; i < length ; i++ ) {
switch (*(mseq+i)) {
case 'A': // 00
k++;
break;
case 'C': // 0 1
modifyBit(&base, k, 1);
k++;
break;
case 'G': //10
k++;
modifyBit(&base,k , 1);
break;
case 'T': // 11
modifyBit(&base, k, 1);
k++;
modifyBit(&base, k,1);
break;
default:
break;
} //end of switch
k++;
}//end of for
char * generatedSeq ;
//convert the base to hex ??
return dna;
}
void bin(unsigned n){
unsigned i;
for (i = 1 << 7; i > 0; i = i / 2){
(n & i) ? printf("1") : printf("0");
}
}
and if we print the base, the value is 11100100b as expected,
how to store the hexadecimal representation as String to the char *mseq in the struct ?
any direction or exact solutions or is there any better approach?
and also later i want to get the letter using only the index for Example
DSGet(dsStruct , '0')--> will return 'A' hence dsStruct contains the "ACGT" before Encode?
There are several ways you can approach encoding the sequence. Your enum is fine, but for your encoded sequence, a struct that captures the bytes as unsigned char, the original sequence length and the encoded size in bytes will allow an easy decoding. You will get 4-to-1 compression (plus 1 byte if you sequence isn't evenly divisible by 4). The enum and struct could be:
enum { A, C, G, T };
typedef struct {
unsigned char *seq;
size_t len, size;
} encoded;
To map characters in your string to the encoded values a simple function that returns the enum value matching the character is all you need (don't forget to handle any errors)
/* convert character to encoded value */
unsigned char getencval (const char c)
{
if (c == 'A')
return A;
else if (c == 'C')
return C;
else if (c == 'G')
return G;
else if (c == 'T')
return T;
/* exit on anything other than A, C, G, T */
fprintf (stderr, "error: invalid sequence character '%c'\n", c);
exit (EXIT_FAILURE);
}
To encode the original sequence, you will populate the encoded struct with the original length (len) and number of bytes (size) needed to hold the encoded string. Don't forget that any 1-character of the next 4-characters will require another byte of storage. You can use a simple add-and-divide to account for any partial 4-character ending portion of the sequence, e.g.
/* encode sequence of characters as 2-bit pairs (4-characters per-byte)
* returns encoded struct with allocated .seq member, on failure the .seq
* member is NULL. User is resposible for freeing .seq member when done.
*/
encoded encode_seq (const char *seq)
{
size_t len = strlen(seq),
size = (len + 3) / 4; /* integer division intentional */
encoded enc = { .seq = calloc (1, size), /* encoded sequence struct */
.len = len,
.size = size };
if (!enc.seq) { /* validate allication */
perror ("calloc-enc.seq");
return enc;
}
/* loop over each char (i) with byte index (ndx)
* shifting each 2-bit pair by (shift * 2) amount.
*/
for (int i = 0, ndx = 0, shift = 4; seq[i] && seq[i] != '\n'; i++) {
if (!shift--) /* decrement shift, reset if 0 */
shift = 3;
if (i && i % 4 == 0) /* after each 4th char, increment ndx */
ndx += 1;
/* shift each encoded value (multiply by 2 for shift of 6, 4, 2, 0) */
enc.seq[ndx] |= getencval (seq[i]) << shift * 2;
}
return enc; /* return encoded struct with allocated .seq member */
}
To get the original sequence back from your encoded struct, the use of a lookup table (shown below with the full code) makes it a breeze. You simply loop over all stored byte values appending the corresponding strings from the lookup table until the final byte. For the final byte, you need to determine if it is a partial string and, if so, how many characters remain to copy. (that's why you store the original sequence length in your struct). Then simply use strncat to append that many characters from the final byte, e.g.
/* decodes encoded sequence. Allocates storage for decoded sequence
* and loops over each encoded byte using lookup-table to obtain
* original 4-character string from byte value. User is responsible
* for freeing returned string when done. Returns NULL on allocation
* failure.
*/
char *decode_seq (encoded *eseq)
{
char *seq = malloc (eseq->len + 1); /* allocate storage for sequence */
size_t i = 0, offset = 0, remain;
if (!seq) { /* validate allocation */
perror ("malloc-seq");
return NULL;
}
/* loop appending strings from lookup table for all but last byte */
for (; i < eseq->size - 1; i++) {
memcpy (seq + offset, lookup[eseq->seq[i]], 4);
offset += 4; /* increment offset by 4 */
}
/* determine the number of characters in last byte */
remain = eseq->len - (eseq->size - 1) * 4;
memcpy (seq + offset, lookup[eseq->seq[i]], remain);
seq[offset + remain] = 0; /* nul-terminate seq */
return seq; /* return allocated sequence */
}
Adding the lookup table and putting all the pieces together, one way to approach this problem is:
(edit: lookup table reordered to match your byte-value encoding, optimized decode_seq() to not scan for end-of-string on copy)
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
enum { A, C, G, T };
typedef struct {
unsigned char *seq;
size_t len, size;
} encoded;
const char lookup[][5] = {
"AAAA","CAAA","GAAA","TAAA","ACAA","CCAA","GCAA","TCAA",
"AGAA","CGAA","GGAA","TGAA","ATAA","CTAA","GTAA","TTAA",
"AACA","CACA","GACA","TACA","ACCA","CCCA","GCCA","TCCA",
"AGCA","CGCA","GGCA","TGCA","ATCA","CTCA","GTCA","TTCA",
"AAGA","CAGA","GAGA","TAGA","ACGA","CCGA","GCGA","TCGA",
"AGGA","CGGA","GGGA","TGGA","ATGA","CTGA","GTGA","TTGA",
"AATA","CATA","GATA","TATA","ACTA","CCTA","GCTA","TCTA",
"AGTA","CGTA","GGTA","TGTA","ATTA","CTTA","GTTA","TTTA",
"AAAC","CAAC","GAAC","TAAC","ACAC","CCAC","GCAC","TCAC",
"AGAC","CGAC","GGAC","TGAC","ATAC","CTAC","GTAC","TTAC",
"AACC","CACC","GACC","TACC","ACCC","CCCC","GCCC","TCCC",
"AGCC","CGCC","GGCC","TGCC","ATCC","CTCC","GTCC","TTCC",
"AAGC","CAGC","GAGC","TAGC","ACGC","CCGC","GCGC","TCGC",
"AGGC","CGGC","GGGC","TGGC","ATGC","CTGC","GTGC","TTGC",
"AATC","CATC","GATC","TATC","ACTC","CCTC","GCTC","TCTC",
"AGTC","CGTC","GGTC","TGTC","ATTC","CTTC","GTTC","TTTC",
"AAAG","CAAG","GAAG","TAAG","ACAG","CCAG","GCAG","TCAG",
"AGAG","CGAG","GGAG","TGAG","ATAG","CTAG","GTAG","TTAG",
"AACG","CACG","GACG","TACG","ACCG","CCCG","GCCG","TCCG",
"AGCG","CGCG","GGCG","TGCG","ATCG","CTCG","GTCG","TTCG",
"AAGG","CAGG","GAGG","TAGG","ACGG","CCGG","GCGG","TCGG",
"AGGG","CGGG","GGGG","TGGG","ATGG","CTGG","GTGG","TTGG",
"AATG","CATG","GATG","TATG","ACTG","CCTG","GCTG","TCTG",
"AGTG","CGTG","GGTG","TGTG","ATTG","CTTG","GTTG","TTTG",
"AAAT","CAAT","GAAT","TAAT","ACAT","CCAT","GCAT","TCAT",
"AGAT","CGAT","GGAT","TGAT","ATAT","CTAT","GTAT","TTAT",
"AACT","CACT","GACT","TACT","ACCT","CCCT","GCCT","TCCT",
"AGCT","CGCT","GGCT","TGCT","ATCT","CTCT","GTCT","TTCT",
"AAGT","CAGT","GAGT","TAGT","ACGT","CCGT","GCGT","TCGT",
"AGGT","CGGT","GGGT","TGGT","ATGT","CTGT","GTGT","TTGT",
"AATT","CATT","GATT","TATT","ACTT","CCTT","GCTT","TCTT",
"AGTT","CGTT","GGTT","TGTT","ATTT","CTTT","GTTT","TTTT"};
/* convert character to encoded value */
unsigned char getencval (const char c)
{
if (c == 'A')
return A;
else if (c == 'C')
return C;
else if (c == 'G')
return G;
else if (c == 'T')
return T;
/* exit on anything other than A, C, G, T */
fprintf (stderr, "error: invalid sequence character '%c'\n", c);
exit (EXIT_FAILURE);
}
/* encode sequence of characters as 2-bit pairs (4-characters per-byte)
* returns encoded struct with allocated .seq member, on failure the .seq
* member is NULL. User is resposible for freeing .seq member when done.
*/
encoded encode_seq (const char *seq)
{
size_t len = strlen(seq),
size = (len + 3) / 4; /* integer division intentional */
encoded enc = { .seq = calloc (1, size), /* encoded sequence struct */
.len = len,
.size = size };
if (!enc.seq) { /* validate allication */
perror ("calloc-enc.seq");
return enc;
}
/* loop over each char (i) with byte index (ndx)
* shifting each 2-bit pair by (shift * 2) amount.
*/
for (int i = 0, ndx = 0, shift = 0; seq[i] && seq[i] != '\n'; i++, shift++) {
if (shift == 4) /* reset to 0 */
shift = 0;
if (i && i % 4 == 0) /* after each 4th char, increment ndx */
ndx += 1;
/* shift each encoded value (multiply by 2 for shift of 0, 2, 4, 6) */
enc.seq[ndx] |= getencval (seq[i]) << shift * 2;
}
return enc; /* return encoded struct with allocated .seq member */
}
/* decodes encoded sequence. Allocates storage for decoded sequence
* and loops over each encoded byte using lookup-table to obtain
* original 4-character string from byte value. User is responsible
* for freeing returned string when done. Returns NULL on allocation
* failure.
*/
char *decode_seq (encoded *eseq)
{
char *seq = malloc (eseq->len + 1); /* allocate storage for sequence */
size_t i = 0, offset = 0, remain;
if (!seq) { /* validate allocation */
perror ("malloc-seq");
return NULL;
}
/* loop appending strings from lookup table for all but last byte */
for (; i < eseq->size - 1; i++) {
memcpy (seq + offset, lookup[eseq->seq[i]], 4);
offset += 4; /* increment offset by 4 */
}
/* determine the number of characters in last byte */
remain = eseq->len - (eseq->size - 1) * 4;
memcpy (seq + offset, lookup[eseq->seq[i]], remain);
seq[offset + remain] = 0; /* nul-terminate seq */
return seq; /* return allocated sequence */
}
/* short example program that takes string to encode as 1st argument
* using "ACGT" if no argument is provided by default
*/
int main (int argc, char **argv) {
char *seq = NULL;
encoded enc = encode_seq(argc > 1 ? argv[1] : "ACGT");
if (!enc.seq) /* validate encoded allocation */
return 1;
/* output original string, length and encoded size */
printf ("encoded str : %s\nencoded len : %zu\nencoded size : %zu\n",
argc > 1 ? argv[1] : "ACGT", enc.len, enc.size);
/* loop outputting byte-values of encoded string */
fputs ("encoded seq :", stdout);
for (size_t i = 0; i < enc.size; i++)
printf (" 0x%02x", enc.seq[i]);
putchar ('\n');
seq = decode_seq (&enc); /* decode seq from byte values */
printf ("decoded seq : %s\n", seq); /* output decoded string */
free (seq); /* don't forget to free what you allocated */
free (enc.seq);
}
In most cases a lookup-table provides a great deal of efficiency advantage compared to computing and building each 4-character string during decoding. This is enhanced by the lookup table staying resident in cache for most cases.
The length of the DNA sequence you can encode and decode is limited only by the amount of virtual memory you have available.
Example Use/Output
The program takes the sequence to encode and decode as the first argument (default "ACGT"). So the default output is:
$ ./bin/dnaencodedecode
encoded str : ACGT
encoded len : 4
encoded size : 1
encoded seq : 0xe4
decoded seq : ACGT
4-byte encoded in 1-byte. Note the byte value of 0x1b and not 0xe4 due to the table ordering.
A longer example:
./bin/dnaencodedecode ACGTGGGTCAGACTTA
encoded str : ACGTGGGTCAGACTTA
encoded len : 16
encoded size : 4
encoded seq : 0xe4 0xea 0x21 0x3d
decoded seq : ACGTGGGTCAGACTTA
16-character encoded in 4-bytes.
Finally, what of a sequence that isn't divisible by 4 so you have a partial number of characters in the last encoded byte? That is handled as well, e.g.
$ ./bin/dnaencodedecode ACGTGGGTCAGACTTAG
encoded str : ACGTGGGTCAGACTTAG
encoded len : 17
encoded size : 5
encoded seq : 0xe4 0xea 0x21 0x3d 0x02
decoded seq : ACGTGGGTCAGACTTAG
17 characters encoded in 5-bytes. (not the pure 4-to-1 compression, but as the sequence size increases, the significance of any partial group of characters in the last byte becomes negligible)
As far a perfomance, for a sequence of 100,000 characters and output of the the byte values and strings replaced with a simple loop that compares the decoded seq to the original argv[1] it only takes a few thousandth of a second (on an old i7 Gen2 laptop with SSD) to encode and decode and validate, e.g.
$
time ./bin/dnaencodedecodet2big $(< dat/dnaseq100k.txt)
encoded len : 100000
encoded size : 25000
all tests passed
real 0m0.014s
user 0m0.012s
sys 0m0.003s
There are a lot of ways to do this, but given your description, this was what came to my mind that you were trying to accomplish. There is a lot here, so take your time going through it.
Look things over (the code is commented), and let me know if you have further questions. Just drop a comment below.
This should do what you want. I thought the compression was a pretty cool idea so I wrote this real quick. As mentioned by #kaylum, hex encoding is just a way to read the underlying data in memory, which is always just bits. So, you only need to worry about that on print statements.
Let me know if this works or you have any questions about what I did.
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
typedef struct {
unsigned char *bits;
unsigned long length; // use this to store the number of letters encoded, for safety
} DNA;
typedef enum {
A = 0,
C = 1,
G = 2,
T = 3
} NucleicAc;
This returns the base at a given index with some bounds checking
char base_at_index(DNA *dna, unsigned long index) {
if (index >= dna->length) {
fputs("error: base_at_index: index out of range", stderr);
exit(EXIT_FAILURE);
}
// offset is index / 4, this gives us the correct byte
// shift amount is index % 4 to give us the correct 2 bits within the byte.
// This must then be multiplied by 2 because
// each base takes 2 bits to encode
// then we have to bitwise-and this value with
// 3 (0000 0011 in binary) to retrieve the bits we want.
// so, the formula we need is
// (dna->bits[index / 4] >> (2 * (index % 4))) & 3
switch((dna->bits[index / 4] >> 2 * (index % 4)) & 3) {
case A: return 'A';
case C: return 'C';
case G: return 'G';
case T: return 'T';
default:
fputs("error: base_at_index: invalid encoding", stderr);
exit(EXIT_FAILURE);
}
}
This encodes a string of bases to bytes
/* you can fit four 2-bit DNA codes in each byte (unsigned char).
len is the maximum number of characters to read. result must be at least len bytes long
*/
void encode_dna(unsigned char *result, char *sequence, unsigned long len) {
// keep track of what byte we are on in the result
unsigned result_index = 0;
// our shift for writing to the correct position in the byte
unsigned shift = 0;
// first clear result or else bitwise operations will produce errors
// this could be removed if you were certain result parameter was zero-filled
memset(result, 0, len);
// iterate through characters of the sequence
while(*sequence) {
switch (*sequence) {
// do nothing for 'A' since it is just zero
case 'A': break;
case 'C':
// we are doing a bitwise or with the current byte
// and C (1) shifted to the appropriate position within
// the byte, and then assigning the byte with the result
result[result_index] |= C << shift;
break;
case 'G':
result[result_index] |= G << shift;
break;
case 'T':
result[result_index] |= T << shift;
break;
default:
fputs("error: encode_dna: invalid base pair", stderr);
exit(EXIT_FAILURE);
}
// increase shift amount by 2 to the next 2-bit slot in the byte
shift += 2;
// on every 4th iteration, reset our shift to zero since the byte is now full
// and move to the next byte in our result buffer
if (shift == 8) {
shift = 0;
result_index++;
}
// advance sequence to next nucleotide character
sequence++;
}
}
And here's a test
int main(int argc, char **argv) {
// allocate some storage for encoded DNA
unsigned char encoded_dna[32];
const unsigned long sample_length = 15;
// encode the given sample sequence
encode_dna(encoded_dna, "ACGTAGTCGTCATAG", sample_length);
// hh here means half of half word, which is a byte
// capital X for capitalized hex output
// here we print some bytes
printf("0x%hhX\n", encoded_dna[0]); // should output 0xE4
printf("0x%hhX\n", encoded_dna[1]); // should be 0x78
printf("0x%hhX\n", encoded_dna[2]); // should be 0x1E
printf("0x%hhX\n", encoded_dna[3]); // should be 0x23
DNA test_dna; // allocate a sample DNA structure
test_dna.bits = encoded_dna;
test_dna.length = sample_length; // length of the sample sequence above
// test some indices and see if the results are correct
printf("test_dna index 4: %c\n", base_at_index(&test_dna, 4));
printf("test_dna index 7: %c\n", base_at_index(&test_dna, 7));
printf("test_dna index 12: %c\n", base_at_index(&test_dna, 12));
return 0;
}
Output:
0xE4
0x78
0x1E
0x23
test_dna index 4: A
test_dna index 7: C
test_dna index 12: T
Assuming you really do want to encode your dna string into a hex string and that you want to read the input string from left to right, but output hex chars right to left, here's a simple, but slightly slow implementation.
First, your DNAString needs to keep track whether there are really an even or odd number of acid sequences in the list. This will make additional appendages easier.
struct DNAString
{
char* seq;
bool odd; // if odd bit is set, then the front char is already allocated and holds one acid
};
And now let's introduce a little helper function to convert ACGT into 0,1,2,3.
char acid_to_value(char c)
{
switch (c)
{
case 'A': return 0;
case 'C': return 1;
case 'G': return 2;
case 'T': return 3;
}
// ASSERT(false)
return 0;
}
Then the core implementation is to keep "prepending" new hexchars onto the string your are building. If the string is already of an odd length, the code will just "fixup" the front character by converting it from hex to integer, then shifting the new acid value into it, then converting it back to a hex char
extern char fixup(char previous, char acid);
{
char hexchars[16] = { '0','1','2','3','4','5','6','7','8','9','A','B','C','D','E','F' };
char tmp[2] = { previous, '\0' };
unsigned long asnumber = strtol(tmp, nullptr, 16);
asnumber = asnumber & 0x3; // last two bits
asnumber = asnumber | (acid_to_value(acid) << 2);
return hexchars[asnumber];
}
void prepend_nucleic_acid_to_hexstring(struct DNAString* dnastring, char acid)
{
if (dnastring->odd)
{
// find the first char in the string and fix it up hexwise
dnastring->seq[0] = fixup(dnastring->seq[0], acid);
dnastring->odd = false;
}
else
{
size_t currentlength = dnastring->seq ? strlen(dnastring->seq) : 0;
const char* currentstring = dnastring->seq ? dnastring->seq : "";
char* newseq = (char*)calloc(currentlength + 2, sizeof(char)); // +1 for new char and +1 for null char
newseq[0] = acid_to_value(acid) + '0'; // prepend the next hex char
strcpy(newseq + 1, currentstring); // copy the old string into the new string space
free(dnastring->seq);
dnastring->seq = newseq;
dnastring->odd = true;
}
}
Then your DNACreate function is real simple:
struct DNAString DSCreate(const char* mseq)
{
DNAString dnastring = { 0 };
while (*mseq)
{
prepend_nucleic_acid_to_hexstring(&dnastring, *mseq);
mseq++;
}
return dnastring;
}
I don't claim this approach to be efficient since he literally keeps reallocating memory for each char. But it does enable you to have flexability to invoke the prepend function later for additional sequencing.
And then to test it:
int main()
{
struct DNAString dnastring = DSCreate("ACGT");
printf("0x%s\n", dnastring.seq);
return 0;
}
I am trying to determine a function to extract the individual digits of a long data type which the user enters.
int remain(int digit)
{
while(number != 0)
{
digit = number % 10;
number = number / 10;
}
return digit;
}
In this code the number variable is the number entered by user.
I want to extract all the digits of the number (e.g. a 16 digit number). So when I print remain(16) it prints 16 instead of 16th digit or prints 1 if I print remain(1). And also it prints the first digit if the number is less than 13 or greater than 16 and prints the 1 or 2 or 3 if i print remain(1) or remain(2) or remain(3) instead of printing the 1st or 2nd or 3rd digit, if the number is 13 digit long or 16 digit long or 15 digit long.
Okay, after your edit, I understand you want to print the return of the function and have all digits print. While you can simply use printf(), extracting with % and / is another way to extract digits. But, as you have found, when you extract digits with % and /, the digits will end up in reverse order. The solve that problem, you simply fill an array with digits, working from the end of the array back to the beginning.
Now before looking at a solution, if you want to "... extract the individual digits of a long data..." -- you will need to change the type in your function from int to long or you will experience a mismatch of type-size on systems where int and long are different sizes (like on x86_64).
In order for the array to survive the return of your function, you can either pass in an array to fill using another parameter, or you can declare your array with static storage duration so it survives return (but not that make the function not thread_safe in multithreaded programs -- not a concern here)
You can do something like the following:
#include <stdio.h>
#include <stdlib.h>
#define NCHR 32 /* if you need a constant, #define one (or more) */
#define BASE 10
char *extract_digits (long n)
{
static char digits[NCHR]; /* static, so digits survives return */
char *p = digits + NCHR - 1; /* pointer to last char in digits */
int sign = n < 0; /* check sign of n (negative, sign == 1) */
if (sign) /* process positive number */
n = -n;
if (!n) { /* handle zero case, sign irrelevant */
*--p = '0';
return p;
}
do { /* convert each digit to char */
*--p = n % BASE + '0'; /* fill from end of digits array */
n /= BASE;
} while (n);
if (sign) /* if sign, add '-' at front */
*--p = '-';
return p; /* return ptr to start of digits in digits[] */
}
int main (int argc, char **argv) {
long v = argc > 1 ? strtol(argv[1], NULL, BASE) : -2381;
printf ("digits: %s\n", extract_digits(v));
}
(note: I have change the function name to extract_digits(), you can rename it as you please)
The program prints the extracted digits directly using the function return -- which is what I take was your intent from the question.
Example Use/Output
Using default value:
$ ./bin/extractdigits_fnc
digits: -2381
Passing value:
$ ./bin/extractdigits_fnc 54823
digits: 54823
Passing zero:
$ ./bin/extractdigits_fnc 0
digits: 0
Passing negative zero:
$ ./bin/extractdigits_fnc -0
digits: 0
Your '16' example:
$ ./bin/extractdigits_fnc 16
digits: 16
Look things over and let me know if I understood your question correctly.
If you are looking for a function that can extract the n'th digit in a number, it can be something like:
int extract_digit(unsigned long long number, unsigned digit)
{
int res = -1;
if (digit > 0)
{
unsigned count = 1;
unsigned long long tmp = number;
while(tmp/10 > 0)
{
++count;
tmp /= 10;
}
if (digit <= count)
{
tmp = number;
while ((count - digit) > 0)
{
--count;
tmp /= 10;
}
res = tmp % 10;
}
}
return res;
}
Notice that the function assumes that the left-most digit is digit 1.
The function will return a -1 if the requested "digit" doesn't exists. Otherwise the function returns the digit.
The function can be used like:
int main(void){
unsigned long long number = 31415926535ULL;
printf("number: %llu\n", number);
for (unsigned i = 0; i < 13; ++i)
{
int n = extract_digit(number, i); // Get i'th digit
if (n < 0)
{
printf("Digit %u is out of range\n", i);
}
else
{
printf("Digit %u is %d\n", i, n);
}
}
return 0;
}
Output
number: 31415926535
Digit 0 is out of range
Digit 1 is 3
Digit 2 is 1
Digit 3 is 4
Digit 4 is 1
Digit 5 is 5
Digit 6 is 9
Digit 7 is 2
Digit 8 is 6
Digit 9 is 5
Digit 10 is 3
Digit 11 is 5
Digit 12 is out of range
Short story. I made a program that does addition for binary integers. I need to make it work for binary real numbers (e.g. 1010.1010(binary)=10.625(decimal)
The input is given as a binary string.
I made a lot of attempts and I couldn't find a simple way to do it. Please help create such a program.
Example: {input: 1010.1010(10.625 in decimal) 0.1(0.5 in decimal)
output: 1011.001 (11.125 in decimal)}
Code:
#include <stdio.h>
#include <string.h>
void bin_add(int c[400], int d[400])
{
int car[400]; //carry
int i = 199;
car[i] = 0;
while (i >= 0)
{
//find carry and shift it left
//find the sum
car[i - 1] = (c[i] & d[i]) | (c[i] & car[i]) | (d[i] & car[i]);
c[i] = (c[i] ^ d[i]) ^ car[i];
printf("car[i-1]=%d c[i]=%d\n", car[i - 1], c[i]);
i--;
}
// printf("\n");
}
int main()
{
int l, l1, i;//l and l1 are lengths
char a[200], b[200]; //a and b are the inputs
int c[200], d[200]; //c and d are used for processing
for (i = 0; i < 200; i++)
{
c[i] = 0;
d[i] = 0;
}
gets(a);
gets(b);
l = strlen(a);
l1 = strlen(b);
for (int i = 0; i < l; i++)
{
c[200 - l + i] = a[i] - 48;
}
////////////////////////////////////////////
for (int i = 0; i < l1; i++)
{
d[200 - l1 + i] = b[i] - 48;
}
////////////////////////////////
bin_add(c, d);
for (i = 0; i < 200; i++)
printf("%d", c[i]);
return 0;
}
What you really want to do, is handle each digit in order of increasing importance. To make that easier, you should implement the following functions:
/* Return the number of fractional bits in bs */
int bs_fractbits(const char *bs);
/* Return the number of integer bits in bs */
int bs_intbits(const char *bs);
/* Return the bit in bs corresponding to value 2**i,
0 if outside the bit string */
int bs_bit(const char *bs, int i);
/* Return -1 if bs is negative,
0 if bs is zero or NULL,
+1 if bs is positive */
int bs_sign(const char *bs);
/* Return -1 if bs1 < bs2,
0 if bs1 == bs2,
+1 if bs1 > bs2. */
int bs_cmp(const char *bs1, const char *bs2);
To support negative values, you'll need to implement both addition and subtraction (of "unsigned" bit strings):
Addition: The result has as many fractional bits as the term that has most fractional bits, and possibly one more integer bit than the term that has most integer bits. Start at the least significant bit in either term, and work your way up to the most significant bit in either term, summing each bit, and keeping the "carry bit" along, just like you'd do by hand. If the carry is nonzero at end, you'll get that one additional bit.
Subtraction: Always subtract smaller from larger. If that changes the order of the terms, negate the result. The result has at most as many fractional bits as the term that has most fractional bits, and at most as many integer bits as the term that has most integer bits. This is just like addition, except you subtract the bits, and instead of "carry bit", you use a "borrow bit". Because you subtract smaller unsigned value from larger unsigned value, the "borrow bit" will be zero at end.
Multiplication: The integer part has the number of integer bits, and the number of fractional bits, as the terms have in total (summed). You can implement the operation as if multiplying two unsigned integer values, and just insert the bit at end. (So that the result has as many fractional bits as the input terms have in total.) This usually involves a double loop, just like in long multiplication by hand.
Note that the same logic also works if you use larger radix instead of 2. The "carry"/"borrow" is a digit, between zero and one less than the radix.
Personally, I'd be very tempted to use a structure to describe each digit string:
typedef struct {
int idigits; /* Number of integral digits before point */
int fdigits; /* Number of fractional digits after point */
int size; /* Number of chars dynamically allocated at data */
char *point; /* Location of decimal point */
char *data; /* Dynamically allocated buffer */
} digitstring;
#define DIGITSTRING_INIT { 0, 0, 0, NULL, NULL }
with an additional flag if negative digit strings are to be supported.
Digit D with numerical value D×Bi, where B is the radix (number of unique digits used) and i being the position of said digit, is located at point[-i] if i < 0 (and -i <= fdigits), or at point[-i-1] if i >= 0 (and i < idigits). point[0] itself is where the decimal point is, if there is one.
For example, if we have string 0100.00, then idigits = 4, fdigits = 2, and the only nonzero digit is at position 2. (Position 0 is on the left side of the decimal point, and -1 on the right side.)
size and data fields allow reuse of the dynamically allocated buffer. Each declaration of a digitstring must be initialized, digitstring value = DIGITSTRING_INIT;, because there is no initialization function; this way you are less likely to leak memory (unless you forget to free a digitstring when no longer needed):
/* Free the specified digit string. */
static inline void digitstring_free(digitstring *ds)
{
if (ds) {
if (ds->data)
free(ds->data);
ds->idigits = 0;
ds->fdigits = 0;
ds->size = 0;
ds->point = NULL;
ds->data = NULL;
}
}
To use the digit string as a C string, you use a helper function to obtain the pointer to the most significant digit in the digit string:
/* Return a pointer to a printable version of the digit string. */
static const char *digitstring_str(const digitstring *ds, const char *none)
{
if (ds && ds->point)
return (const char *)(ds->point - ds->idigits);
else
return none;
}
I've found that rather than crash, it is often useful to pass an extra parameter that is only used for the return value when the return value is otherwise undefined. For example, if you have an initialized digit string foo without any contents, then digitstring_str(&foo, "0") returns the string literal "0".
The main point of the digit string structure is to have accessor functions that get and set each individual digit:
/* Get the value of a specific digit. */
static inline unsigned int digitstring_get(const digitstring *ds, const int position)
{
if (ds) {
if (position < 0) {
if (-position <= ds->fdigits)
return digit_to_value(ds->point[-position]);
else
return 0;
} else {
if (position < ds->idigits)
return digit_to_value(ds->point[-position-1]);
else
return 0;
}
} else
return 0;
}
/* Set the value of a specific digit. */
static inline void digitstring_set(digitstring *ds, const int position, const unsigned int value)
{
if (!ds) {
fprintf(stderr, "digitstring_set(): NULL digitstring specified.\n");
exit(EXIT_FAILURE);
} else
if (position < 0) {
if (-position > ds->fdigits) {
fprintf(stderr, "digitstring_set(): Digit position underflow (in fractional part).\n");
exit(EXIT_FAILURE);
}
ds->point[-position] = value_to_digit(value);
} else {
if (position >= ds->idigits) {
fprintf(stderr, "digitstring_set(): Digit position overflow (in integer part).\n");
exit(EXIT_FAILURE);
}
ds->point[-position-1] = value_to_digit(value);
}
}
Above, value_to_digit() is a helper function that converts a numerical value to the corresponding character, and digit_to_value() converts a character to the corresponding numerical value.
All operations (from parsing to arithmetic operators) really need a "constructor", that creates a new digit string with sufficient number of digits. (The number of digits is known beforehand for each operation, and depends only on the number of significant digits in the terms.) For this, I created a function that constructs a zero of desired size:
/* Clear the specified digit string to zero. */
static inline void digitstring_zero(digitstring *ds, int idigits, int fdigits)
{
int size;
char *data;
if (!ds) {
fprintf(stderr, "digitstring_zero(): No digitstring specified.\n");
exit(EXIT_FAILURE);
}
/* Require at least one integral digit. */
if (idigits < 1)
idigits = 1;
if (fdigits < 0)
fdigits = 0;
/* Total number of chars needed, including decimal point
and string-terminating nul char. */
size = idigits + 1 + fdigits + 1;
/* Check if dynamically allocated buffer needs resizing. */
if (ds->size < size) {
if (ds->data)
data = realloc(ds->data, size);
else
data = malloc(size);
if (!data) {
fprintf(stderr, "digitstring_zero(): Out of memory.\n");
exit(EXIT_FAILURE);
}
ds->data = data;
ds->size = size;
} else {
data = ds->data;
size = ds->size;
}
/* Fill it with zeroes. */
memset(data, value_to_digit(0), idigits + 1 + fdigits);
/* Pad the unused space with nul chars, terminating the string. */
memset(data + idigits + 1 + fdigits, '\0', size - idigits - 1 - fdigits);
/* Assign the decimal point. */
ds->point = data + idigits;
/* If there are no decimals, no need for a decimal point either. */
if (fdigits > 0)
ds->point[0] = decimal_point;
else
ds->point[0] = '\0';
/* After setting the desired digits, use digitstring_trim(). */
ds->idigits = idigits;
ds->fdigits = fdigits;
}
It will ensure the digit string has enough room for the specified number of digits, reallocating its dynamically allocated buffer if necessary, reusing it if already large enough.
The idea is that to implement an operation, you first find out the maximum number of integral and fractional digits the result can have. You use the above to create the result digit string, then digitstring_set() to set each digit to their respective values. You will typically operate in increasing digit significance, which means increasing digit "positions".
If we have additional helper functions int digits(const char *src), which returns the number of consecutive valid digit characters starting at src, and int decimal_points(const char *src), which returns 1 if src points to a decimal point, and 0 otherwise, we can parse input strings into digit strings using
/* Parse a string into a digit string, returning the pointer
to the first unparsed character, or NULL if an error occurs. */
static const char *digitstring_parse(digitstring *ds, const char *src)
{
const int zero = value_to_digit(0);
const char *idigit, *fdigit;
int idigits, fdigits, fextra, n;
/* Fail if nothing to parse. */
if (!src)
return NULL;
/* Skip leading whitespace. */
while (isspace((unsigned char)(*src)))
src++;
/* Fail if nothing to parse. */
if (*src == '\0')
return NULL;
/* Scan integer digits. */
idigit = src;
src += digits(src);
idigits = (int)(src - idigit);
/* Decimal point? */
fextra = 0;
n = decimal_points(src);
if (n > 0) {
src += n;
/* Scan fractional digits. */
fdigit = src;
src += digits(src);
fdigits = (int)(src - fdigit);
if (fdigits < 1)
fextra = 1;
} else {
fdigit = src;
fdigits = 0;
}
/* No digits? */
if (idigit == 0 && fdigit == 0)
return NULL;
/* Trim leading zeroes. */
while (idigits > 1 && *idigit == zero) {
idigits--;
idigit++;
}
/* Trim trailing zeroes. */
while (fdigits > 1 && fdigit[fdigits - 1] == zero)
fdigits--;
/* Create the necessary digit string, */
digitstring_zero(ds, idigits, fdigits + fextra);
/* copy the integer digits, if any, */
if (idigits > 0)
memcpy(ds->point - idigits, idigit, idigits);
/* and the fractional digits, if any. */
if (fdigits > 0)
memcpy(ds->point + 1, fdigit, fdigits);
/* Return a pointer to the first unparsed character. */
return src;
}
After updating its digits, one can call a helper function to remove any extra leading zeroes:
static inline void digitstring_ltrim(digitstring *ds)
{
if (ds && ds->point) {
const int zero = value_to_digit(0);
while (ds->idigits > 1 && ds->point[-ds->idigits] == zero)
ds->idigits--;
}
}
Adding two (unsigned) digit strings, possibly reusing one of the terms, is now quite simple to implement:
static void digitstring_add(digitstring *to, const digitstring *src1, const digitstring *src2)
{
digitstring result = DIGITSTRING_INIT;
unsigned int carry = 0;
int i, idigits, fdigits;
if (!to || !src1 || !src2) {
fprintf(stderr, "digitstring_add(): NULL digitstring specified.\n");
exit(EXIT_FAILURE);
}
/* For addition, the result has as many digits
as the longer source term. */
idigits = (src1->idigits >= src2->idigits) ? src1->idigits : src2->idigits;
fdigits = (src1->fdigits >= src2->fdigits) ? src1->fdigits : src2->fdigits;
/* Result needs possibly one more integer digit,
in case carry overflows. */
digitstring_zero(&result, idigits + 1, fdigits);
/* Addition loop, in order of increasing digit significance. */
for (i = -fdigits; i < idigits; i++) {
const unsigned int sum = digitstring_get(src1, i)
+ digitstring_get(src2, i)
+ carry;
digitstring_set(&result, i, sum % RADIX);
carry = sum / RADIX;
}
digitstring_set(&result, idigits, carry);
/* Trim leading zeroes. */
digitstring_ltrim(&result);
/* At this point, we can discard the target, even if it is actually
one of the sources, and copy the result to it. */
digitstring_free(to);
*to = result;
}
where RADIX is the radix used (the number of unique digits, 2 for binary). Pay extra attention to the digit loop. -fdigits is the least significant position in the result, and idigits-1 the most significant position. We need the accessor functions, because the source terms might not contain those digits at all (they are logically zero then).
These functions have been tested to work on both binary and octal number strings. I like this implementation, because it omits the decimal point if all terms are integers (so you get 12 + 33 = 45), but (due to fextra in digitstring_parse()) if any of the terms have a decimal point, then the result will have at least one fractional digit (so 12. + 33 = 45.0).
After all the beautiful ideas in Animals' answer I felt the strange urge, to present my own solution:
#include <stdbool.h>
#include <stddef.h>
#include <string.h>
#include <stdlib.h>
#include <stdio.h>
#define MAX(x, y) ((x) > (y) ? (x) : (y))
size_t gpp(char const *s)
{
char *n = strchr(s, '.');
return n ? n - s + 1 : 0;
}
char* bin_add(char const *a, char const *b)
{
char const *inp[] = { a, b };
size_t ll[] = { strlen(a), strlen(b) };
size_t pp[] = { gpp(a), gpp(b) };
size_t OO[2], off[2];
for (size_t i = 0; i < 2; ++i) {
OO[i] = pp[i] ? pp[i] - 1 : ll[i];
pp[i] = pp[i] ? ll[i] - pp[i] : 0;}
for (size_t i = 0; i < 2; ++i)
off[i] = OO[i] < OO[!i] ? OO[!i] - OO[i] : 0;
size_t ML = MAX(OO[0], OO[1]) + MAX(pp[0], pp[1]) + (!!pp[0] || !!pp[1]);
char *Ol = calloc(ML + 2, 1);
if(!Ol) return Ol;
char ops[2];
int xc = 0;
size_t lO = ML;
unsigned cc[2] = { 0 };
for (size_t i = ML; i; --i) {
bool pt = false;
for (size_t l = 0; l < 2; ++l) {
ops[l] = i <= ll[l] + off[l] && i - off[l] - 1
< ll[l] ? inp[l][i - off[l] - 1] : '0';
if (ops[l] == '.') {
if (cc[l]) {
free(Ol);
return NULL;
}
pt = true;
++cc[l];
}
ops[l] -= '0';
}
if (pt) {
Ol[i] = '.';
continue;
}
if ((Ol[i] = ops[0] + ops[1] + xc) > 1) {
Ol[i] = 0;
xc = 1;
}
else xc = 0;
lO = (Ol[i] += '0') == '1' ? i : lO;
}
if((Ol[0] = '0' + xc) == '1') return Ol;
for (size_t i = 0; i <= ML - lO + 1; ++i)
Ol[i] = Ol[lO + i];
return Ol;
}
int main(void)
{
char a[81], b[81];
while (scanf(" %80[0.1] %80[0.1]", a, b) & 1 << 1) {
char *c = bin_add(a, b);
if (!c && errno == ENOMEM) {
fputs("Not enough memory :(\n\n", stderr);
return EXIT_FAILURE;
}
else if (!c) {
fputs("Input error :(\n\n", stderr);
goto clear;
}
char* O[] = { a, b, c };
size_t lO[3], Ol = 0;
for (size_t i = 0; i < 3; ++i) {
lO[i] = gpp(O[i]);
lO[i] = lO[i] ? lO[i] : strlen(i[O]) + 1;
Ol = lO[i] > Ol ? lO[i] : Ol;
}
putchar('\n');
for (size_t i = 0; i < 3; ++i) {
for (size_t l = 0; l < Ol - lO[i]; ++l, putchar(' '));
puts(O[i]);
}
putchar('\n');
free(c);
clear :{ int c; while ((c = getchar()) != '\n' && c != EOF); }
}
}
Sample Output:
11001001 .11001001
11001001
.11001001
11001001.11001001
11001001 1010
11001001
1010
11010011
111111 1
111111
1
1000000
1010101 010111001.0101110101010
1010101
010111001.0101110101010
100001110.0101110101010
1001001.010111010101 10100101100.10010111101
1001001.010111010101
10100101100.10010111101
10101110101.111000001111
. .
.
.
0
.. .
Input error :(
A
Press any key to continue . . .
I contemplated wheter I should ask for a review at codereview. But I think I schould rather not.
There are two answers, depending upon whether you desire fixed- or floating- point arithmetic.
The first issue is reading the number. strtol() is your friend here:
char input[BUFFER_SIZE];
char * tmp;
long integral, fractional;
fgets(input, BUFFER_SIZE-1, stdin);
integral = strtol(input, &tmp, 2); /* Read BINARY integral part */
tmp++; /* Pass over the binary point. You may want to check that it is actually a dot */
fractional = strtol(tmp, null, 2); /* Read BINARY fractional part */
The next issue is figuring out how you will do the arithmetic. fractional must be bit-shifted an amount depending on how many digits past the point were provided and your desired precision. Fixed point arithmetic is simple: fractional <<= FRAC_BITS - strlen(tmp) then add the fractional parts together. Mask by ((1<<FRAC_BITS)-1) for the fractional part of the sum, shift the remaining bits and add them to the integral parts for the integral part of the sum. Floating-point is a little more finicky, but not too much harder.
For real numbers, convert non-fraction and fraction part to decimal, do the addition and print it as binary. This will require function to convert a number to binary string. Just a note that real numbers are float numbers in C and they are represented in binary with mantessa form like 2e^3 which is 2 multiplied by exponent to the power of 3.
I am trying obtain 9 digit numbers that all have unique digits. My first approach seems a bit too complex and would be tedious to write.
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
int main()
{
int indx;
int num;
int d1, d2, d3, d4, d5, d6, d7, d8, d9;
for(indx = 123456789; indx <= 987654321; indx++)
{
num = indx;
d1 = num % 10;
d2 = ( num / 10 ) % 10;
d3 = ( num / 100 ) % 10;
d4 = ( num / 1000 ) % 10;
d5 = ( num / 10000 ) % 10;
d6 = ( num / 100000 ) % 10;
d7 = ( num / 1000000 ) % 10;
d8 = ( num / 10000000 ) % 10;
d9 = ( num / 100000000 ) % 10;
if( d1 != d2 && d1 != d3 && d1 != d3 && d1 != d4 && d1 != d5
&& d1 != d6 && d1 != d7 && d1 != d8 && d1 != d9 )
{
printf("%d\n", num);
}
}
}
That is just comparing the first number to the rest. I would have to do that many more to compare the other numbers. Is there a better way to do this?
This is a pretty typical example of a problem involving combinatorics.
There are exactly 9⋅8⋅7⋅6⋅5⋅4⋅3⋅2⋅1 = 9! = 362880 nine-digit decimal numbers, where each digit occurs exactly once, and zero is not used at all. This is because there are nine possibilities for the first digit, eight for the second, and so on, since each digit is used exactly once.
So, you can easily write a function, that takes in the seed, 0 ≤ seed < 362880, that returns one of the unique combinations, such that each combination corresponds to exactly one seed. For example,
unsigned int unique9(unsigned int seed)
{
unsigned char digit[9] = { 1U, 2U, 3U, 4U, 5U, 6U, 7U, 8U, 9U };
unsigned int result = 0U;
unsigned int n = 9U;
while (n) {
const unsigned int i = seed % n;
seed = seed / n;
result = 10U * result + digit[i];
digit[i] = digit[--n];
}
return result;
}
The digit array is initialized to the set of nine thus far unused digits. i indicates the index to that array, so that digit[i] is the actual digit used. Since the digit is used, it is replaced by the last digit in the array, and the size of the array n is reduced by one.
Some example results:
unique9(0U) == 198765432U
unique9(1U) == 218765439U
unique9(10U) == 291765438U
unique9(1000U) == 287915436U
unique9(362878U) == 897654321U
unique9(362879U) == 987654321U
The odd order for the results is because the digits in the digit array switch places.
Edited 20150826: If you want the indexth combination (say, in lexicographic order), you can use the following approach:
#include <stdlib.h>
#include <string.h>
#include <errno.h>
typedef unsigned long permutation_t;
int permutation(char *const buffer,
const char *const digits,
const size_t length,
permutation_t index)
{
permutation_t scale = 1;
size_t i, d;
if (!buffer || !digits || length < 1)
return errno = EINVAL;
for (i = 2; i <= length; i++) {
const permutation_t newscale = scale * (permutation_t)i;
if ((permutation_t)(newscale / (permutation_t)i) != scale)
return errno = EMSGSIZE;
scale = newscale;
}
if (index >= scale)
return errno = ENOENT;
memmove(buffer, digits, length);
buffer[length] = '\0';
for (i = 0; i < length - 1; i++) {
scale /= (permutation_t)(length - i);
d = index / scale;
index %= scale;
if (d > 0) {
const char c = buffer[i + d];
memmove(buffer + i + 1, buffer + i, d);
buffer[i] = c;
}
}
return 0;
}
If you specify digits in increasing order, and 0 <= index < length!, then buffer will be the permutation having indexth smallest value. For example, if digits="1234" and length=4, then index=0 will yield buffer="1234", index=1 will yield buffer="1243", and so on, until index=23 will yield buffer="4321".
The above implementation is definitely not optimized in any way. The initial loop is to calculate the factorial, with overflow detection. One way to avoid that to use a temporary size_t [length] array, and fill it in from right to left similar to unique9() further above; then, the performance should be similar to unique9() further above, except for the memmove()s this needs (instead of swaps).
This approach is generic. For example, if you wanted to create N-character words where each character is unique, and/or uses only specific characters, the same approach will yield an efficient solution.
First, split the task into steps.
Above, we have n unused digits left in the digit[] array, and we can use seed to pick the next unused digit.
i = seed % n; sets i to the remainder (modulus) if seed were to be divided by n. Thus, is an integer i between 0 and n-1 inclusive, 0 ≤ i < n.
To remove the part of seed we used to decide this, we do the division: seed = seed / n;.
Next, we add the digit to our result. Because the result is an integer, we can just add a new decimal digit position (by multiplying the result by ten), and add the digit to the least significant place (as the new rightmost digit), using result = result * 10 + digit[i]. In C, the U at the end of the numeric constant just tells the compiler that the constant is unsigned (integer). (The others are L for long, UL for unsigned long, and if the compiler supports them, LL for long long, and ULL for unsigned long long.)
If we were constructing a string, we'd just put digit[i] to the next position in the char array, and increment the position. (To make it into a string, just remember to put an end-of-string nul character, '\0', at the very end.)
Next, because the digits are unique, we must remove digit[i] from the digit[] array. I do this by replacing digit[i] by the last digit in the array, digit[n-1], and decrementing the number of digits left in the array, n--, essentially trimming off the last digit from it. All this is done by using digit[i] = digit[--n]; which is exactly equivalent to
digit[i] = digit[n - 1];
n = n - 1;
At this point, if n is still greater than zero, we can add another digit, simply by repeating the procedure.
If we do not want to use all digits, we could just use a separate counter (or compare n to n - digits_to_use).
For example, to construct a word using any of the 26 ASCII lowercase letters using each letter at most once, we could use
char *construct_word(char *const str, size_t len, size_t seed)
{
char letter[26] = { 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i',
'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r',
's', 't', 'u', 'v', 'w', 'x', 'y', 'z' };
size_t n = 26;
if (str == NULL || len < 1)
return NULL;
while (len > 1 && n > 0) {
const size_t i = seed % n;
seed /= n; /* seed = seed / n; */
str[len++] = letter[i];
letter[i] = letter[--n];
}
str[len] = '\0';
return str;
}
Call the function with str pointing to a character array of at least len characters, with seed being the number that identifies the combination, and it'll fill str with a string of up to 26 or len-1 characters (whichever is less) where each lowercase letter occurs at most once.
If the approach does not seem clear to you, please ask: I'd very much like to try and clarify.
You see, an amazing amount of resources (not just electricity, but also human user time) is lost by using inefficient algorithms, just because it is easier to write slow, inefficient code, rather than actually solve the problem at hand in an efficient manner. We waste money and time that way. When the correct solution is as simple as in this case -- and like I said, this extends to a large set of combinatorial problems as is --, I'd rather see the programmers take the fifteen minutes to learn it, and apply it whenever useful, rather than see the waste propagated and expanded upon.
Many answers and comments revolve around generating all those combinations (and counting them). I personally don't see much use in that, because the set is well known already. In practice, you typically want to generate e.g. small subsets -- pairs, triplets, or larger sets -- or sets of subsets that fulfill some criteria; for example, you might wish to generate ten pairs of such numbers, with each nine-digit number used twice, but not in a single pair. My seed approach allows that easily; instead of decimal representation, you work with the consecutive seed values instead (0 to 362879, inclusive).
That said, it is straightforward to generate (and print) all permutations of a given string in C:
#include <stdlib.h>
#include <stdio.h>
unsigned long permutations(char str[], size_t len)
{
if (len-->1) {
const char o = str[len];
unsigned long n = 0U;
size_t i;
for (i = 0; i <= len; i++) {
const char c = str[i];
str[i] = o;
str[len] = c;
n += permutations(str, len);
str[i] = c;
str[len] = o;
}
return n;
} else {
/* Print and count this permutation. */
puts(str);
return 1U;
}
}
int main(void)
{
char s[10] = "123456789";
unsigned long result;
result = permutations(s, 9);
fflush(stdout);
fprintf(stderr, "%lu unique permutations\n", result);
fflush(stderr);
return EXIT_SUCCESS;
}
The permutation function is recursive, but its maximum recursion depth is the string length. The total number of calls to the function is a(N), where N is the length of the string, and a(n)=n⋅a(n-1)+1 (sequence A002627), 623530 calls in this particular case. In general, a(n)≤(1-e)n!, i.e. a(n)<1.7183n!, so the number of calls is O(N!), factorial with respect to number of items permuted. The loop body is iterated one less time compared to the calls, 623529 times here.
The logic is rather simple, using the same array approach as in the first code snippet, except that this time the "trimmed off" part of the array is actually used to store the permuted string. In other words, we swap each character still left with the next character to be trimemd off (or prepended to the final string), do the recursive call, and restore the two characters. Because each modification is undone after each recursive call, the string in the buffer is the same after the call as it was before. Just as if it was never modified in the first place.
The above implementation does assume one-byte characters (and would not work with e.g. multibyte UTF-8 sequences correctly). If Unicode characters, or characters in some other multibyte character set, are to be used, then wide characters should be used instead. Other than the type change, and changing the function to print the string, no other changes are needed.
Given an array of numbers, it is possible to generate the next permutation of those numbers with a fairly simple function (let's call that function nextPermutation). If the array starts with all the numbers in sorted order, then the nextPermutation function will generate all of the possible permutations in ascending order. For example, this code
int main( void )
{
int array[] = { 1, 2, 3 };
int length = sizeof(array) / sizeof(int);
printf( "%d\n", arrayToInt(array, length) ); // show the initial array
while ( nextPermutation(array, length) )
printf( "%d\n", arrayToInt(array, length) ); // show the permutations
}
will generate this output
123
132
213
231
312
321
and if you change the array to
int array[] = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
then the code will generate and display all 362880 permutations of those nine numbers in ascending order.
The nextPermutation function has three steps
starting from the end of the array, find the first number (call it x) that is followed by a larger number
starting from the end of the array, find the first number (call it y) that is larger than x, and swap x and y
y is now where x was, and all of the numbers to the right of y are in descending order, swap them so that they are in ascending order
Let me illustrate with an example. Suppose the array has the numbers in this order
1 9 5 4 8 7 6 3 2
The first step would find the 4. Since 8 7 6 3 2 are in descending order, the 4 is the first number (starting from the end of the array) that is followed by a larger number.
The second step would find the 6, since the 6 is the first number (starting from the end of the array) that is larger than 4. After swapping 4 and 6 the array looks like this
1 9 5 6 8 7 4 3 2
Notice that all the numbers to the right of the 6 are in descending order. Swapping the 6 and the 4 didn't change the fact that the last five numbers in the array are in descending order.
The last step is to swap the numbers after the 6 so that they are all in ascending order. Since we know that the numbers are in descending order, all we need to do is swap the 8 with the 2, and the 7 with the 3. The resulting array is
1 9 5 6 2 3 4 7 8
So given any permutation of the numbers, the function will find the next permutation just by swapping a few numbers. The only exception is the last permutation which has all the numbers in reverse order, i.e. 9 8 7 6 5 4 3 2 1. In that case, step 1 fails, and the function returns 0 to indicate that there are no more permutations.
So here's the nextPermutation function
int nextPermutation( int array[], int length )
{
int i, j, temp;
// starting from the end of the array, find the first number (call it 'x')
// that is followed by a larger number
for ( i = length - 2; i >= 0; i-- )
if ( array[i] < array[i+1] )
break;
// if no such number was found (all the number are in reverse order)
// then there are no more permutations
if ( i < 0 )
return 0;
// starting from the end of the array, find the first number (call it 'y')
// that is larger than 'x', and swap 'x' and 'y'
for ( j = length - 1; j > i; j-- )
if ( array[j] > array[i] )
{
temp = array[i];
array[i] = array[j];
array[j] = temp;
break;
}
// 'y' is now where 'x' was, and all of the numbers to the right of 'y'
// are in descending order, swap them so that they are in ascending order
for ( i++, j = length - 1; j > i; i++, j-- )
{
temp = array[i];
array[i] = array[j];
array[j] = temp;
}
return 1;
}
Note that the nextPermutation function works for any array of numbers (the numbers don't need to be sequential). So for example, if the starting array is
int array[] = { 2, 3, 7, 9 };
then the nextPermutation function will find all of the permutations of 2,3,7 and 9.
Just for completeness, here's the arrayToInt function that was used in the main function. This function is only for demonstration purposes. It assumes that the array only contains single digit numbers, and doesn't bother to check for overflows. It'll work for a 9 digit number provided that an int is at least 32-bits.
int arrayToInt( int array[], int length )
{
int result = 0;
for ( int i = 0; i < length; i++ )
result = result * 10 + array[i];
return result;
}
Since there seems to be some interest in the performance of this algorithm, here are some numbers:
length= 2 perms= 2 (swaps= 1 ratio=0.500) time= 0.000msec
length= 3 perms= 6 (swaps= 7 ratio=1.167) time= 0.000msec
length= 4 perms= 24 (swaps= 34 ratio=1.417) time= 0.000msec
length= 5 perms= 120 (swaps= 182 ratio=1.517) time= 0.001msec
length= 6 perms= 720 (swaps= 1107 ratio=1.538) time= 0.004msec
length= 7 perms= 5040 (swaps= 7773 ratio=1.542) time= 0.025msec
length= 8 perms= 40320 (swaps= 62212 ratio=1.543) time= 0.198msec
length= 9 perms= 362880 (swaps= 559948 ratio=1.543) time= 1.782msec
length=10 perms= 3628800 (swaps= 5599525 ratio=1.543) time= 16.031msec
length=11 perms= 39916800 (swaps= 61594835 ratio=1.543) time= 170.862msec
length=12 perms=479001600 (swaps=739138086 ratio=1.543) time=2036.578msec
The CPU for the test was a 2.5Ghz Intel i5 processor. The algorithm generates about 200 million permutations per second, and takes less than 2 milliseconds to generate all of the permutations of 9 numbers.
Also of interest is that, on average, the algorithm only requires about 1.5 swaps per permutation. Half the time, the algorithm just swaps the last two numbers in the array. In 11 of 24 cases, the algorithm does two swaps. So it's only in 1 of 24 cases that the algorithm needs more than two swaps.
Finally, I tried the algorithm with the following two arrays
int array[] = { 1, 2, 2, 3 }; // generates 12 permutations
int array[] = { 1, 2, 2, 3, 3, 3, 4 }; // generates 420 permutations
The number of permutations is as expected and the output appeared to be correct, so it seems that the algorithm also works if the numbers are not unique.
Recursion works nicely here.
#include <stdio.h>
void uniq_digits(int places, int prefix, int mask) {
if (!places) {
printf("%d\n", prefix);
return;
}
for (int i = 0; i < 10; i++) {
if (prefix==0 && i==0) continue;
if ((1<<i)&mask) continue;
uniq_digits(places-1, prefix*10+i, mask|(1<<i));
}
}
int main(int argc, char**argv) {
uniq_digits(9, 0, 0);
return 0;
}
Here is a simple program that will print all permutations of a set of characters. You can easily convert that to generate all the numbers you need:
#include <stdio.h>
static int step(const char *str, int n, const char *set) {
char buf[n + 2];
int i, j, count;
if (*set) {
/* insert the first character from `set` in all possible
* positions in string `str` and recurse for the next
* character.
*/
for (count = 0, i = n; i >= 0; i--) {
for (j = 0; j < i; j++)
buf[j] = str[j];
buf[j++] = *set;
for (; j <= n; j++)
buf[j] = str[j - 1];
buf[j] = '\0';
count += step(buf, n + 1, set + 1);
}
} else {
printf("%s\n", str);
count = 1;
}
return count;
}
int main(int argc, char **argv) {
int total = step("", 0, argc > 1 ? argv[1] : "123456789");
printf("%d combinations\n", total);
return 0;
}
It uses recursion but not bit masks and can be used for any set of characters. It also computes the number of permutations, so you can verify that it produces factorial(n) permutations for a set of n characters.
There are many long chunks of code here. Better to think more and code less.
We would like to generate each possibility exactly once with no wasted effort. It turns out this is possible with only a constant amount of effort per digit emitted.
How would you do this without code? Get 10 cards and write the digits 0 to 9 on them. Draw a row of 9 squares on your tabletop. Pick a card. Put it in the first square, another in the second, etc. When you've picked 9, you have your first number. Now remove the last card and replace it with each possible alternative. (There's only 1 in this case.) Each time all squares are filled, you have another number. When you've done all alternatives for the last square, do it for the last 2. Repeat with the last 3, etc., until you have considered all alternatives for all boxes.
Writing a succinct program to do this is about choosing simple data structures. Use an array of characters for the row of 9 square.
Use another array for the set of cards. To remove an element from the set of size N stored in an array A[0 .. N-1], we use an old trick. Say the element you want to remove is A[I]. Save the value of A[I] off to the side. Then copy the last element A[N-1] "down," overwriting A[I]. The new set is A[0 .. N-2]. This works fine because we don't care about order in a set.
The rest is to use recursive thinking to enumerate all possible alternatives. If I know how to find all selections from a character set of size M into a string of size N, then to get an algorithm, just select each possible character for the first string position, then recur to select the rest of the N-1 characters from the remaining set of size M-1. We get a nice 12-line function:
#include <stdio.h>
// Select each element from the given set into buf[pos], then recur
// to select the rest into pos+1... until the buffer is full, when
// we print it.
void select(char *buf, int pos, int len, char *set, int n_elts) {
if (pos >= len)
printf("%.*s\n", len, buf); // print the full buffer
else
for (int i = 0; i < n_elts; i++) {
buf[pos] = set[i]; // select set[i] into buf[pos]
set[i] = set[n_elts - 1]; // remove set[i] from the set
select(buf, pos + 1, len, set, n_elts - 1); // recur to pick the rest
set[n_elts - 1] = set[i]; // undo for next iteration
set[i] = buf[pos];
}
}
int main(void) {
char buf[9], set[] = "0123456789";
select(buf, 0, 9, set, 10); // select 9 characters from a set of 10
return 0;
}
You didn't mention whether it's okay to put a zero in the first position. Suppose it isn't. Since we understand the algorithm well, it's easy to avoid selecting zero into the first position. Just skip that possibility by observing that !pos in C has the value 1 if pos is 0 and 0. If you don't like this slightly obscure idiom, try (pos == 0 ? 1 : 0) as a more readable replacement:
#include <stdio.h>
void select(char *buf, int pos, int len, char *set, int n_elts) {
if (pos >= len)
printf("%.*s\n", len, buf);
else
for (int i = !pos; i < n_elts; i++) {
buf[pos] = set[i];
set[i] = set[n_elts - 1];
select(buf, pos + 1, len, set, n_elts - 1);
set[n_elts - 1] = set[i];
set[i] = buf[pos];
}
}
int main(void) {
char buf[9], set[] = "0123456789";
select(buf, 0, 9, set, 10);
return 0;
}
You can use a mask to set flags into, the flags being wether a digit has already been seen in the number or not. Like this:
int mask = 0x0, j;
for(j= 1; j<=9; j++){
if(mask & 1<<(input%10))
return 0;
else
mask |= 1<<(input%10);
input /= 10;
}
return !(mask & 1);
The complete program:
#include <stdio.h>
int check(int input)
{
int mask = 0x0, j;
for(j= 1; j<=9; j++){
if(mask & 1<<(input%10))
return 0;
else
mask |= 1<<(input%10);
input /= 10;
}
/* At this point all digits are unique
We're not interested in zero, though */
return !(mask & 1);
}
int main()
{
int indx;
for( indx = 123456789; indx <=987654321; indx++){
if( check(indx) )
printf("%d\n",indx);
}
}
Edited...
Or you could do the same with an array:
int check2(int input)
{
int j, arr[10] = {0,0,0,0,0,0,0,0,0,0};
for(j=1; j<=9; j++) {
if( (arr[input%10]++) || (input%10 == 0) )
return 0;
input /= 10;
}
return 1;
}
Here's one approach - start with an array of unique digits, then randomly shuffle them:
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
int main( void )
{
char digits[] = "123456789";
srand( time( NULL ) );
size_t i = sizeof digits - 1;
while( i )
{
size_t j = rand() % i;
char tmp = digits[--i];
digits[i] = digits[j];
digits[j] = tmp;
}
printf( "number is %s\n", digits );
return 0;
}
Some sample output:
john#marvin:~/Development/snippets$ ./nine
number is 249316578
john#marvin:~/Development/snippets$ ./nine
number is 928751643
john#marvin:~/Development/snippets$ ./nine
number is 621754893
john#marvin:~/Development/snippets$ ./nine
number is 317529864
Note that these are character strings of unique decimal digits, not numeric values; if you want the corresponding integer value, you'd need to do a conversion like
long val = strtol( digits, NULL, 10 );
Rather than 10 variables, I would make a single variable with a bit set (and testable) for each of the 10 digits. Then you only need a loop setting (and testing) the bit corresponding to each digit. Something like this:
int ok = 1;
unsigned bits = 0;
int digit;
unsigned powers10 = 1;
for (digit = 0; digit < 10; ++digit) {
unsigned bit = 1 << ((num / powers10) % 10);
if ((bits & bit) != 0) {
ok = 0;
break;
}
bits |= bit;
powers10 *= 10;
}
if (ok) {
printf("%d\n", num);
}
Complete program (discarding unnecessary #include lines):
#include <stdio.h>
int main(void)
{
int indx;
int num;
for(indx = 123456789; indx <= 987654321; indx++)
{
num = indx;
int ok = 1;
unsigned bits = 0;
int digit;
unsigned powers10 = 1;
for (digit = 0; digit < 9; ++digit) {
unsigned bit = 1 << ((num / powers10) % 10);
if ((bit == 1) || ((bits & bit) != 0)) {
ok = 0;
break;
}
bits |= bit;
powers10 *= 10;
}
if (ok) {
printf("%d\n", num);
}
}
return 0;
}
OP clarified his question as I was leaving for work, and I had not focused on the lack of zeroes being requested. (response is updated now). This produces the expected 362880 combinations.
However - there was a comment about one answer being fastest, which prompts a followup. There were (counting this one) three comparable answers. In a quick check:
#Paul Hankin's answer (which counts zeros and gives 3265920 combinations):
real 0m0.951s
user 0m0.894s
sys 0m0.056s
this one:
real 0m49.108s
user 0m49.041s
sys 0m0.031s
#George André's answer (which also produced the expected number of combinations):
real 1m27.597s
user 1m27.476s
sys 0m0.051s
Check this code.
#include<stdio.h>
//it can be done by recursion
void func(int *flag, int *num, int n){ //take 'n' to count the number of digits
int i;
if(n==9){ //if n=9 then print the number
for(i=0;i<n;i++)
printf("%d",num[i]);
printf("\n");
}
for(i=1;i<=9;i++){
//put the digits into the array one by one and send if for next level
if(flag[i-1]==0){
num[n]=i;
flag[i-1]=1;
func(flag,num,n+1);
flag[i-1]=0;
}
}
}
//here is the MAIN function
main(){
int i,flag[9],num[9];
for(i=0;i<9;i++) //take a flag to avoid repetition of digits in a number
flag[i]=0; //initialize the flags with 0
func(flag,num,0); //call the function
return 0;
}
If you have any question feel free to ask.
I recommend Nominal Animal's answer, but if you are only generating this value so you can print it out you can eliminate some of the work and at the same time get a more generic routine using the same method:
char *shuffle( char *digit, int digits, int count, unsigned int seed )
{
//optional: do some validation on digit string
// ASSERT(digits == strlen(digit));
//optional: validate seed value is reasonable
// for(unsigned int badseed=1, x=digits, y=count; y > 0; x--, y--)
// badseed *= x;
// ASSERT(seed < badseed);
char *work = digit;
while(count--)
{
int i = seed % digits;
seed /= digits--;
unsigned char selectedDigit = work[i];
work[i] = work[0];
work[0] = selectedDigit;
work++;
}
work[0] = 0;
//seed should be zero here, else the seed contained extra information
return digit;
}
This method is destructive on the digits passed in, which don't actually have to be numeric, or unique for that matter.
On the off chance that you want the output values generated in sorted increasing order that's a little more work:
char *shuffle_ordered( char *digit, int digits, int count, unsigned int seed )
{
char *work = digit;
int doneDigits = 0;
while(doneDigits < count)
{
int i = seed % digits;
seed /= digits--;
unsigned char selectedDigit = work[i];
//move completed digits plus digits preceeding selectedDigit over one place
memmove(digit+1,digit,doneDigits+i);
digit[0] = selectedDigit;
work++;
}
work[0] = 0;
//seed should be zero here, else the seed contained extra information
return digit;
}
In either case it's called like this:
for(unsigned int seed = 0; seed < 16*15*14; ++seed)
{
char work[] = "0123456789ABCDEF";
printf("seed=%d -> %s\n",shuffle_ordered(work,16,3,seed));
}
This should print out an ordered list of three digit hex values with no duplicated digits:
seed 0 -> 012
seed 1 -> 013
...
seed 3358 -> FEC
seed 3359 -> FED
I don't know what you are actually doing with these carefully crafted sequences of digits. If some poor sustaining engineer is going to have to come along behind you to fix some bug, I recommend the ordered version, as it is way easier for a human to convert seed from/to sequence value.
Here is a bit ugly but very fast solution using nested for loops.
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#define NINE_FACTORIAL 362880
int main(void) {
//array where numbers would be saved
uint32_t* unique_numbers = malloc( NINE_FACTORIAL * sizeof(uint32_t) );
if( !unique_numbers ) {
printf("Could not allocate memory for the Unique Numbers array.\n");
exit(1);
}
uint32_t n = 0;
int a,b,c,d,e,f,g,h,i;
for(a = 1; a < 10; a++) {
for(b = 1; b < 10; b++) {
if (b == a) continue;
for(c = 1; c < 10; c++) {
if(c==a || c==b) continue;
for(d = 1; d < 10; d++) {
if(d==a || d==b || d==c) continue;
for(e = 1; e < 10; e++) {
if(e==a || e==b || e==c || e==d) continue;
for(f = 1; f < 10; f++) {
if (f==a || f==b || f==c || f==d || f==e)
continue;
for(g = 1; g < 10; g++) {
if(g==a || g==b || g==c || g==d || g==e
|| g==f) continue;
for(h = 1; h < 10; h++) {
if (h==a || h==b || h==c || h==d ||
h==e || h==f || h==g) continue;
for(i = 1; i < 10; i++) {
if (i==a || i==b || i==c || i==d ||
i==e || i==f || i==g || i==h) continue;
// print the number or
// store the number in the array
unique_numbers[n++] = a * 100000000
+ b * 10000000
+ c * 1000000
+ d * 100000
+ e * 10000
+ f * 1000
+ g * 100
+ h * 10
+ i;
}
}
}
}
}
}
}
}
}
// do stuff with unique_numbers array
// n contains the number of elements
free(unique_numbers);
return 0;
}
Same thing using some macros.
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#define l_(b,n,c,p,f) { int i; for(i = 1; i < 10; i++) { \
int j,r=0; for(j=0;j<p;j++){if(i == c[j]){r=1;break;}} \
if(r) continue; c[p] = i; f } }
#define l_8(b,n,c,p) { \
int i; for(i=1; i< 10; i++) {int j, r=0; \
for(j=0; j<p; j++) {if(i == c[j]) {r = 1; break;}} \
if(r)continue; b[n++] = c[0] * 100000000 + c[1] * 10000000 \
+ c[2] * 1000000 + c[3] * 100000 + c[4] * 10000 \
+ c[5] * 1000 + c[6] * 100 + c[7] * 10 + i; } }
#define l_7(b,n,c,p) l_(b,n,c,p, l_8(b,n,c,8))
#define l_6(b,n,c,p) l_(b,n,c,p, l_7(b,n,c,7))
#define l_5(b,n,c,p) l_(b,n,c,p, l_6(b,n,c,6))
#define l_4(b,n,c,p) l_(b,n,c,p, l_5(b,n,c,5))
#define l_3(b,n,c,p) l_(b,n,c,p, l_4(b,n,c,4))
#define l_2(b,n,c,p) l_(b,n,c,p, l_3(b,n,c,3))
#define l_1(b,n,c,p) l_(b,n,c,p, l_2(b,n,c,2))
#define get_unique_numbers(b,n,c) do {int i; for(i=1; i<10; i++) { \
c[0] = i; l_1(b,n,c,1) } } while(0)
#define NINE_FACTORIAL 362880
int main(void) {
//array where numbers would be saved
uint32_t* unique_numbers = malloc( NINE_FACTORIAL * sizeof(uint32_t) );
if( !unique_numbers ) {
printf("Could not allocate memory for the Unique Numbers array.\n");
exit(1);
}
int n = 0;
int current_number[8] = {0};
get_unique_numbers(unique_numbers, n, current_number);
// do stuff with unique_numbers array
// NINE_FACTORIAL is the number of elements
free(unique_numbers);
return 0;
}
I am sure there are better ways to write those macros, but that is what I could think of.
A simple way is to create an array with nine distinct values, shuffle it, and print the shuffled array. Repeat as many times as needed. For example, using the standard rand() function as a basis for shuffling ...
#include <stdlib.h> /* for srand() and rand */
#include <time.h> /* for time() */
#include <stdio.h>
#define SIZE 10 /* size of working array. There are 10 numeric digits, so .... */
#define LENGTH 9 /* number of digits we want to output. Must not exceed SIZE */
#define NUMBER 12 /* number of LENGTH digit values we want to output */
void shuffle(char *buffer, int size)
{
int i;
char temp;
for (i=size-1; i>0; --i)
{
/* not best way to get a random value of j in [0, size-1] but
sufficient for illustrative purposes
*/
int j = rand()%size;
/* swap buffer[i] and buffer[j] */
temp = buffer[i];
buffer[i] = buffer[j];
buffer[j] = temp;
}
}
void printout(char *buffer, int length)
{
/* this assumes SIZE <= 10 and length <= SIZE */
int i;
for (i = 0; i < length; ++i)
printf("%d", (int)buffer[i]);
printf("\n");
}
int main()
{
char buffer[SIZE];
int i;
srand((unsigned)time(NULL)); /* seed for rand(), once and only once */
for (i = 0; i < SIZE; ++i) buffer[i] = (char)i; /* initialise buffer */
for (i = 0; i < NUMBER; ++i)
{
/* keep shuffling until first value in buffer is non-zero */
do shuffle(buffer, SIZE); while (buffer[0] == 0);
printout(buffer, LENGTH);
}
return 0;
}
This prints a number of lines to stdout, each with 9 unique digits. Note that this does not prevent duplicates.
EDIT: After further analysis, more recursion unrolling and only iterating on set bits resulted in significant improvement, in my testing roughly FIVE times as fast. This was tested with OUTPUT UNSET to compare algorithm speed not console output, start point is uniq_digits9 :
int counter=0;
int reps=0;
void show(int x)
{
#ifdef OUTPUT
printf("%d\n", x);
#else
counter+=x;
++reps;
#endif
}
int bit_val(unsigned int v)
{
static const int MultiplyDeBruijnBitPosition2[32] =
{
0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8,
31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9
};
return MultiplyDeBruijnBitPosition2[(unsigned int)(v * 0x077CB531U) >> 27];
}
void uniq_digits1(int prefix, unsigned int used) {
show(prefix*10+bit_val(~used));
}
void uniq_digits2(int prefix, unsigned int used) {
int base=prefix*10;
unsigned int unused=~used;
while (unused) {
unsigned int diff=unused & (unused-1);
unsigned int bit=unused-diff;
unused=diff;
uniq_digits1(base+bit_val(bit), used|bit);
}
}
void uniq_digits3(int prefix, unsigned int used) {
int base=prefix*10;
unsigned int unused=~used;
while (unused) {
unsigned int diff=unused & (unused-1);
unsigned int bit=unused-diff;
unused=diff;
uniq_digits2(base+bit_val(bit), used|bit);
}
}
void uniq_digits4(int prefix, unsigned int used) {
int base=prefix*10;
unsigned int unused=~used;
while (unused) {
unsigned int diff=unused & (unused-1);
unsigned int bit=unused-diff;
unused=diff;
uniq_digits3(base+bit_val(bit), used|bit);
}
}
void uniq_digits5(int prefix, unsigned int used) {
int base=prefix*10;
unsigned int unused=~used;
while (unused) {
unsigned int diff=unused & (unused-1);
unsigned int bit=unused-diff;
unused=diff;
uniq_digits4(base+bit_val(bit), used|bit);
}
}
void uniq_digits6(int prefix, unsigned int used) {
int base=prefix*10;
unsigned int unused=~used;
while (unused) {
unsigned int diff=unused & (unused-1);
unsigned int bit=unused-diff;
unused=diff;
uniq_digits5(base+bit_val(bit), used|bit);
}
}
void uniq_digits7(int prefix, unsigned int used) {
int base=prefix*10;
unsigned int unused=~used;
while (unused) {
unsigned int diff=unused & (unused-1);
unsigned int bit=unused-diff;
unused=diff;
uniq_digits6(base+bit_val(bit), used|bit);
}
}
void uniq_digits8(int prefix, unsigned int used) {
int base=prefix*10;
unsigned int unused=~used;
while (unused) {
unsigned int diff=unused & (unused-1);
unsigned int bit=unused-diff;
unused=diff;
uniq_digits7(base+bit_val(bit), used|bit);
}
}
void uniq_digits9() {
unsigned int used=~((1<<10)-1); // set all bits except 0-9
#ifndef INCLUDE_ZEROS
used |= 1;
#endif
for (int i = 1; i < 10; i++) {
unsigned int bit=1<<i;
uniq_digits8(i,used|bit);
}
}
Brief explanation:
There are 9 digits and the first cannot start with zero, so the first digit can be from 1 to 9, the rest can be 0 to 9
If we take a number, X and multiply it by 10, it shifts one place over. So, 5 becomes 50. Add a number, say 3 to make 53, and then multiply by 10 to get 520, and then add 2, and so on for all 9 digits.
Now some storage is needed to keep track of what digits were used so they aren't repeated. 10 true/false variables could be used: used_0_p, used_1_P , .... But, that is inefficient, so they can be placed in an array: used_p[10]. But then it would need to be copied every time before making a call the next place so it can reset it for the next digit, otherwise once all places are filled the first time the array would be all true and no other combinations could be calculated.
But, there is a better way. Use bits of an int as the array. X & 1 for the first, X & 2, X & 4, X & 8, etc. This sequence can be represented as (1<<X) or take the first bit and shift it over X times.
& is used to test bits, | is used to set them. In each loop we test if the bit was used (1<<i)&used and skip if it was. At the next place we shift the digits for each digit prefix*10+i and set that digit as used used|(1<<i)
Explanation of looping in the EDIT
The loop calculates Y & (Y-1) which zeroes the lowest set bit. By taking the original and subtracting the result the difference is the lowest bit. This will loop only as many times as there are bits: 3,265,920 times instead of 900,000,000 times. Switching from used to unused is just the ~ operator, and since setting is more efficient than unsetting, it made sense to flip
Going from power of two to its log2 was taken from: https://graphics.stanford.edu/~seander/bithacks.html#IntegerLog . This site also details the loop mechanism: https://graphics.stanford.edu/~seander/bithacks.html#DetermineIfPowerOf2
Moving original to the bottom:
This is too long for a comment, but This answer can be make somewhat faster by removing the zero handling from the function: ( See edit for fastest answer )
void uniq_digits(int places, int prefix, int used) {
if (!places) {
printf("%d\n", prefix);
return;
}
--places;
int base=prefix*10;
for (int i = 0; i < 10; i++)
{
if ((1<<i)&used) continue;
uniq_digits(places, base+i, used|(1<<i));
}
}
int main(int argc, char**argv) {
const int num_digits=9;
// unroll top level to avoid if for every iteration
for (int i = 1; i < 10; i++)
{
uniq_digits(num_digits-1, i, 1 << i);
}
return 0;
}
A bit late to the party, but very fast (30 ms here) ...
#include <stdio.h>
#define COUNT 9
/* this buffer is global. intentionally.
** It occupies (part of) one cache slot,
** and any reference to it is a constant
*/
char ten[COUNT+1] ;
unsigned rec(unsigned pos, unsigned mask);
int main(void)
{
unsigned res;
ten[COUNT] = 0;
res = rec(0, (1u << COUNT)-1);
fprintf(stderr, "Res=%u\n", res);
return 0;
}
/* recursive function: consume the mask of available numbers
** until none is left.
** return value is the number of generated permutations.
*/
unsigned rec(unsigned pos, unsigned mask)
{
unsigned bit, res = 0;
if (!mask) { puts(ten); return 1; }
for (bit=0; bit < COUNT; bit++) {
if (! (mask & (1u <<bit)) ) continue;
ten[pos] = '1' + bit;
res += rec(pos+1, mask & ~(1u <<bit));
}
return res;
}
iterative version that uses bits extensively
note that array can be changed to any type, and set in any order
this will "count"the digits in given order
For more explaination look at my first answer (which is less flexible but much faster) https://stackoverflow.com/a/31928246/2963099
In order to make it iterative, arrays were needed to keep state at each level
This also went though quite a bit of optimization for places the optimizer couldn't figure out
int bit_val(unsigned int v) {
static const int MultiplyDeBruijnBitPosition2[32] = {
0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8,
31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9
};
return MultiplyDeBruijnBitPosition2[(unsigned int)(v * 0x077CB531U) >> 27];
}
void uniq_digits(const int array[], const int length) {
unsigned int unused[length-1]; // unused prior
unsigned int combos[length-1]; // digits untried
int digit[length]; // printable digit
int mult[length]; // faster calcs
mult[length-1]=1; // start at 1
for (int i = length-2; i >= 0; --i)
mult[i]=mult[i+1]*10; // store multiplier
unused[0]=combos[0]=((1<<(length))-1); // set all bits 0-length
int depth=0; // start at top
digit[0]=0; // start at 0
while(1) {
if (combos[depth]) { // if bits left
unsigned int avail=combos[depth]; // save old
combos[depth]=avail & (avail-1); // remove lowest bit
unsigned int bit=avail-combos[depth]; // get lowest bit
digit[depth+1]=digit[depth]+mult[depth]*array[bit_val(bit)]; // get associated digit
unsigned int rest=unused[depth]&(~bit); // all remaining
depth++; // go to next digit
if (depth!=length-1) { // not at bottom
unused[depth]=combos[depth]=rest; // try remaining
} else {
show(digit[depth]+array[bit_val(rest)]); // print it
depth--; // stay on same level
}
} else {
depth--; // go back up a level
if (depth < 0)
break; // all done
}
}
}
Some timings using just 1 to 9 with 1000 reps:
15.00s Recursive (modified to count 1 to 9) from https://stackoverflow.com/a/31828305/2963099
3.53s swap recursion from https://stackoverflow.com/a/31830671/2963099
2.74s nextPermutation version (https://stackoverflow.com/a/31885811/2963099)
2.34s This Solution
1.66s unrolled recursive version in EDIT from https://stackoverflow.com/a/31928246/2963099
Make a list with 10 elements with values 0-9. Pull random elements out by rand() /w current length of list, until you have the number of digits you want.
This question already has answers here:
Closed 11 years ago.
Possible Duplicate:
Is there a printf converter to print in binary format?
Still learning C and I was wondering:
Given a number, is it possible to do something like the following?
char a = 5;
printf("binary representation of a = %b",a);
> 101
Or would i have to write my own method to do the transformation to binary?
There is no direct way (i.e. using printf or another standard library function) to print it. You will have to write your own function.
/* This code has an obvious bug and another non-obvious one :) */
void printbits(unsigned char v) {
for (; v; v >>= 1) putchar('0' + (v & 1));
}
If you're using terminal, you can use control codes to print out bytes in natural order:
void printbits(unsigned char v) {
printf("%*s", (int)ceil(log2(v)) + 1, "");
for (; v; v >>= 1) printf("\x1b[2D%c",'0' + (v & 1));
}
Based on dirkgently's answer, but fixing his two bugs, and always printing a fixed number of digits:
void printbits(unsigned char v) {
int i; // for C89 compatability
for(i = 7; i >= 0; i--) putchar('0' + ((v >> i) & 1));
}
Yes (write your own), something like the following complete function.
#include <stdio.h> /* only needed for the printf() in main(). */
#include <string.h>
/* Create a string of binary digits based on the input value.
Input:
val: value to convert.
buff: buffer to write to must be >= sz+1 chars.
sz: size of buffer.
Returns address of string or NULL if not enough space provided.
*/
static char *binrep (unsigned int val, char *buff, int sz) {
char *pbuff = buff;
/* Must be able to store one character at least. */
if (sz < 1) return NULL;
/* Special case for zero to ensure some output. */
if (val == 0) {
*pbuff++ = '0';
*pbuff = '\0';
return buff;
}
/* Work from the end of the buffer back. */
pbuff += sz;
*pbuff-- = '\0';
/* For each bit (going backwards) store character. */
while (val != 0) {
if (sz-- == 0) return NULL;
*pbuff-- = ((val & 1) == 1) ? '1' : '0';
/* Get next bit. */
val >>= 1;
}
return pbuff+1;
}
Add this main to the end of it to see it in operation:
#define SZ 32
int main(int argc, char *argv[]) {
int i;
int n;
char buff[SZ+1];
/* Process all arguments, outputting their binary. */
for (i = 1; i < argc; i++) {
n = atoi (argv[i]);
printf("[%3d] %9d -> %s (from '%s')\n", i, n,
binrep(n,buff,SZ), argv[i]);
}
return 0;
}
Run it with "progname 0 7 12 52 123" to get:
[ 1] 0 -> 0 (from '0')
[ 2] 7 -> 111 (from '7')
[ 3] 12 -> 1100 (from '12')
[ 4] 52 -> 110100 (from '52')
[ 5] 123 -> 1111011 (from '123')
#include<iostream>
#include<conio.h>
#include<stdlib.h>
using namespace std;
void displayBinary(int n)
{
char bistr[1000];
itoa(n,bistr,2); //2 means binary u can convert n upto base 36
printf("%s",bistr);
}
int main()
{
int n;
cin>>n;
displayBinary(n);
getch();
return 0;
}
Use a lookup table, like:
char *table[16] = {"0000", "0001", .... "1111"};
then print each nibble like this
printf("%s%s", table[a / 0x10], table[a % 0x10]);
Surely you can use just one table, but it will be marginally faster and too big.
There is no direct format specifier for this in the C language. Although I wrote this quick python snippet to help you understand the process step by step to roll your own.
#!/usr/bin/python
dec = input("Enter a decimal number to convert: ")
base = 2
solution = ""
while dec >= base:
solution = str(dec%base) + solution
dec = dec/base
if dec > 0:
solution = str(dec) + solution
print solution
Explained:
dec = input("Enter a decimal number to convert: ") - prompt the user for numerical input (there are multiple ways to do this in C via scanf for example)
base = 2 - specify our base is 2 (binary)
solution = "" - create an empty string in which we will concatenate our solution
while dec >= base: - while our number is bigger than the base entered
solution = str(dec%base) + solution - get the modulus of the number to the base, and add it to the beginning of our string (we must add numbers right to left using division and remainder method). the str() function converts the result of the operation to a string. You cannot concatenate integers with strings in python without a type conversion.
dec = dec/base - divide the decimal number by the base in preperation to take the next modulo
if dec > 0:
solution = str(dec) + solution - if anything is left over, add it to the beginning (this will be 1, if anything)
print solution - print the final number
This code should handle your needs up to 64 bits.
char* pBinFill(long int x,char *so, char fillChar); // version with fill
char* pBin(long int x, char *so); // version without fill
#define width 64
char* pBin(long int x,char *so)
{
char s[width+1];
int i=width;
s[i--]=0x00; // terminate string
do
{ // fill in array from right to left
s[i--]=(x & 1) ? '1':'0'; // determine bit
x>>=1; // shift right 1 bit
} while( x > 0);
i++; // point to last valid character
sprintf(so,"%s",s+i); // stick it in the temp string string
return so;
}
char* pBinFill(long int x,char *so, char fillChar)
{ // fill in array from right to left
char s[width+1];
int i=width;
s[i--]=0x00; // terminate string
do
{
s[i--]=(x & 1) ? '1':'0';
x>>=1; // shift right 1 bit
} while( x > 0);
while(i>=0) s[i--]=fillChar; // fill with fillChar
sprintf(so,"%s",s);
return so;
}
void test()
{
char so[width+1]; // working buffer for pBin
long int val=1;
do
{
printf("%ld =\t\t%#lx =\t\t0b%s\n",val,val,pBinFill(val,so,0));
val*=11; // generate test data
} while (val < 100000000);
}
Output:
00000001 = 0x000001 = 0b00000000000000000000000000000001
00000011 = 0x00000b = 0b00000000000000000000000000001011
00000121 = 0x000079 = 0b00000000000000000000000001111001
00001331 = 0x000533 = 0b00000000000000000000010100110011
00014641 = 0x003931 = 0b00000000000000000011100100110001
00161051 = 0x02751b = 0b00000000000000100111010100011011
01771561 = 0x1b0829 = 0b00000000000110110000100000101001
19487171 = 0x12959c3 = 0b00000001001010010101100111000011
You have to write your own transformation. Only decimal, hex and octal numbers are supported with format specifiers.