Lets assume I have an input array like below
int input_arr[100] = {10,20,1255,1200,50,55,1,5,6,1000};
Here to store each elements of array it took 32 bits even though value of array elements is very small i.e 1255 is the maximum elements in array and to store that I need only 11 bit that means in 11 bit I can fit all other elements of array.
So my task to compress 32-bit elements of array into 11-bit array elements ? Expected compressed array looks like
int output_arr[] = {00000001010 00000010100 .... 10011111111 ... }
| | |
11 bits(1) 11 bits(2) 11 bits( 1255)
To do the above task what I did is here
find the maximum elements in given array
find the bits required to store maximum elements(previous step)
find bytes required to store no of bits for e.g to store 11 bits I need equivalent 2 bytes(in below code new_size contains this). Here is I need your help. Here is the memory wastage as told by my manager because to store 11 bits my new_size is 2 bytes i.e 5 bits are still extra or wastage. How can I avoid this.
Here is what I tried
int my_pow(int input_num,int p) {
int temp = 1;
for(int iter = 0;iter < p; iter++) {
temp = temp * input_num;
}
return temp;
}
int main() {
#if 0
int input_array[53069] = {1,2,2,3,4,1,2,4,6,1255,1,2,5,1233};
#endif
int input_array[] = {1,2,3,4,6,1255,1,2,5,1233};
int max = input_array[0], ele = sizeof(input_array)/sizeof(input_array[0]);
/* finding max elements in a array */
for(int i = 0;i < ele; i++) {
if(input_array[i] > max) {
max = input_array[i];
}
}
/* finding no of bits required to store highest elements of array */
int bit_required = 0;
while(1) {
if(max < my_pow(2,bit_required))
break;
bit_required+=1;
}
/* when above loop fails bit_required is nothing
but no of bit required to store the highest element of array */
/* finding size of new/compressed array */
int new_size = 0;
if(bit_required % 8 == 0) {
new_size = bit_required/8;
}
else {
new_size = (bit_required/8) + 1;
}
/* construct the new array again */
typedef struct array_task {
unsigned char new_array[new_size];/* in each cmp_arr, can store new_size char
now for each B[] I'm not using 32 bits , its new_size bits */
}cmp_arr;/* creating new array of ele elements */
cmp_arr cmpressed[ele];
/* store elements of input_array[] into output_array[] */
for(int row = 0 ; row < ele ;row++) {
for(int col = bit_required - 1; col >= 0; col-- ) {
cmpressed[row].new_array[col] = ((input_array[row] >> col & 1) + 48) ;
printf("%d",(cmpressed[row].new_array[col]) - 48);
}
printf("\n");
}
#if 0
printf("Size of A before %d\n",sizeof(input_array)); /* 40 bytes */
printf("size of compressed array %d\n",sizeof(cmp_arr));/* same task, it perform in 2 bytes,
each elements won't take 32 bits */
#endif
return 0;
}
Is there any other way to do the same task efficiently ? All suggestion are most welcome ?
To put values shifted by 11 bits instead of 8, 16 or 32 will require manipulations with bits. You will basically have to emulate an array of bits in an array of (say 32 bits) integers. In this case if a value is stored at a bit offset X it will be (possibly) stored in your array somewhere on indexes X/32 and X/32+1 (if it is crossing border of 32 bits). Each time when you have to set a value into the array you have to load those two values and "place" your number there. The implementation is a bit technical, try the following code:
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#define MASK32 ((uint64_t)0xffffffff)
void setValue(uint32_t *a, int bits, int i, int n) {
int bitoffset = i * bits;
int index = bitoffset / 32;
int shift = bitoffset % 32;
uint64_t maskbits = (~(uint64_t)0) >> (64-bits);
uint64_t val = ((uint64_t)a[index+1]<<32) + a[index];
val = val & ~(maskbits << shift) | ((n & maskbits) << shift);
a[index] = (val & MASK32);
a[index+1] = (val >> 32) & MASK32;
}
int getValue(const uint32_t *a, int bits, int i) {
int bitoffset = i * bits;
int index = bitoffset / 32;
int shift = bitoffset % 32;
uint64_t maskbits = (~(uint64_t)0) >> (64-bits);
int val = ((((uint64_t)a[index+1]<<32) + a[index]) >> shift) & maskbits;
return(val);
}
int input_arr[100] = {10,20,1255,1200,50,55,1,5,6,1000};
int main() {
int i, j;
uint32_t a[100*11/32+2];
for(i=0; i<100; i++) setValue(a,11,i,input_arr[i]);
for(j=0; j<100; j++) printf("a[%d/11] == %d\n", j, getValue(a,11,j));
}
Another approach that I find "interesting" is allocating an array of chars and doing a cast to an type that fits the maximum value. Something like this:
NumBytesMaxValue = ...;
void* pointers = malloc(NumBytesMaxValue * NumValues);
if (NumBytesMaxValue == 1)
cast_pointer_to_char_and_fill_it();
else if (NumBytesMaxValue == 2)
cast_pointer_to_short_and_fill_it();
...
Data compression is a vast subject, an active area of research... compressing your data can be done in so many different ways as to make it off topic.
Finding the smallest type for the array can however be done by a utility program or a preliminary phase:
#include <limits.h>
#include <stdio.h>
int main() {
int input_array[] = { 1, 2, 2, 3, 4, 1, 2, 4, 6, 1255, 1, 2, 5, 1233 };
size_t i, count = sizeof(input_array) / sizeof(input_array[0]);
int min, max;
int nc = 0;
min = max = input_array[0];
for (i = 1; i < count; i++) {
if (min > input_array[i]) min = intput_array[i];
if (max < input_array[i]) max = intput_array[i];
}
printf("min value is %d, max value is %d\n", min, max);
if (min >= SCHAR_MIN && max <= SCHAR_MAX)
nc += printf("type signed char is appropriate\n");
if (min >= 0 && max <= UCHAR_MAX)
nc += printf("type unsigned char is appropriate\n");
if (min >= SHRT_MIN && max <= SHRT_MAX)
nc += printf("type short is appropriate\n");
if (min >= 0 && max <= USHRT_MAX)
nc += printf("type unsigned short is appropriate\n");
if (nc == 0)
printf("no type smaller than int is appropriate\n");
return 0;
}
You can use the same approach for a set of numbers with values unknown at compile time with these steps:
start with an allocated array of a small type such as signed char.
read the next value: if it fits in the current type, add it to the array and continue.
if not, allocate an array of a larger type such as short, copy the values parsed so far into it, free the previous array, store the new value and continue.
if the new value does not fit in a short, use a larger type such as int.
you could write code for even larger types such as long and long long, but you need specific code for each type.
at the end of the read phase, you have an array of the smallest type that handles all the values in the dataset. Handle this array with code for its specific type. This means you have to duplicate the processing code for each type, which can be tricky.
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.
I have an array of unsigned chars in c I am trying to print in base 10, and I am stuck. I think this will be better explained in code, so, given:
unsigned char n[3];
char[0] = 1;
char[1] = 2;
char[2] = 3;
I would like to print 197121.
This is trivial with small base 256 arrays. One can simply 1 * 256 ^ 0 + 2 * 256 ^ 1 + 3 * 256 ^ 2.
However, if my array was 100 bytes large, then this quickly becomes a problem. There is no integral type in C that is 100 bytes large, which is why I'm storing numbers in unsigned char arrays to begin with.
How am I supposed to efficiently print this number out in base 10?
I am a bit lost.
There's no easy way to do it using only the standard C library. You'll either have to write the function yourself (not recommended), or use an external library such as GMP.
For example, using GMP, you could do:
unsigned char n[100]; // number to print
mpz_t num;
mpz_import(num, 100, -1, 1, 0, 0, n); // convert byte array into GMP format
mpz_out_str(stdout, 10, num); // print num to stdout in base 10
mpz_clear(num); // free memory for num
When I saw this question, I purpose to solve it, but at that moment I was very busy.
This last weekend I've could gain some prize hours of free time so I considered my pending challenge.
First of all, I suggest you to considered above response. I never use GMP library but I'm sure that it's better solution than a handmade code.
Also, you could be interest to analyze code of bc calculator; it can works with big numbers and I used to test my own code.
Ok, if you are still interested in a code do it by yourself (only with support C language and Standard C library) may be I can give you something.
Before all, a little bit theory. In basic numeric theory (modular arithmetic level) theres is an algorithm that inspire me to arrive at one solution; Multiply and Power algorithm to solve a^N module m:
Result := 1;
for i := k until i = 0
if n_i = 1 then Result := (Result * a) mod m;
if i != 0 then Result := (Result * Result) mod m;
end for;
Where k is number of digits less one of N in binary representation, and n_i is i binary digit. For instance (N is exponent):
N = 44 -> 1 0 1 1 0 0
k = 5
n_5 = 1
n_4 = 0
n_3 = 1
n_2 = 1
n_1 = 0
n_0 = 0
When we make a module operation, as an integer division, we can lose part of the number, so we only have to modify algorithm to don't miss relevant data.
Here is my code (take care that it is an adhoc code, strong dependency of may computer arch. Basically I play with data length of C language so, be carefully because my data length could not be the same):
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
enum { SHF = 31, BMASK = 0x1 << SHF, MODULE = 1000000000UL, LIMIT = 1024 };
unsigned int scaleBigNum(const unsigned short scale, const unsigned int lim, unsigned int *num);
unsigned int pow2BigNum(const unsigned int lim, unsigned int *nsrc, unsigned int *ndst);
unsigned int addBigNum(const unsigned int lim1, unsigned int *num1, const unsigned int lim2, unsigned int *num2);
unsigned int bigNum(const unsigned short int base, const unsigned int exp, unsigned int **num);
int main(void)
{
unsigned int *num, lim;
unsigned int *np, nplim;
int i, j;
for(i = 1; i < LIMIT; ++i)
{
lim = bigNum(i, i, &num);
printf("%i^%i == ", i, i);
for(j = lim - 1; j > -1; --j)
printf("%09u", num[j]);
printf("\n");
free(num);
}
return 0;
}
/*
bigNum: Compute number base^exp and store it in num array
#base: Base number
#exp: Exponent number
#num: Pointer to array where it stores big number
Return: Array length of result number
*/
unsigned int bigNum(const unsigned short int base, const unsigned int exp, unsigned int **num)
{
unsigned int m, lim, mem;
unsigned int *v, *w, *k;
//Note: mem has the exactly amount memory to allocate (dinamic memory version)
mem = ( (unsigned int) (exp * log10( (float) base ) / 9 ) ) + 3;
v = (unsigned int *) malloc( mem * sizeof(unsigned int) );
w = (unsigned int *) malloc( mem * sizeof(unsigned int) );
for(m = BMASK; ( (m & exp) == 0 ) && m; m >>= 1 ) ;
v[0] = (m) ? 1 : 0;
for(lim = 1; m > 1; m >>= 1)
{
if( exp & m )
lim = scaleBigNum(base, lim, v);
lim = pow2BigNum(lim, v, w);
k = v;
v = w;
w = k;
}
if(exp & 0x1)
lim = scaleBigNum(base, lim, v);
free(w);
*num = v;
return lim;
}
/*
scaleBigNum: Make an (num[] <- scale*num[]) big number operation
#scale: Scalar that multiply big number
#lim: Length of source big number
#num: Source big number (array of unsigned int). Update it with new big number value
Return: Array length of operation result
Warning: This method can write in an incorrect position if we don't previous reallocate num (if it's necessary). bigNum method do it for us
*/
unsigned int scaleBigNum(const unsigned short scale, const unsigned int lim, unsigned int *num)
{
unsigned int i;
unsigned long long int n, t;
for(n = 0, t = 0, i = 0; i < lim; ++i)
{
t = (n / MODULE);
n = ( (unsigned long long int) scale * num[i] );
num[i] = (n % MODULE) + t; // (n % MODULE) + t always will be smaller than MODULE
}
num[i] = (n / MODULE);
return ( (num[i]) ? lim + 1 : lim );
}
/*
pow2BigNum: Make a (dst[] <- src[] * src[]) big number operation
#lim: Length of source big number
#src: Source big number (array of unsigned int)
#dst: Destination big number (array of unsigned int)
Return: Array length of operation result
Warning: This method can write in an incorrect position if we don't previous reallocate num (if it's necessary). bigNum method do it for us
*/
unsigned int pow2BigNum(const unsigned int lim, unsigned int *src, unsigned int *dst)
{
unsigned int i, j;
unsigned long long int n, t;
unsigned int k, c;
for(c = 0, dst[0] = 0, i = 0; i < lim; ++i)
{
for(j = i, n = 0; j < lim; ++j)
{
n = ( (unsigned long long int) src[i] * src[j] );
k = i + j;
if(i != j)
{
t = 2 * (n % MODULE);
n = 2 * (n / MODULE);
// (i + j)
dst[k] = ( (k > c) ? ((c = k), 0) : dst[k] ) + (t % MODULE);
++k; // (i + j + 1)
dst[k] = ( (k > c) ? ((c = k), 0) : dst[k] ) + ( (t / MODULE) + (n % MODULE) );
++k; // (i + j + 2)
dst[k] = ( (k > c) ? ((c = k), 0) : dst[k] ) + (n / MODULE);
}
else
{
dst[k] = ( (k > c) ? ((c = k), 0) : dst[k] ) + (n % MODULE);
++k; // (i + j)
dst[k] = ( (k > c) ? ((c = k), 0) : dst[k] ) + (n / MODULE);
}
for(k = i + j; k < (lim + j); ++k)
{
dst[k + 1] += (dst[k] / MODULE);
dst[k] %= MODULE;
}
}
}
i = lim << 1;
return ((dst[i - 1]) ? i : i - 1);
}
/*
addBigNum: Make a (num2[] <- num1[] + num2[]) big number operation
#lim1: Length of source num1 big number
#num1: First source operand big number (array of unsigned int). Should be smaller than second
#lim2: Length of source num2 big number
#num2: Second source operand big number (array of unsigned int). Should be equal or greater than first
Return: Array length of operation result or 0 if num1[] > num2[] (dosen't do any op)
Warning: This method can write in an incorrect position if we don't previous reallocate num2
*/
unsigned int addBigNum(const unsigned int lim1, unsigned int *num1, const unsigned int lim2, unsigned int *num2)
{
unsigned long long int n;
unsigned int i;
if(lim1 > lim2)
return 0;
for(num2[lim2] = 0, n = 0, i = 0; i < lim1; ++i)
{
n = num2[i] + num1[i] + (n / MODULE);
num2[i] = n % MODULE;
}
for(n /= MODULE; n; ++i)
{
num2[i] += n;
n = (num2[i] / MODULE);
}
return (lim2 > i) ? lim2 : i;
}
To compile:
gcc -o bgn <name>.c -Wall -O3 -lm //Math library if you wants to use log func
To check result, use direct output as and input to bc. Easy shell script:
#!/bin/bash
select S in ` awk -F '==' '{print $1 " == " $2 }' | bc`;
do
0;
done;
echo "Test Finished!";
We have and array of unsigned int (4 bytes) where we store at each int of array a number of 9 digits ( % 1000000000UL ); hence num[0] we will have the first 9 digits, num[1] we will have digit 10 to 18, num[2]...
I use convencional memory to work but an improvement can do it with dinamic memory. Ok, but how length It could be the array? (or how many memory we need to allocate?). Using bc calculator (bc -l with mathlib) we can determine how many digits has a number:
l(a^N) / l(10) // Natural logarith to Logarithm base 10
If we know digits, we know amount integers we needed:
( l(a^N) / (9 * l(10)) ) + 1 // Truncate result
If you work with value such as (2^k)^N you can resolve it logarithm with this expression:
( k*N*l(2)/(9*l(10)) ) + 1 // Truncate result
to determine the exactly length of integer array. Example:
256^800 = 2^(8*800) ---> l(2^(8*800))/(9*l(10)) + 1 = 8*800*l(2)/(9*l(10)) + 1
The value 1000000000UL (10^9) constant is very important. A constant like 10000000000UL (10^10) dosen't work because can produce and indetected overflow (try what's happens with number 16^16 and 10^10 constant) and a constant more little such as 1000000000UL (10^8) are correct but we need to reserve more memory and do more steps. 10^9 is key constant for unsigned int of 32 bits and unsigned long long int of 64 bits.
The code has two parts, Multiply (easy) and Power by 2 (more hard). Multiply is just multiplication and scale and propagate the integer overflow. It take the principle of associative property in math to do exactly the inverse principle, so if k(A + B + C) we want kA + kB + kC where number will be k*A*10^18 + k*B*10^9 + kC. Obiously, kC operation can generate a number bigger than 999 999 999, but never more bigger than 0xFF FF FF FF FF FF FF FF. A number bigger than 64 bits can never occur in a multiplication because C is an unsigned integer of 32 bits and k is a unsigned short of 16 bits. In worts case, we will have this number:
k = 0x FF FF;
C = 0x 3B 9A C9 FF; // 999999999
n = k*C = 0x 3B 9A | 8E 64 36 01;
n % 1000000000 = 0x 3B 99 CA 01;
n / 1000000000 = 0x FF FE;
After Mul kB we need to add 0x FF FE from last multiplication of C ( B = kB + (C / module) ), and so on (we have 18 bits arithmetic offset, enough to guarantee correct values).
Power is more complex but is in essencial, the same problem (multiplication and add), so I give some tricks about code power:
Data types are important, very important
If you try to multiplication an unsigned integer with unsigned integer, you get another unsigned integer. Use explicit cast to get unsigned long long int and don't lose data.
Always use unsigned modifier, dont forget it!
Power by 2 can directly modify 2 index ahead of current index
gdb is your friend
I've developed another method that add big numbers. These last I don't prove so much but I think it works well. Don't be cruels with me if it has a bug.
...and that's all!
PD1: Developed in a
Intel(R) Pentium(R) 4 CPU 1.70GHz
Data length:
unsigned short: 2
unsigned int: 4
unsigned long int: 4
unsigned long long int: 8
Numbers such as 256^1024 it spend:
real 0m0.059s
user 0m0.033s
sys 0m0.000s
A bucle that's compute i^i where i goes to i = 1 ... 1024:
real 0m40.716s
user 0m14.952s
sys 0m0.067s
For numbers such as 65355^65355, spent time is insane.
PD2: My response is so late but I hope my code it will be usefull.
PD3: Sorry, explain me in english is one of my worst handicaps!
Last update: I just have had an idea that with same algorithm but other implementation, improve response and reduce amount memory to use (we can use the completely bits of unsigned int). The secret: n^2 = n * n = n * (n - 1 + 1) = n * (n - 1) + n.
(I will not do this new code, but if someone are interested, may be after exams... )
I don't know if you still need a solution, but I wrote an article about this problem. It shows a very simple algorithm which can be used to convert an arbitrary long number with base X to a corresponding number of base Y. The algorithm is written in Python, but it is really only a few lines long and doesn't use any Python magic. I needed such an algorithm for a C implementation, too, but decided to describe it using Python for two reasons. First, Python is very readable by anyone who understands algorithms written in a pseudo programming language and, second, I am not allowed to post the C version, because it I did it for my company. Just have a look and you will see how easy this problem can be solved in general. An implementation in C should be straight forward...
Here is a function that does what you want:
#include <math.h>
#include <stddef.h> // for size_t
double getval(unsigned char *arr, size_t len)
{
double ret = 0;
size_t cur;
for(cur = 0; cur < len; cur++)
ret += arr[cur] * pow(256, cur);
return ret;
}
That looks perfectly readable to me. Just pass the unsigned char * array you want to convert and the size. Note that it won't be perfect - for arbitrary precision, I suggest looking into the GNU MP BigNum library, as has been suggested already.
As a bonus, I don't like your storing your numbers in little-endian order, so here's a version if you want to store base-256 numbers in big-endian order:
#include <stddef.h> // for size_t
double getval_big_endian(unsigned char *arr, size_t len)
{
double ret = 0;
size_t cur;
for(cur = 0; cur < len; cur++)
{
ret *= 256;
ret += arr[cur];
}
return ret;
}
Just things to consider.
It may be too late or too irrelevant to make this suggestion, but could you store each byte as two base 10 digits (or one base 100) instead of one base 256? If you haven't implemented division yet, then that implies all you have is addition, subtraction, and maybe multiplication; those shouldn't be too hard to convert. Once you've done that, printing it would be trivial.
As I was not satisfied with the other answers provided, I decided to write an alternative solution myself:
#include <stdlib.h>
#define BASE_256 256
char *largenum2str(unsigned char *num, unsigned int len_num)
{
int temp;
char *str, *b_256 = NULL, *cur_num = NULL, *prod = NULL, *prod_term = NULL;
unsigned int i, j, carry = 0, len_str = 1, len_b_256, len_cur_num, len_prod, len_prod_term;
//Get 256 as an array of base-10 chars we'll use later as our second operand of the product
for ((len_b_256 = 0, temp = BASE_256); temp > 0; len_b_256++)
{
b_256 = realloc(b_256, sizeof(char) * (len_b_256 + 1));
b_256[len_b_256] = temp % 10;
temp = temp / 10;
}
//Our first operand (prod) is the last element of our num array, which we'll convert to a base-10 array
for ((len_prod = 0, temp = num[len_num - 1]); temp > 0; len_prod++)
{
prod = realloc(prod, sizeof(*prod) * (len_prod + 1));
prod[len_prod] = temp % 10;
temp = temp / 10;
}
while (len_num > 1) //We'll stay in this loop as long as we still have elements in num to read
{
len_num--; //Decrease the length of num to keep track of the current element
//Convert this element to a base-10 unsigned char array
for ((len_cur_num = 0, temp = num[len_num - 1]); temp > 0; len_cur_num++)
{
cur_num = (char *)realloc(cur_num, sizeof(char) * (len_cur_num + 1));
cur_num[len_cur_num] = temp % 10;
temp = temp / 10;
}
//Multiply prod by 256 and save that as prod_term
len_prod_term = 0;
prod_term = NULL;
for (i = 0; i < len_b_256; i++)
{ //Repeat this loop 3 times, one for each element in {6,5,2} (256 as a reversed base-10 unsigned char array)
carry = 0; //Set the carry to 0
prod_term = realloc(prod_term, sizeof(*prod_term) * (len_prod + i)); //Allocate memory to save prod_term
for (j = i; j < (len_prod_term); j++) //If we have digits from the last partial product of the multiplication, add it here
{
prod_term[j] = prod_term[j] + prod[j - i] * b_256[i] + carry;
if (prod_term[j] > 9)
{
carry = prod_term[j] / 10;
prod_term[j] = prod_term[j] % 10;
}
else
{
carry = 0;
}
}
while (j < (len_prod + i)) //No remaining elements of the former prod_term, so take only into account the results of multiplying mult * b_256
{
prod_term[j] = prod[j - i] * b_256[i] + carry;
if (prod_term[j] > 9)
{
carry = prod_term[j] / 10;
prod_term[j] = prod_term[j] % 10;
}
else
{
carry = 0;
}
j++;
}
if (carry) //A carry may be present in the last term. If so, allocate memory to save it and increase the length of prod_term
{
len_prod_term = j + 1;
prod_term = realloc(prod_term, sizeof(*prod_term) * (len_prod_term));
prod_term[j] = carry;
}
else
{
len_prod_term = j;
}
}
free(prod); //We don't need prod anymore, prod will now be prod_term
prod = prod_term;
len_prod = len_prod_term;
//Add prod (formerly prod_term) to our current number of the num array, expressed in a b-10 array
carry = 0;
for (i = 0; i < len_cur_num; i++)
{
prod[i] = prod[i] + cur_num[i] + carry;
if (prod[i] > 9)
{
carry = prod[i] / 10;
prod[i] -= 10;
}
else
{
carry = 0;
}
}
while (carry && (i < len_prod))
{
prod[i] = prod[i] + carry;
if (prod[i] > 9)
{
carry = prod[i] / 10;
prod[i] -= 10;
}
else
{
carry = 0;
}
i++;
}
if (carry)
{
len_prod++;
prod = realloc(prod, sizeof(*prod) * len_prod);
prod[len_prod - 1] = carry;
carry = 0;
}
}
str = malloc(sizeof(char) * (len_prod + 1)); //Allocate memory for the return string
for (i = 0; i < len_prod; i++) //Convert the numeric result to its representation as characters
{
str[len_prod - 1 - i] = prod[i] + '0';
}
str[i] = '\0'; //Terminate our string
free(b_256); //Free memory
free(prod);
free(cur_num);
return str;
}
The idea behind it all derives from simple math. For any base-256 number, its base-10 representation can be calculated as:
num[i]*256^i + num[i-1]*256^(i-1) + (···) + num[2]*256^2 + num[1]*256^1 + num[0]*256^0
which expands to:
(((((num[i])*256 + num[i-1])*256 + (···))*256 + num[2])*256 + num[1])*256 + num[0]
So all we have to do is to multiply, step-by step, each element of the number array by 256 and add to it the next element, and so on... That way we can get the base-10 number.