Finding the sum of all primes under 2 million - c

I just wanted to know why my code doesn't give the right answer.
I've tried it with Euler 7 and it works fine.
Here is my code:
int main(void)
{
int prime = 1;
int number = 3;
int counter = 0;
int sum = 0;
while (number <= 2000000)
{
counter = 0;
for (int i = 2; i < (sqrt(number) + 1); i++)
{
if (number % i == 0)
{
counter++;
}
}
if (counter == 0)
{
printf("Number: %d Prime: %d\n", number, prime);
prime++;
sum = sum + number;
}
number++;
}
printf("The sum is: %d\n", sum);
system("PAUSE");
return (0);
}

Issue 1
The sum of all primes below 2000000 is 142913828922 (~1.4*10^11 ).
The maximum number that fits into an 32bit int is 2147483647 = 2^31-1 (~2.1*10^9).
So you are getting an integer overflow.
Fix 1
unsigned long long sum = 0;
and
printf("The sum is: %lld\n", sum);
should give the expected result.
Issue 2
2 is also a prime, but you are not counting it.
Fix 2
A quick hack would be to initialize sum with 2.

2 is also a prime number. So, you can initialize sum = 2 (according #sergej).
In
if (number % i == 0)
{
counter++;
break;
}
You should use a break for reducing extra iteration because if (number % i == 0) is true then counter value is increase and it will be 1 and also perfectly work.
And you should use unsigned long long int sum = 0 because for 2 million, sum is much higher from 2^31-1 (if you use int).
And you display your sum value by printf("%lld", sum)

Related

finding how many times number2 is showing in number1

I am solving an exercise in C and I got stuck. I don't know the logic of the code to get to my solution. For example we enter 2 numbers from input let the numbers be 123451289 and 12 and I want to see how many times number 2 is showing at number 1 (if this is confusing let me know). For the numbers earlier the program outputs 2. I tried solving it here is my code:
#include <stdio.h>
int main() {
int num1, num2, counter = 0;
scanf("%d%d", num1, num2);
if (num1 < num2) {
int temp = num1;
num1 = num2;
num2 = temp;
}
int copy1 = num1;
int copy2 = num2;
while (copy2 > 0) {
counter++; // GETTING THE LENGHT OF THE SECOND NUMBER
copy2 /= 10;
// lastdigits = copy1 % counter //HERE I WANT TO GET THE LAST DIGITS OF THE FIRST NUMBER
// But it does not work
}
}
My question is how can I get the last digits of the first number according to the second one for example if the second number have 3 digits I want to get the last 3 digits of the first number. For the other part I think I can figure it out.
I must solve this problem WITHOUT USING ARRAYS.
The problem: find all the needles (e.g. 12) in a haystack (e.g. 123451289).
This can be done simply without arrays using a modulus of the needle. For 12, this is 100. That is, 12 is two digits wide. Using the modulus, we can
isolate the rightmost N digits of the haystack and compare them against the needle.
We "scan" haystack repeatedly by dividing by 10 until we reach zero.
Here is the code:
#include <stdio.h>
int
main(void)
{
int need, hay, counter = 0;
scanf(" %d %d", &hay, &need);
// ensure that the numbers are _not_ reversed
if (hay < need) {
int temp = need;
need = hay;
hay = temp;
}
// get modulus for needle (similar to number of digits)
int mod = 1;
for (int copy = need; copy != 0; copy /= 10)
mod *= 10;
// search haystack for occurences of needle
// examine the rightmost "mod" digits of haystack and check for match
// reduce haystack digit by digit
for (int copy = hay; copy != 0; copy /= 10) {
if ((copy % mod) == need)
++counter;
}
printf("%d appears in %d exactly %d times\n",need,hay,counter);
return 0;
}
UPDATE:
I'm afraid this does not work for 10 0. –
chqrlie
A one line fix for to the modulus calculation for the 10/0 case. But, I've had to add a special case for the 0/0 input.
Also, I've added a fix for negative numbers and allowed multiple lines of input:
#include <stdio.h>
int
main(void)
{
int need, hay, counter;
while (scanf(" %d %d", &hay, &need) == 2) {
counter = 0;
// we can scan for -12 in -1237812
if (hay < 0)
hay = -hay;
if (need < 0)
need = -need;
// ensure that the numbers are _not_ reversed
if (hay < need) {
int temp = need;
need = hay;
hay = temp;
}
// get modulus for needle (similar to number of digits)
int mod = need ? 1 : 10;
for (int copy = need; copy != 0; copy /= 10)
mod *= 10;
// search haystack for occurences of needle
// examine the rightmost "mod" digits of haystack and check for match
// reduce haystack digit by digit
for (int copy = hay; copy != 0; copy /= 10) {
if ((copy % mod) == need)
++counter;
}
// special case for 0/0 [yecch]
if ((hay == 0) && (need == 0))
counter = 1;
printf("%d appears in %d exactly %d times\n", need, hay, counter);
}
return 0;
}
Here is the program output:
12 appears in 123451289 exactly 2 times
0 appears in 10 exactly 1 times
0 appears in 0 exactly 1 times
UPDATE #2:
Good fixes, including tests for negative numbers... but I'm afraid large numbers still pose a problem, such as 2000000000 2000000000 and -2147483648 8 –
chqrlie
Since OP has already posted an answer, this is bit like beating a dead horse, but I'll take one last attempt.
I've changed from calculating a modulus of needle into calculating the number of digits in needle. This is similar to the approach of some of the other answers.
Then, the comparison is now done digit by digit from the right.
I've also switched to unsigned and allow for the number to be __int128 if desired/supported with a compile option.
I've added functions to decode and print numbers so it works even without libc support for 128 bit numbers.
I may be ignoring [yet] another edge case, but this is an academic problem (e.g. we can't use arrays) and my solution is to just use larger types for the numbers. If we could use arrays, we'd keep things as strings and this would be similar to using strstr.
Anyway, here's the code:
#include <stdio.h>
#ifndef NUM
#define NUM long long
#endif
typedef unsigned NUM num_t;
FILE *xfin;
int
numget(num_t *ret)
{
int chr;
num_t acc = 0;
int found = 0;
while (1) {
chr = fgetc(xfin);
if (chr == EOF)
break;
if ((chr == '\n') || (chr == ' ')) {
if (found)
break;
}
if ((chr >= '0') && (chr <= '9')) {
found = 1;
acc *= 10;
chr -= '0';
acc += chr;
}
}
*ret = acc;
return found;
}
#define STRMAX 16
#define STRLEN 100
const char *
numprt(num_t val)
{
static char strbuf[STRMAX][STRLEN];
static int stridx = 0;
int dig;
char *buf;
buf = strbuf[stridx++];
stridx %= STRMAX;
char *rhs = buf;
do {
if (val == 0) {
*rhs++ = '0';
break;
}
for (; val != 0; val /= 10, ++rhs) {
dig = val % 10;
*rhs = dig + '0';
}
} while (0);
*rhs = 0;
if (rhs > buf)
--rhs;
for (char *lhs = buf; lhs < rhs; ++lhs, --rhs) {
char tmp = *lhs;
*lhs = *rhs;
*rhs = tmp;
}
return buf;
}
int
main(int argc,char **argv)
{
num_t need, hay, counter;
--argc;
++argv;
if (argc > 0)
xfin = fopen(*argv,"r");
else
xfin = stdin;
while (1) {
if (! numget(&hay))
break;
if (! numget(&need))
break;
counter = 0;
// we can scan for -12 in -1237812
if (hay < 0)
hay = -hay;
if (need < 0)
need = -need;
// ensure that the numbers are _not_ reversed
if (hay < need) {
num_t temp = need;
need = hay;
hay = temp;
}
// get number of digits in needle (zero has one digit)
int ndig = 0;
for (num_t copy = need; copy != 0; copy /= 10)
ndig += 1;
if (ndig == 0)
ndig = 1;
// search haystack for occurences of needle
// starting from the right compare digit-by-digit
// "shift" haystack right on each iteration
num_t hay2 = hay;
for (; hay2 != 0; hay2 /= 10) {
num_t hcopy = hay2;
// do the rightmost ndig digits match in both numbers?
int idig = ndig;
int match = 0;
for (num_t need2 = need; idig != 0;
--idig, need2 /= 10, hcopy /= 10) {
// get single current digits from each number
int hdig = hcopy % 10;
int ndig = need2 % 10;
// do they match
match = (hdig == ndig);
if (! match)
break;
}
counter += match;
}
// special case for 0/0 et. al. [yecch]
if (hay == need)
counter = 1;
printf("%s appears in %s exactly %s times\n",
numprt(need), numprt(hay), numprt(counter));
}
return 0;
}
Here's the program output:
12 appears in 123451289 exactly 2 times
123 appears in 123451289 exactly 1 times
1234 appears in 123451289 exactly 1 times
1 appears in 123451289 exactly 2 times
0 appears in 10 exactly 1 times
0 appears in 0 exactly 1 times
1000000000 appears in 1000000000 exactly 1 times
2000000000 appears in 2000000000 exactly 1 times
This looks along the lines of what you're attempting.
You can use the pow() function from math.h to raise 10 to the power of how many digits you need for your modulus operation.
Compile with -lm or make your own function to calculate 10^num_digits
#include <stdio.h>
#include <math.h>
int main() {
int x = 123456789;
double num_digits = 3.0;
int last_digits = x % (int)pow(10.0, num_digits);
printf("x = %d\nLast %d Digits of x = %d\n", x, (int)num_digits, last_digits);
return 0;
}
Outputs:
x = 123456789
Last 3 Digits of x = 789
I think you are trying to ask :- if number1 = 1234567 and number2 = 673, then, length of number2 or number2 has 3 digits, so, you now want the last 3 digits in number1, i.e, '456', if I'm not wrong.
If that is the case, then, what you did to find the number of digits in num2 is correct, i.e,
while (copy2>0) {
counter++; // GETTING THE LENGHT OF THE SECOND NUMBER
copy2/=10;
}
you can do the same for number1 and find out its number of digits, then you can compare whether the number of digits in number2 is less than that in number1. Ex, 3 is less than number of digits in number1, so you can proceed further. Let's say number of digits in number1 is 7 and you want the last 3 digits, so you can do iterate over the digits in number1 till count of digits in number2 and pop out each last digit and store them in an array.
The code:
#include <stdio.h>
int main()
{
int num1,num2;
int count1 = 0, count2 = 0;
scanf("%d",&num1);
scanf("%d",&num2);
if(num1<num2){
int temp = num1;
num1 = num2;
num2 = temp;
}
int copy1 = num1;
int copy2 = num2;
while (copy1>0)
{
count1++;
copy1/=10;
}
while (copy2>0)
{
count2++;
copy2/=10;
}
// printf("num1 has %d digits and num2 has %d digits\n", count1, count2);
if (count1 >= count2)
{
int arr[count2];
int x = count2;
int p = num1;
int i = 0;
while (x > 0)
{
arr[i++] = p%10;
x --;
p/=10;
}
for (int j = 0; j < i; j++)
{
printf("%d ", arr[j]);
}
}
return 0;
}
output : 8 7 6
let's say, num1 = 12345678, num2 = 158, then arr = {8,7,6}.
You must determine the number of digits N of num2 and test if num1 ends with num2 modulo 10N.
Note these tricky issues:
you should not sort num1 and num2: If num2 is greater than num1, the count is obviously 0.
num2 has at least 1 digit even if it is 0.
if num1 and num2 are both 0, the count is 1.
if num2 is greater then INT_MAX / 10, the computation for mod would overflow, but there can only be one match, if num1 == num2.
it is unclear whether the count for 1111 11 should be 2 or 3. We will consider all matches, including overlapping ones.
to handle larger numbers, we shall use unsigned long long instead of int type.
Here is a modified version:
#include <limits.h>
#include <stdio.h>
int main() {
int counter = 0;
unsigned long long num1, num2;
if (scanf("%llu%llu", &num1, &num2) != 2) {
printf("invalid input\n");
return 1;
}
if (num1 == num2) {
/* special case for "0 0" */
counter = 1;
} else
if (num1 > num2 && num2 <= ULLONG_MAX / 10) {
unsigned long long copy1 = num1;
unsigned long long mod = 10;
while (mod < num2) {
mod *= 10;
}
while (copy1 > 0) {
if (copy1 % mod == num2)
counter++;
copy1 /= 10;
}
}
printf("count=%d\n", counter);
return 0;
}
Note that leading zeroes are not supported in either number: 101 01 should produce a count of 1 but after conversion by scanf(), the numbers are 101 and 1 leading to a count of 2. It is non trivial to handle leading zeroes as well as numbers larger than ULLONG_MAX without arrays.
This was the answer that i was looking for but thank you all for helping :)
#include <stdio.h>
#include <math.h>
int main(){
int num1,counter1,counter2,num2,temp,digit,copy1,copy2;
scanf("%d%d",&num1,&num2);
if(num1<num2){
temp = num1;
num1 = num2;
num2 = temp;
}
copy1 = num1;
copy2 = num2;
counter1 = counter2 = 0;
while (copy2>0) {
counter1++;
copy2/=10;
}
counter1 = pow(10,counter1);
if(num1> 1 && num2>1)
while (copy1>0) {
digit = copy1%counter1;
if(digit==num2){
counter2++;
}
copy1/=10;
} else{
if(num2<1){
while (copy1>0) {
digit = copy1%10;
if(digit==copy2){
counter2++;
}
copy1/=10;
}
}
}
printf("%d",counter2);
}

How to display smallest and biggest divisor?

I have to make a program that displays all the proper divisors of a number(given by the user),basically all except the number itself and 1. If it doesn't have any print that it's prime.All good,done that.
There is one more thing I need to do though in case it does have proper divisors and that is to display the smallest and biggest divisor which I can't figure out how to do ,I tried to do it as if the printed divisors were just one number ignoring the "\n" and using "number % 10" to find the last number and the while loop to find the first number,but that won't work in case let's say the given number is 33 and the biggest divisor is 11.
I'll provide the code for better understanding since my question is kinda fuzzy. Everything is how I want it to be except I don't know how to display the smallest divisor and the biggest divisor.
#include <stdio.h>
int main() {
int n, divisor, smallest, biggest, count = 0;
scanf("%d", &n);
for (divisor = 2; divisor < n; divisor++) {
if (n % divisor == 0) {
printf("%d is divisor of %d\n", divisor, n);
}
}
for (divisor = 1; divisor <= n; divisor++) {
if (n % divisor == 0) {
count++;
}
}
if (count == 2) {
printf("The number does not have proper divisors(it is prime)");
}
return 0;
}
I would modify your code as follows:
#include <stdio.h>
int main()
{
int n,divisor,smallest,biggest,count=0;
scanf("%d",&n);
for(divisor = 2;divisor < n;divisor++)
{
if(n % divisor == 0)
{
count++;
if (count == 1) smallest = divisor;
biggest = divisor;
printf("%d is divisor of %d\n",divisor,n);
}
}
if (count == 0) printf("The number does not have proper divisors(it is prime)");
else printf("%d and %d are the smallest and biggest divisors respectively", smallest, biggest);
return 0;
}
Instead of using two for loops, I merged them into one since they're doing the same thing. Every positive number will be divisible by 1 and itself so it's redundant to use the second for loop. When count is 1, I know that I have found the first divisor so I set smallest equal to that. Also,everytime I find a divisor, I set biggest equal to that so that in the end, biggest is set to the last divisor found (note that you should not use an else clause here, since that will cause the program to not work when the smallest and biggest divisors are equal). I also increment count by 1 everytime a divisor is found in order to check whether the number is prime without modifying your approach too much (there are efficient ways to check for prime numbers, and I encourage you to take a look at them). And finally, I print the smallest and biggest divisors only if they exist, else I print that it is prime.
You can implement minDivisor only, then to find max divisor you can divide value by min divisor:
#include <math.h>
...
/* Returns the smallest non-trivial divisor or 1 if it doesn't exist */
int minDivisor(int value) {
if (value <= 3)
return 1;
/* let's check n for being even */
if (value % 2 == 0)
return 2;
/* We should check up to sqrt(n) only */
int n = (int) (sqrt(value) + 0.5);
for (int divisor = 3; divisor <= n; divisor += 2)
if (value % divisor == 0)
return divisor;
/* prime number */
return 1;
}
Then
int main() {
int n, divisor, smallest, biggest, count = 0;
...
smallest = minDivisor(n);
biggest = n / smallest;
...
Please, fiddle yourself

Armstrong number program in C returns wrong value

I am writing a program to see if a user entered number is Armstrong or not, here is my code:
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
int main(){
int x = 0;
printf("Enter a natural number: ");
scanf("%d", &x);
int ans = x;
// Digit Counter
int counter = 0; //Variable for number of digits in the user entered number
int b = x; //For each time number can be divided by 10 and isnt 0
for (int i = 1; i <= x; i++){ // Then counter variable is incremented by 1
b /= 10;
if (b != 0){
counter += 1;
}
}
++counter;
//Digit Counter
int sum = 0;
// Digit Finder
int D;
for (int j = 1; j <= x; j++){
D = x % 10; //Shows remainder of number (last digit) when divided by 10
sum += pow(D, counter); //Raises Digit found by counter and adds to sum
printf("%d\n", sum);
x /= 10; // Divides user entered number by 10 to get rid of digit found
}
if (sum == ans){
printf("%d is a Armstrong number! :)", ans);
}else
printf("%d is not an Armstrong number :(", ans);
//Digit Finder
return 0;
}
My problem is that the program works fine apart from one point, when the program is given a Armstrong number which does not start with 1 then it behaves normally and indicates if it is an Armstrong number or not, but when i input a Armstrong number which start with 1 then it will print out the Armstrong number but -1.
For example: If i input something such as 371 which is an Armstrong number it will show that it is an Armstrong number. However if i input 1634 it will output 1633 which is 1 less than 1634.
How can i fix this problem?, also by the way could someone comment on my code and tell me if it seems good and professional/efficient because i am a beginner in C and would like someone else's opinion on my code.
How can I fix this problem.
You know the number of iterations you want to make once you have calculated the digit count. So instead of looping till you reach the value of x:
for (int j = 1; j <= x; j++){
use the digit counter instead:
for (int j = 1; j <= counter; j++) {
also by the way could someone comment on my code and tell me if it seems good and professional/efficient because i am a beginner in C and would like someone else's opinion on my code.
There's a number of things you can do to improve your code.
First and foremost, any piece of code should be properly indented and formatted. Right now your code has no indenting, which makes it more difficult to read and it just looks ugly in general. So, always indent your code properly. Use an IDE or a good text editor, it will help you.
Be consistent in your code style. If you are writing
if (some_cond) {
...
}
else
//do this
It is not consistent. Wrap the else in braces as well.
Always check the return value of a function you use, especially for scanf. It will save you from many bugs in the future.
if (scanf("%d", &x) == 1)
//...all OK...
else
// ...EOF or conversion failure...
exit(EXIT_FAILURE);
Your first for loop will iterate x times uselessly. You can stop when you know that you have hit 0:
for (int i = 1; i <= x; i++){ // Then counter variable is incremented by 1
b /= 10;
if (b == 0){
break;
}
counter += 1;
}
C has ++ operator. Use that instead of doing counter += 1
int D; you create this, but don't initialize it. Always initialize your variables as soon as possible
C has const qualifier keyword, which makes a value immutable. This makes your code more readable, as the reader can immediately tell that this value will not change. In your code, you can change ans variable and make it a const int because it never changes:
const int ans = x;
Use more descriptive names for your variables. ans, D don't tell me anything. Use proper names, so that the reader of your code can easily understand your code.
These are some of the things that in my opinion you should do and keep doing to improve your code and coding skills. I am sure there can be more things though. Keep your code readable and as simple as possible.
The condition in this loop
for (int i = 1; i <= x; i++){ // Then counter variable is incremented by 1
b /= 10;
if (b != 0){
counter += 1;
}
}
does not make sense because there will be numerous redundant iterations of the loop.
For example if x is equal to 153 that is contains only 3 digits the loop will iterate exactly 153 times.
Also additional increment of the variable counter after the loop
++counter;
makes the code logically inconsistent.
Instead of the loop you could write at least the following way
int counter = 0;
int b = x;
do
{
++counter;
} while ( b /= 10 );
This loop iterates exactly the number of times equal to the number of digits in a given number.
In this loop
for (int j = 1; j <= x; j++){
D = x % 10; //Shows remainder of number (last digit) when divided by 10
sum += pow(D, counter); //Raises Digit found by counter and adds to sum
printf("%d\n", sum);
x /= 10; // Divides user entered number by 10 to get rid of digit found
}
it seems you did not take into account that the variable x is decreased inside the body of the loop
x /= 10; // Divides user entered number by 10 to get rid of digit found
So the loop can interrupt its iterations too early. In any case the condition of the loop again does not make great sense the same way as the condition of the first loop and only adds a bug.
The type of used variables that store a given number should be unsigned integer type. Otherwise the user can enter a negative number.
You could write a separate function that checks whether a given number is an Armstrong number.
Here you are.
#include <stdio.h>
int is_armstrong( unsigned int x )
{
const unsigned int Base = 10;
size_t n = 0;
unsigned int tmp = x;
do
{
++n;
} while ( tmp /= Base );
unsigned int sum = 0;
tmp = x;
do
{
unsigned int digit = tmp % Base;
unsigned int power = digit;
for ( size_t i = 1; i < n; i++ ) power *= digit;
sum += power;
} while ( ( tmp /= Base ) != 0 && !( x < sum ) );
return tmp == 0 && x == sum;
}
int main(void)
{
unsigned int a[] =
{
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407,
1634, 8208, 9474, 54748, 92727, 93084, 548834
};
const size_t N = sizeof( a ) / sizeof( *a );
for ( size_t i = 0; i < N; i++ )
{
printf( "%u is %san Armstrong number.\n", a[i], is_armstrong( a[i] ) ? "": "not " );
}
return 0;
}
The program output is
0 is an Armstrong number.
1 is an Armstrong number.
2 is an Armstrong number.
3 is an Armstrong number.
4 is an Armstrong number.
5 is an Armstrong number.
6 is an Armstrong number.
7 is an Armstrong number.
8 is an Armstrong number.
9 is an Armstrong number.
153 is an Armstrong number.
370 is an Armstrong number.
371 is an Armstrong number.
407 is an Armstrong number.
1634 is an Armstrong number.
8208 is an Armstrong number.
9474 is an Armstrong number.
54748 is an Armstrong number.
92727 is an Armstrong number.
93084 is an Armstrong number.
548834 is an Armstrong number.
Please remove j++ from 2nd loop for (int j = 1; j <= x; j++)
I tried this:
void armstrong(int x)
{
// count digits
int counter = 0, temp = x, sum = 0;
while(temp != 0)
{
temp = temp/10;
++counter; // Note: pre increment faster
}
// printf("count %d\n",counter);
temp = x;
while(temp != 0)
{
sum += pow(temp % 10, counter);
temp = temp/10;
}
// printf("sum %d\n",sum);
if(x == sum)
{
printf("Armstrong\n");
}
else
{
printf("No Armstrong\n");
}
}
int main(){
armstrong(371);
armstrong(1634);
return 0;
}
Let's take this and add the ability to handle multiple numeric bases while we're at it. Why? BECAUSE WE CAN!!!! :-)
#include <stdio.h>
#include <math.h>
double log_base(int b, double n)
{
return log(n) / log((double)b);
}
int is_armstrong_number(int b, /* base */
int n)
{
int num_digits = trunc(log_base(b, (double)n)) + 1;
int sum = 0;
int remainder = n;
while(remainder > 0)
{
sum = sum + pow(remainder % b, num_digits);
remainder = (int) (remainder / b);
}
return sum == n;
}
int main()
{
printf("All the following are valid Armstrong numbers\n");
printf(" 407 base 10 - result = %d\n", is_armstrong_number(10, 407));
printf(" 0xEA1 base 16 - result = %d\n", is_armstrong_number(16, 0xEA1));
printf(" 371 base 10 - result = %d\n", is_armstrong_number(10, 371));
printf(" 1634 base 10 - result = %d\n", is_armstrong_number(10, 1634));
printf(" 0463 base 8 - result = %d\n", is_armstrong_number(8, 0463));
printf("All the following are NOT valid Armstrong numbers\n");
printf(" 123 base 10 - result = %d\n", is_armstrong_number(10, 123));
printf(" 0x2446 base 16 - result = %d\n", is_armstrong_number(16, 0x2446));
printf(" 022222 base 8 - result = %d\n", is_armstrong_number(8, 022222));
}
At the start of is_armstrong_number we compute the number of digits directly instead of looping through the number. We then loop through the digits of n in base b, summing up the value of the digit raised to the number of digits in the number, for the given numeric base. Once the remainder hits zero we know there are no more digits to compute and we return a flag indicating if the given number is an Armstrong number in the given base.

Finding prime factors in C

I am trying to generate all the prime factors of a number n. When I give it the number 126 it gives me 2, 3 and 7 but when I give it say 8 it gives me 2, 4 and 8. Any ideas as to what I am doing wrong?
int findPrime(unsigned long n)
{
int testDivisor, i;
i = 0;
testDivisor = 2;
while (testDivisor < n + 1)
{
if ((testDivisor * testDivisor) > n)
{
//If the test divisor squared is greater than the current n, then
//the current n is either 1 or prime. Save it if prime and return
}
if (((n % testDivisor) == 0))
{
prime[i] = testDivisor;
if (DEBUG == 1) printf("prime[%d] = %d\n", i, prime[i]);
i++;
n = n / testDivisor;
}
testDivisor++;
}
return i;
}
You are incrementing testDivisor even when you were able to divide n by it. Only increase it when it is not divisible anymore. This will result in 2,2,2, so you have to modify it a bit further so you do not store duplicates, but since this is a homework assignment I think you should figure that one out yourself :)
Is this based on an algorithm your professor told you to implement or is it your own heuristic? In case it helps, some known algorithms for prime factorization are the Quadratic Sieve and the General Number Field Sieve.
Right now, you aren't checking if any divisors you find are prime. As long as n % testDivisor == 0 you are counting testDivisor as a prime factor. Also, you are only dividing through by testDivisor once. You could fix this a number of ways, one of which would be to replace the statement if (((n % testDivisor) == 0)) with while (((n % testDivisor) == 0)).
Fixing this by adding the while loop also ensures that you won't get composite numbers as divisors, as if they still divide n, a smaller prime factor must have also divided n and the while loop for that prime factor wouldn't have left early.
Here is code to find the Prime Factor:
long GetPrimeFactors(long num, long *arrResult)
{
long count = 0;
long arr[MAX_SIZE];
long i = 0;
long idx = 0;
for(i = 2; i <= num; i++)
{
if(IsPrimeNumber(i) == true)
arr[count++] = i;
}
while(1)
{
if(IsPrimeNumber(num) == true)
{
arrResult[idx++] = num;
break;
}
for(i = count - 1; i >= 0; i--)
{
if( (num % arr[i]) == 0)
{
arrResult[idx++] = arr[i];
num = num / arr[i];
break;
}
}
}
return idx;
}
Reference: http://www.softwareandfinance.com/Turbo_C/Prime_Factor.html
You can use the quadratic sieve algorithm, which factors 170-bit integers in second and 220-bit integers in minute. There is a pure C implementation here that does not require GMP or an external library : https://github.com/michel-leonard/C-Quadratic-Sieve, it's able to provide you a list of the prime factors of N. Thank You.

Finding largest prime factor of a composite number in c

I am accepting a composite number as an input. I want to print all its factors and also the largest prime factor of that number. I have written the following code. It is working perfectly ok till the number 51. But if any number greater than 51 is inputted, wrong output is shown. how can I correct my code?
#include<stdio.h>
void main()
{
int i, j, b=2, c;
printf("\nEnter a composite number: ");
scanf("%d", &c);
printf("Factors: ");
for(i=1; i<=c/2; i++)
{
if(c%i==0)
{
printf("%d ", i);
for(j=1; j<=i; j++)
{
if(i%j > 0)
{
b = i;
}
if(b%3==0)
b = 3;
else if(b%2==0)
b = 2;
else if(b%5==0)
b = 5;
}
}
}
printf("%d\nLargest prime factor: %d\n", c, b);
}
This is a bit of a spoiler, so if you want to solve this yourself, don't read this yet :). I'll try to provide hints in order of succession, so you can read each hint in order, and if you need more hints, move to the next hint, etc.
Hint #1:
If divisor is a divisor of n, then n / divisor is also a divisor of n. For example, 100 / 2 = 50 with remainder 0, so 2 is a divisor of 100. But this also means that 50 is a divisor of 100.
Hint #2
Given Hint #1, what this means is that we can loop from i = 2 to i*i <= n when checking for prime factors. For example, if we are checking the number 100, then we only have to loop to 10 (10*10 is <= 100) because by using hint #1, we will get all the factors. That is:
100 / 2 = 50, so 2 and 50 are factors
100 / 5 = 20, so 5 and 20 are factors
100 / 10 = 10, so 10 is a factor
Hint #3
Since we only care about prime factors for n, it's sufficient to just find the first factor of n, call it divisor, and then we can recursively find the other factors for n / divisor. We can use a sieve approach and mark off the factors as we find them.
Hint #4
Sample solution in C:
bool factors[100000];
void getprimefactors(int n) {
// 0 and 1 are not prime
if (n == 0 || n == 1) return;
// find smallest number >= 2 that is a divisor of n (it will be a prime number)
int divisor = 0;
for(int i = 2; i*i <= n; ++i) {
if (n % i == 0) {
divisor = i;
break;
}
}
if (divisor == 0) {
// we didn't find a divisor, so n is prime
factors[n] = true;
return;
}
// we found a divisor
factors[divisor] = true;
getprimefactors(n / divisor);
}
int main() {
memset(factors,false,sizeof factors);
int f = 1234;
getprimefactors(f);
int largest;
printf("prime factors for %d:\n",f);
for(int i = 2; i <= f/2; ++i) {
if (factors[i]) {
printf("%d\n",i);
largest = i;
}
}
printf("largest prime factor is %d\n",largest);
return 0;
}
Output:
---------- Capture Output ----------
> "c:\windows\system32\cmd.exe" /c c:\temp\temp.exe
prime factors for 1234:
2
617
largest prime factor is 617
> Terminated with exit code 0.
I presume you're doing this to learn, so I hope you don't mind a hint.
I'd start by stepping through your algorithm on a number that fails. Does this show you where the error is?
You need to recode so that your code finds all the prime numbers of a given number, instead of just calculating for the prime numbers 2,3, and 5. In other words, your code can only work with the number you are calculating is a prime number or is a multiple of 2, 3, or 5. But 7, 11, 13, 17, 19 are also prime numbers--so your code should simply work by finding all factors of a particular number and return the largest factor that is not further divisible.
Really, this is very slow for all but the smallest numbers (below, say, 100,000). Try finding just the prime factors of the number:
#include <cmath>
void addfactor(int n) {
printf ("%d\n", n);
}
int main()
{
int d;
int s;
int c = 1234567;
while (!(c&1)) {
addfactor(2);
c >>= 1;
}
while (c%3 == 0) {
addfactor(3);
c /= 3;
}
s = (int)sqrt(c + 0.5);
for (d = 5; d <= s;) {
while (c % d == 0) {
addfactor(d);
c /= d;
s = (int)sqrt(c + 0.5);
}
d += 2;
while (c % d == 0) {
addfactor(d);
c /= d;
s = (int)sqrt(c + 0.5);
}
d += 4;
}
if (c > 1)
addfactor(c);
return 0;
}
where addfactor is some kind of macro that adds the factor to a list of prime factors. Once you have these, you can construct a list of all the factors of the number.
This is dramatically faster than the other code snippets posted here. For a random input like 10597959011, my code would take something like 2000 bit operations plus 1000 more to re-constitute the divisors, while the others would take billions of operations. It's the difference between 'instant' and a minute in that case.
Simplification to dcp's answer(in an iterative way):
#include <stdio.h>
void factorize_and_print(unsigned long number) {
unsigned long factor;
for(factor = 2; number > 1; factor++) {
while(number % factor == 0) {
number = number / factor;
printf("%lu\n",factor);
}
}
}
/* example main */
int main(int argc,char** argv) {
if(argc >= 2) {
long number = atol(argv[1]);
factorize_and_print(number);
} else {
printf("Usage: %s <number>%<number> is unsigned long", argv[0]);
}
}
Note: There is a number parsing bug here that is not getting the number in argv correctly.

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