# Generate Combinations

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Code generates all the combinations of n elements choosing k elements.
See this for definition.
See this for explanation.
``````
#include
```
/* Prints out a combination like {1, 2} */
void printc(int comb[], int k) {
printf("{");
int i;
for (i = 0; i < k; ++i)
printf("%d, ", comb[i] + 1);
printf("\b\b}\n");
}
/*
next_comb(int comb[], int k, int n)
Generates the next combination of n elements as k after comb
comb => the previous combination ( use (0, 1, 2, ..., k) for first)
k => the size of the subsets to generate
n => the size of the original set
Returns: 1 if a valid combination was found
0, otherwise
*/
int next_comb(int comb[], int k, int n) {
int i = k - 1;
++comb[i];
while ((i >= 0) && (comb[i] >= n - k + 1 + i)) {
--i;
++comb[i];
}
if (comb[0] > n - k) /* Combination (n-k, n-k+1, ..., n) reached */
return 0; /* No more combinations can be generated */
/* comb now looks like (..., x, n, n, n, ..., n).
Turn it into (..., x, x + 1, x + 2, ...) */
for (i = i + 1; i < k; ++i)
comb[i] = comb[i - 1] + 1;
return 1;
}
int main(int argc, char *argv[]) {
int n = 5; /* The size of the set; for {1, 2, 3, 4} it's 4 */
int k = 3; /* The size of the subsets; for {1, 2}, {1, 3}, ... it's 2 */
int comb[16]; /* comb[i] is the index of the i-th element in the
combination */
/* Setup comb for the initial combination */
int i;
for (i = 0; i < k; ++i)
comb[i] = i;
/* Print the first combination */
printc(comb, k);
/* Generate and print all the other combinations */
while (next_comb(comb, k, n))
printc(comb, k);
return 0;
}

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