Question

I’m working on a solution to a variant of the subset sum problem, using the below code. The problem entails generating subsets of 11 ints from a larger set (superset) and check if it matches a specific value (endsum).

#include <stdio.h>
#include <stdlib.h>
#include <assert.h>

int endsum = 0, supersetsize = 0, done = 0;
int superset[] = {1,30,10,7,11,27,3,5,6,50,45,32,25,67,13,37,19,52,18,9};
int combo = 0;

int searchForPlayerInArray(int arr[], int player) {
    for (int i=0; i<11; i++) {
        if (arr[i] == player) {
            return 1;
        }
    }
    return 0;
}

int sumOfArray(int arr[]) {
    int res = 0;
    for (int i=0; i<11; i++) {
        res+=arr[i];
    }
    return res;
}

void printArray(int arr[], int arrSize) {
    for (int j=0; j<arrSize; j++) {
        printf("%2d ",arr[j]);
    }
    printf("= %d\n",endsum);
}

void permute(int subset[], int pos, int sspos) {
    if (done) { //when a correct solution has been found, stop recursion
        return;
    }
    if (sspos == supersetsize) { // out of possible additions
        return;
    }
    if (pos == 11) { //is the current subset 11 ints long?
        int res = sumOfArray(subset);
        combo++;
        if (res == endsum) { //if the sum of the array matches the wanted sum, print
            printArray(subset,11);
            done = 1;
        }
        return;
    }
    for (int i=sspos; i<supersetsize; i++) {
        //assert(pos < 11);
        //assert(i+1 <= supersetsize);
        subset[pos] = superset[i];
        permute(subset,pos+1,i+1);
    }
}

int main(void) {
    endsum = 110;
    supersetsize = 20;
    int *arr;
    arr = malloc(supersetsize*sizeof(int));
    int i;
    for (i=0; i<supersetsize; i++) {
        arr[i] = 0;
    }

    permute(arr,0,0);

    printf("Combinations: %d",combo);
    return 0;
}

Although this solution works for small supersets (<15) it is slow and inefficient because it generates every possible permutation instead of just the unique ones. How can I optimize it to generate only unique subsets?

Edit: Complete source code added by popular demand.

Answer 1

One way to only generate unique subsets is to add the elements from the superset in order, and use an additional argument to permute (eg. supersetPos) to indicate where you are in the superset. This generates sorted permutations which will be unique.

EDIT: Code that AFAIK runs correctly on your sample:

#include <stdio.h>

int superset[] = {
 1, 30, 10, 7, 11,
 27, 3, 5, 6, 50,
 45, 32, 25, 67, 13,
 37, 19, 52, 18, 9
};
int supersetsize = 20;
int endsum = 110;
int done = 0;

int sumOfArray(int array[]) {
  int sum = 0;
  for(int i = 0; i < 11; i++)
      sum += array[i];
  return sum;
}

void permute(int subset[], int pos, int sspos) {

    if (pos == 11) { //is the current subset 11 ints long?
        if (sumOfArray(subset) == endsum) { //if the sum of the array matches the wanted sum, print
            for (int j=0; j<11; j++) {
                printf("%d ",subset[j]);
            }
            printf("\n");
            done = 1;
        }
        return;
    }
    for (int i=sspos; i<supersetsize; i++) {
        subset[pos] = superset[i];
        permute(subset,pos+1,i+1);
        if (done) { //when a correct solution has been found, stop recursion
            return;
        }
    }

}
int main() {
  int subset[11] = {0};
  permute(subset, 0, 0);
}