Question

I was trying to understand the code to generate all the subsets from one set. Here is the code

#include <stdio.h>

/* Applies the mask to a set like {1, 2, ..., n} and prints it */
void printv(int mask[], int n) {
    int i;
    printf("{ ");
    for (i = 0; i < n; ++i)
        if (mask[i])
            printf("%d ", i + 1); /*i+1 is part of the subset*/
    printf("\\b }\\n");
}

/* Generates the next mask*/
int next(int mask[], int n) {
    int i;
    for (i = 0; (i < n) && mask[i]; ++i)
        mask[i] = 0;

    if (i < n) {
        mask[i] = 1;
        return 1;
    }
    return 0;
}

int main(int argc, char *argv[]) {
    int n = 3;

    int mask[16]; /* Guess what this is */
    int i;
    for (i = 0; i < n; ++i)
        mask[i] = 0;

    /* Print the first set */
    printv(mask, n);

    /* Print all the others */
    while (next(mask, n))
        printv(mask, n);

    return 0;
}

I am not understand the logic behind this line for (i = 0; (i < n) && mask[i]; ++i) inside the next function. How is the next mask being generated here?

Code and algorithm looked here:
http://compprog.wordpress.com/2007/10/10/generating-subsets/

Answer 1

That is simply an implementation of counting in binary. The basic idea is to change the least-significant (last) zero to a one, and change all the ones after it to zeroes. The “next” mask will be “one more” than the previous if interpreted as a binary number.

Because the array is arranged with the one’s place first, it looks backwards from traditional numeric notation.

Instead of using an array of Boolean values, it could just as well use the bits in the binary representation of one number and the ++ operator.

int next(int &mask, int n) { // using C++ reference
    if ( mask == ( 1u << n ) - 1 ) return 0;
    ++ mask;
    return 1;
}

void printv(int mask, int n) {
    int i;
    printf("{ ");
    for (i = 0; i < n; ++i)
        if (mask & ( 1 << i ) )
            printf("%d ", i + 1); /*i+1 is part of the subset*/
    printf("\\b }\\n");
}

I’ve used a little C++ since you tagged the question as such, but the posted code is plain C.