子集总和，甚至子集大小

Question

So, basically it's the same idea as the subset sum problem, but with one restriction: The found subset needs to have an even size .

For example:

numbers {4, 3, 3, 5, 1, 2, 7, 12}
find subset that sums up to 10
=> solution: {4, 3, 1, 2} (or {3, 7} but not {4, 3, 3} )

Is there a simple method to find such a subset? (The method should be "efficient", not just trying all possible subsets...)

Here is my code to find a "normal" subset:

    int n = 8;
    int m = 11;
    boolean[][] S = new boolean[n][m];
    int[] N = new int[] {4, 3, 3, 5, 1, 2, 7, 12};
    S[0][0] = true;
    S[0][S[0]] = true;

for(int i = 1; i < n; i++) {
        for(int j = 0; j < m; j++) {
            if(N[i] == j) {
                S[i][j] = true;
            } else if(j - N[i] >= 0) {
                S[i][j] = S[i-1][j] || S[i-1][j - N[i]];
            } else {
                S[i][j] = S[i-1][j];
            }
        }
    }

Answer 1

In your current code S[i][j] is true if you can make value j as a subset of numbers up to i.

Instead, compute S[i][j][k] is true if you can make value j as a subset of numbers up to i with the number of numbers used equal to k modulo 2.

In other words, k is either 0 or 1.

This will require around twice the computations of your existing solution.