Balancing the Scale

the main algorithm:

use a array to save the number of the combination(use the way of combination as flag) and multiply the i ans 1<<16-1^i to calculate the total number of this way

code:

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<vector>
#include<cstring>
using namespace std;
int num[16];
const int M = 12000;
const int N = (1<<16);
vector<int> sta[M];//connect the sum and combination, a certain sum reflect to many ways 
int cnt[N], x[16];
void init() {
	sort(num, num+16);
	for(int i=0; i<M; i++) sta[i].clear();
	memset(cnt, 0, sizeof(cnt));
}
bool judge(int s) {
	int count = 0;
	for(int i=0; i<16; i++) {
		if(s & 1<<i) x[count++] = num[i];
	}
	return count==4;
}

long long deal() {
	long long ans = 0;
	int t;
	for(int i=0; i<N; i++) {
		if(judge(i))
		do{//make sure there are four num 
			t = x[0]*4+x[1]*3+x[2]*2+x[3];
			for(int k=0; k<sta[t].size(); k++) {
				if((sta[t][k] & i) == 0) {//al long as them are not same
					cnt[sta[t][k]|i]++;//use the way as a flag
				}
			}
			sta[t].push_back(i);
		}while(next_permutation(x, x+4));

	}
	for(int i=0; i<N; i++) {
		ans += cnt[i]*cnt[i^(N-1)];
	}
	return ans/2;

}


int main() {
	int cas = 1;
	while(scanf("%d", &num[0]) == 1 && num[0]) {
		for(int i=1; i<16; i++) scanf("%d", &num[i]);
		init();
		printf("Case %d: %lld\n", cas++, deal());
	}
	return 0;
}