Problem B

Cubes

Problem source: Bulgarian National Olympiad in Informatics 2003

Problem submitter: Ivaylo Riskov

Problem solution: Ivaylo Riskov, K M Hasan

题意：有12条边，每个边有指定的颜色，组成一个立方体，求种数

思路：参看cxlove GG的博客

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
typedef long long ll;
using namespace std;
const int maxn = 20;

int a[maxn], b[maxn];
ll c[maxn][maxn];

void init() {
	for (int i = 0; i <= 12; i++) {
		c[i][0] = c[i][i] = 1;
		for (int j = 1; j < i; j++)
			c[i][j] += c[i-1][j] + c[i-1][j-1];
	}
}

ll solve(int k) {
	ll sum = 1;
	int n = 0;
	for (int i = 0; i < 6; i++)
		if (b[i] % k == 0) {
			b[i] /= k;
			n += b[i]; 
		}
		else return 0;

	for (int i = 0; i < 6; i++) {
		sum *= c[n][b[i]];
		n -= b[i];
	}
	return sum;
}

ll still() {
	memcpy(b, a, sizeof(a));
	return solve(1);
}

ll point() {
	memcpy(b, a, sizeof(a));
	return 4*2*solve(3);
}

ll plane() {
	memcpy(b, a, sizeof(a));
	ll ans = 3*2*solve(4);
	memcpy(b, a, sizeof(a));
	return ans + 3*solve(2);
}

ll edge() {
	ll ans = 0;
	for (int i = 0; i < 6; i++)
		for (int j = 0; j < 6; j++) {
			memcpy(b, a, sizeof(b));
			b[i]--, b[j]--;
			if (b[i] < 0 || b[j] < 0)
				continue;
			ans += 6 * solve(2);
		}
	return ans;
}

ll polya() {
	ll ans = 0;
	ans += still();
	ans += point();
	ans += plane();
	ans += edge();
	return ans / 24;
}

int main() {
	init();
	int t, k;
	scanf("%d", &t);
	while (t--) {
		memset(a, 0, sizeof(a));
		for (int i = 0; i < 12; i++) {
			scanf("%d", &k);
			a[k-1]++;
		}
		printf("%lld\n", polya());
	}
	return 0;
}