LightOJ1011---Marriage Ceremonies (状压dp)

You work in a company which organizes marriages. Marriages are not that easy to be made, so, the job is quite hard for you.

The job gets more difficult when people come here and give their bio-data with their preference about opposite gender. Some give priorities to family background, some give priorities to education, etc.

Now your company is in a danger and you want to save your company from this financial crisis by arranging as much marriages as possible. So, you collect N bio-data of men and N bio-data of women. After analyzing quite a lot you calculated the priority index of each pair of men and women.

Finally you want to arrange N marriage ceremonies, such that the total priority index is maximized. Remember that each man should be paired with a woman and only monogamous families should be formed.
Input

Input starts with an integer T (≤ 100), denoting the number of test cases.

Each case contains an integer N (1 ≤ n ≤ 16), denoting the number of men or women. Each of the next N lines will contain N integers each. The jth integer in the ith line denotes the priority index between the ith man and jth woman. All the integers will be positive and not greater than 10000.
Output

For each case, print the case number and the maximum possible priority index after all the marriages have been arranged.
Sample Input

Output for Sample Input

2

2

1 5

2 1

3

1 2 3

6 5 4

8 1 2

Case 1: 7

Case 2: 16

dp[i][j] 表示前i行状态为j时的最大值

/************************************************************************* > File Name: LightOJ1011.cpp > Author: ALex > Mail: [email protected] > Created Time: 2015年06月06日 星期六 10时52分57秒 ************************************************************************/

#include <functional>
#include <algorithm>
#include <iostream>
#include <fstream>
#include <cstring>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <queue>
#include <stack>
#include <map>
#include <bitset>
#include <set>
#include <vector>

using namespace std;

const double pi = acos(-1.0);
const int inf = 0x3f3f3f3f;
const double eps = 1e-15;
typedef long long LL;
typedef pair <int, int> PLL;

int dp[20][70000];
int mat[20][20];

int main() {
    int t, icase = 1;
    scanf("%d", &t);
    while (t--) {
        int n;
        scanf("%d", &n);
        for (int i = 1; i <= n; ++i) {
            for (int j = 1; j <= n; ++j) {
                scanf("%d", &mat[i][j]);
            }
        }
        memset(dp, 0, sizeof(dp));
        for (int i = 1; i <= n; ++i) {
            for (int j = 0; j < (1 << n); ++j) {
                int cnt = 0;
                for (int k = 0; k < n; ++k) {
                    if (j & (1 << k)) {
                        ++cnt;
                    }
                }
                if (cnt != i - 1) {
                    continue;
                }
                for (int k = 0; k < n; ++k) {
                    if (j & (1 << k)) {
                        continue;
                    }
                    dp[i][j | (1 << k)] = max(dp[i][j | (1 << k)], dp[i - 1][j] + mat[i][k + 1]);
                }
            }
        }
        printf("Case %d: %d\n", icase++, dp[n][(1 << n) - 1]);
    }
    return 0;
}