hdu 5119 Happy Matt Friends dp

Happy Matt Friends

Time Limit: 6000/6000 MS (Java/Others)    Memory Limit: 510000/510000 K (Java/Others)

Problem Description

Matt has N friends. They are playing a game together.

Each of Matt’s friends has a magic number. In the game, Matt selects some (could be zero) of his friends. If the xor (exclusive-or) sum of the selected friends’magic numbers is no less than M , Matt wins.

Matt wants to know the number of ways to win.

 

 

Input

The first line contains only one integer T , which indicates the number of test cases.

For each test case, the first line contains two integers N, M (1 ≤ N ≤ 40, 0 ≤ M ≤ 10⁶).

In the second line, there are N integers ki (0 ≤ k_i ≤ 10⁶), indicating the i-th friend’s magic number.

 

 

Output

For each test case, output a single line “Case #x: y”, where x is the case number (starting from 1) and y indicates the number of ways where Matt can win.

 

 

Sample Input

2 3 2 1 2 3 3 3 1 2 3

 

 

Sample Output

Case #1: 4 Case #2: 2

Hint

In the first sample, Matt can win by selecting: friend with number 1 and friend with number 2. The xor sum is 3. friend with number 1 and friend with number 3. The xor sum is 2. friend with number 2. The xor sum is 2. friend with number 3. The xor sum is 3. Hence, the answer is 4.

 

 

Source

2014ACM/ICPC亚洲区北京站-重现赛（感谢北师和上交）

题意：N个数，选异或和大于等于M的方案数；

思路：类似求背包方案总数；

#include<bits/stdc++.h>
using namespace std;
#define ll __int64
#define esp 1e-13
const int N=2e3+10,M=1e6+50000,inf=1e9+10,mod=1000000007;
ll dp[42][M];
int a[N];
void init()
{
    memset(dp,0,sizeof(dp));
    dp[0][0]=1;
}
int main()
{
    int x,y,i,z,t;
    int T,cas=1;
    scanf("%d",&T);
    while(T--)
    {
        init();
        scanf("%d%d",&x,&y);
        for(i=1;i<=x;i++)
        scanf("%d",&a[i]);
        for(i=1;i<=x;i++)
        {
            for(t=0;t<M;t++)
            dp[i][t^a[i]]+=dp[i-1][t],dp[i][t]+=dp[i-1][t];
        }
        ll ans=0;
        for(i=y;i<M;i++)
        ans+=dp[x][i];
        printf("Case #%d: %I64d\n",cas++,ans);
    }
    return 0;
}