hdu 5119 dP

E - Happy Matt Friends

Time Limit:6000MS     Memory Limit:510000KB     64bit IO Format:%I64d & %I64u

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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 ≤ 10  ⁶). 

In the second line, there are N integers ki (0 ≤ k  _i ≤ 10  ⁶), 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. 
 

分析：首先看题发现并没有什么明显的规律，然后考虑dp

      dp[i][j]表示 前i个数里面异或值为j的方法数

      找到递推关系即可；
#include <iostream>
#include <stdio.h>
#include <string>
#include <string.h>
#include <algorithm>
using namespace std;
typedef long long ll;

const int maxn=1e6+100;
int n,m,test;
int a[maxn];
ll dp[44][maxn];

ll solve()
{
   memset(dp,0,sizeof(dp));
   dp[1][0]=dp[1][a[1]]=1;
   for(int i=2;i<=n;i++)
   {
      for(int j=0;j<maxn;j++)dp[i][j]+=dp[i-1][j];
      for(int j=0;j<maxn;j++)dp[i][a[i]^j]+=dp[i-1][j];
   }
   ll ans=0;
   for(int i=m;i<maxn;i++)
    ans+=dp[n][i];
   return ans;
}

int main()
{
   int T,test=1;
   scanf("%d",&T);
   while( T-- )
   {
       scanf("%d%d",&n,&m);
       for(int i=1;i<=n;i++)
         scanf("%d",&a[i]);

       ll ans=solve();
       printf("Case #%d: %lld\n",test++,ans);
   }
   return 0;
}