HDU-4901 The Romantic Hero

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The Romantic Hero

Time Limit: 6000/3000 MS (Java/Others) Memory Limit: 131072/131072 K (Java/Others) Total Submission(s): 508 Accepted Submission(s): 191

Problem Description

There is an old country and the king fell in love with a devil. The devil always asks the king to do some crazy things. Although the king used to be wise and beloved by his people. Now he is just like a boy in love and can’t refuse any request from the devil. Also, this devil is looking like a very cute Loli.
You may wonder why this country has such an interesting tradition? It has a very long story, but I won't tell you :).
Let us continue, the party princess's knight win the algorithm contest. When the devil hears about that, she decided to take some action.
But before that, there is another party arose recently, the 'MengMengDa' party, everyone in this party feel everything is 'MengMengDa' and acts like a 'MengMengDa' guy.
While they are very pleased about that, it brings many people in this kingdom troubles. So they decided to stop them.
Our hero z*p come again, actually he is very good at Algorithm contest, so he invites the leader of the 'MengMengda' party xiaod*o to compete in an algorithm contest.
As z*p is both handsome and talkative, he has many girl friends to deal with, on the contest day, he find he has 3 dating to complete and have no time to compete, so he let you to solve the problems for him.
And the easiest problem in this contest is like that:
There is n number a_1,a_2,...,a_n on the line. You can choose two set S(a_s1,a_s2,..,a_sk) and T(a_t1,a_t2,...,a_tm). Each element in S should be at the left of every element in T.(si < tj for all i,j). S and T shouldn't be empty.
And what we want is the bitwise XOR of each element in S is equal to the bitwise AND of each element in T.
How many ways are there to choose such two sets? You should output the result modulo 10^9+7.

Input

The first line contains an integer T, denoting the number of the test cases. For each test case, the first line contains a integers n. The next line contains n integers a_1,a_2,...,a_n which are separated by a single space.
n<=10^3, 0 <= a_i <1024, T<=20.

Output

For each test case, output the result in one line.

Sample Input

2

3

1 2 3

4

1 2 3 3

Sample Output

1

4

题意：在一个给序列， a_1,a_2,...,a_n选出一个子集s和t但是所有的si,tj,下标i要小于j，对于所有的。 

a1[i][j],表示，选第i个数，前i位异或的值为j的有多少个。j每次都枚举从0~1024.

a0[i][j],不选第i个数，前i位异或的值为j的有多少个。j每次都枚举从0~1024.

同理b1和b0，b从好后面开始算起。

最后，结果是：a1[i][j]*b0[i][j]，就是前面选i的值为j的个数乘以后面不选i值为j的个数。

#include<iostream>
#include<cstdio>
#include<cstring>
#define inf 1000000007
using namespace std;
__int64 a1[1034][1034],b1[1034][1034];
__int64 a0[1034][1034],b0[1034][1034];
int main()
{
    int t,i,n,s[1034],j;
    scanf("%d",&t);
    while(t--)
    {
        memset(a1,0,sizeof(a1));
        memset(a0,0,sizeof(a0));
        memset(b1,0,sizeof(b1));
        memset(b0,0,sizeof(b0));
        memset(s,0,sizeof(s));
       scanf("%d",&n);
       for(i=1;i<=n;i++)
        {
            scanf("%d",&s[i]);
            a1[i][s[i]]=b1[i][s[i]]=1;
        }
        for(i=1;i<=n;i++)
        {
            for(j=0;j<=1024;j++)//所有可能的值。
            {
                a1[i][j^s[i]]+=(a1[i-1][j]+a0[i-1][j])%inf;
                 a0[i][j]=(a0[i-1][j]+a1[i-1][j])%inf;

            }
        }
        for(i=n;i>=1;i--)
        {
            for(j=0;j<=1024;j++)
            {

              b1[i][j&s[i]]+=(b1[i+1][j]+b0[i+1][j])%inf;
               b0[i][j]=(b0[i+1][j]+b1[i+1][j])%inf;
            }
        }
        __int64 ans=0;
          for(i=1;i<=n;i++)
        {
          for(j=0;j<=1024;j++)
            {
              ans = (ans+(a1[i][j]*b0[i][j])%inf)%inf;

            }
        }
       //ans=(ans+inf)%inf;
        printf("%I64d
",ans%inf);
    }
    return 0;
}
/*
2
3
1 2 3
4
1 2 3 3
*/