链接：https://www.nowcoder.com/acm/contest/139/A

来源：牛客网

Monotonic Matrix

 

时间限制：C/C++ 1秒，其他语言2秒

空间限制：C/C++ 524288K，其他语言1048576K

64bit IO Format: %lld

题目描述

 

Count the number of n x m matrices A satisfying the following condition modulo (109+7). * Ai, j ∈ {0, 1, 2} for all 1 ≤ i ≤ n, 1 ≤ j ≤ m. * Ai, j ≤ Ai + 1, j for all 1 ≤ i < n, 1 ≤ j ≤ m. * Ai, j ≤ Ai, j + 1 for all 1 ≤ i ≤ n, 1 ≤ j < m.

输入描述:

The input consists of several test cases and is terminated by end-of-file.Each test case contains two integers n and m.

输出描述:

For each test case, print an integer which denotes the result.

 

示例1

 

输入

复制

1 2

2 2

1000 1000

 

输出

复制

6

20

540949876

 

备注:

* 1 ≤ n, m ≤ 103* The number of test cases does not exceed 105.

题意：

求有多少n*m的矩阵满足：

1.每个数都是0或1或2

2.a(i,j)<=a(i+1,j)

3.a(i,j)<=a(i,j+1)

题解：

链接：

 

代码：

#include
     
      using namespace std;typedef long long ll;#define MAX 2005const ll mod=1e9+7;ll C[MAX][MAX];void c(){    for(int i=0;i
      
       >n>>m)    {      cout<<((C[n+m][n]*C[n+m][n])%mod-(C[n+m][n-1]*C[n+m][n+1])%mod+mod)%mod<
      
     

该题是一个定理来着，具体看这个链接：