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Published on 2017-09-02 11:31 in 暂未分类 with qscqesze

# Codeforces Round #594 (Div. 1) A. Ivan the Fool and the Probability Theory 动态规划

## A. Ivan the Fool and the Probability Theory

Recently Ivan the Fool decided to become smarter and study the probability theory. He thinks that he understands the subject fairly well, and so he began to behave like he already got PhD in that area.

To prove his skills, Ivan decided to demonstrate his friends a concept of random picture. A picture is a field of 𝑛 rows and 𝑚 columns, where each cell is either black or white. Ivan calls the picture random if for every cell it has at most one adjacent cell of the same color. Two cells are considered adjacent if they share a side.

Ivan's brothers spent some time trying to explain that it's not how the randomness usually works. Trying to convince Ivan, they want to count the number of different random (according to Ivan) pictures. Two pictures are considered different if at least one cell on those two picture is colored differently. Since the number of such pictures may be quite large, print it modulo 109+7.

## Input

The only line contains two integers 𝑛 and 𝑚 (1≤𝑛,𝑚≤100000), the number of rows and the number of columns of the field.

## Output

Print one integer, the number of random pictures modulo 109+7.

input
2 3
output
8

## Note

The picture below shows all possible random pictures of size 2 by 3.

## 题解

dp就比较简单了，dp[i]表示第i个格子为黑色的方案数，dp[i]=dp[i-1]+dp[i-2]即可。

## 代码

#include<bits/stdc++.h>
using namespace std;
const int maxn = 100005;
const int mod = 1e9+7;
long long dp[maxn];
int n,m;
int main(){
dp[0]=1,dp[1]=1;
for(int i=2;i<maxn;i++){
dp[i]=(dp[i-1]+dp[i-2])%mod;
}
cin>>n>>m;
cout<<(dp[n]+dp[m]-1+mod)*2LL%mod<<endl;
}
posted @ 2019-11-12 14:41  qscqesze  阅读(151)  评论(0编辑  收藏