DP-最长公共子序列

思路:dp[i][j]的含义为str1[0..i]与str2[0..j]的最长公共子序列长度.

#include<iostream>
#include<string>
using namespace std;
const int maxn = 100;
int main()
{
    string str1,str2;
    cin>>str1;
    cin>>str2;
    int dp[maxn][maxn];
    for(int i = 0; i < str1.length(); i++)
    {
        if(dp[i - 1][0] == 1)
        {
            dp[i][0] = 1;
            continue;
        }
        if(str1[i] == str2[0])
        {
            dp[i][0] = 1;
        }
        else
            dp[i][0] = 0;
    }
    for(int j = 0; j < str2.length(); j++)
    {
        if(dp[0][j -1] == 1)
        {
            dp[0][j] = 1;
            continue;
        }
        if(str1[0] == str2[j])
        {
            dp[0][j] = 1;
        }
        else
            dp[0][j] = 0;
    }
    for(int i = 1; i < str1.length(); i++)
    {
        for(int j = 1; j < str2.length(); j++)
        {
            if(str1[i] == str2[j])
            dp[i][j] = max(max(dp[i -1][j],dp[i][j - 1]),dp[i-1][j-1]+1);
            else
            dp[i][j] = max(dp[i - 1][j],dp[i][j - 1]);
        }
    }
    cout<<dp[str1.length() - 1][str2.length() - 1]<<endl;
        return 0;
}