leetcode：1143.最长公共子序列（动态规划）

链接：https://leetcode-cn.com/problems/longest-common-subsequence/
比较经典的DP问题。创建二维数组 $dp$， $dp[i][j]$表示 $text(0,i)$与 $text2(0,j)$的最长公共子序列。
转移方程为：
1. 当 $text1[i] == text2[j]$时， $dp[i+1][j+1] = dp[i][j]+1$
2. 当 $text1[i] != text2[j]$时， $dp[i+1][j+1] = max(dp[i][j+1],dp[i+1][j])$
java代码：

class Solution {public int longestCommonSubsequence(String text1, String text2) {int len1 = text1.length();int len2 = text2.length();int dp[][] = new int [len1+1][len2+1];for(int i = 0;i<len1;i++){for(int j = 0;j<len2;j++){if(text1.charAt(i) == text2.charAt(j))dp[i+1][j+1] = dp[i][j]+1;else dp[i+1][j+1] = Math.max(dp[i][j+1],dp[i+1][j]);}}return dp[len1][len2];}
}