动态规划两个数组dp问题系列一＞最长公共子序列

题目：

  

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解析： 

状态表示+状态转移方程： 

 

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初始化+填表顺序+返回值： 

 

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代码： 

class Solution {public int longestCommonSubsequence(String s1, String s2) {int m = s1.length(), n = s2.length();s1 = " "+ s1; s2 = " "+ s2;int[][] dp = new int[m + 1][n + 1];for(int i = 1; i <= m; i++)for(int j = 1; j <= n; j++){if(s1.charAt(i) == s2.charAt(j)) dp[i][j] = dp[i - 1][j - 1] + 1;elsedp[i][j] = Math.max(dp[i - 1][j], dp[i][j - 1]);}return dp[m][n];}
}