38.最长公共子序列(题号：1143)

public class LCS {
    //动态规划
    public int longestCommonSubsequence(String text1, String text2) {
        int l1 = text1.length();
        int l2 = text2.length();

        //定义一个二位矩阵
        int[][] dp = new int[l1+1][l2+1];

        //遍历所有的状态,递推求解
        for (int i = 1; i <=l1; i++) {
            for (int j = 1;j<=l2;j++){
                //判断两个新增字符关系，进行状态转移
                if(text1.charAt(i-1)==text2.charAt(j-1)){
                    dp[i][j] = dp[i-1][j-1]+1;
                }else {
                    dp[i][j] = Math.max(dp[i-1][j],dp[i][j-1]);
                }
            }
        }
        return dp[l1][l2];
    }

    public static void main(String[] args) {
        String text1 = "abcde", text2 = "ace";
        LCS lcs = new LCS();
        System.out.println(lcs.longestCommonSubsequence(text1,text2));
    }
}