1143. Longest Common Subsequence

Given two strings text1 and text2, return the length of their longest common subsequence. If there is no common subsequence, return 0.

A subsequence of a string is a new string generated from the original string with some characters (can be none) deleted without changing the relative order of the remaining characters.

For example, “ace” is a subsequence of “abcde”.
A common subsequence of two strings is a subsequence that is common to both strings.

动态规划，dp的长和宽分别为两个字符串的长度。
遍历dp字符串的长和宽。（注意在第一层遍历时先保存当前选择的字符可以提升速度。）
当两个字符串相同时，则可以从上一个状态+1。
注意状态转移方程的上一个状态应该是从对角线方向+1。
当两个字符串不同时，则继续保存之前的最大长度。

class Solution {
    public int longestCommonSubsequence(String text1, String text2) {
        int m = text1.length(), n = text2.length();
        int[][] dp = new int[m+1][n+1];
        char[] bin1 = text1.toCharArray();
        char[] bin2 = text2.toCharArray();

        for(int i = 1; i <= m; i++){
            int k = bin1[i-1];
            for(int j = 1; j <= n ; j++){
                if(k == bin2[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[m][n];
    }
}