04-Longest-Common-Subsequence.md

Longest Common Subsequence

Problem Link

https://leetcode.com/problems/longest-common-subsequence/

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Pattern

• String DP

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Approach

Build a DP table for all prefixes of both strings and reuse overlapping subproblems.

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Time Complexity

O(mn)

Space Complexity

O(mn)

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Java Solution

class Solution {
    public int longestCommonSubsequence(String text1, String text2) {
        int m = text1.length(), n = text2.length();
        int[][] dp = new int[m + 1][n + 1];
        for (int i = 1; i <= m; i++) {
            for (int j = 1; j <= n; j++) {
                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[m][n];
    }
}