Longest Common Subsequence

Problem statement:

Given two strings, find the longest common subsequence (LCS).

Your code should return the length of LCS.

Have you met this question in a real interview?

Yes

Clarification

What's the definition of Longest Common Subsequence?

Example

For "ABCD" and "EDCA", the LCS is "A" (or "D", "C"), return 1.

For "ABCD" and "EACB", the LCS is "AC", return 2.

Solution:

This is a DP problem for two sequences. Such as 583. Delete Operation for Two Strings.

The key points is also dp[i][j] means the LCS of first i chars in A and first j char in B, and return dp[m][n]

class Solution {
public:
    /**
     * @param A, B: Two strings.
     * @return: The length of longest common subsequence of A and B.
     */
    int longestCommonSubsequence(string A, string B) {
        // write your code here
        int m = A.size();
        int n = B.size();
        vector<vector<int>> dp(m + 1, vector<int>(n + 1, 0));
        for (int i = 1; i <= m; i++) {
            for (int j = 1; j <= n; j++) {
                if (A[i - 1] == B[j - 1]) {
                    dp[i][j] = dp[i - 1][j - 1] + 1;
                } else {
                    dp[i][j] = max(dp[i - 1][j], dp[i][j - 1]);         
                }
            }
        }
        return dp[m][n];
    }
};