Longest Common Subsequence

Problem

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.

 

Example 1:

Input: text1 = "abcde", text2 = "ace" 
Output: 3  
Explanation: The longest common subsequence is "ace" and its length is 3.

Example 2:

Input: text1 = "abc", text2 = "abc"
Output: 3
Explanation: The longest common subsequence is "abc" and its length is 3.

Example 3:

Input: text1 = "abc", text2 = "def"
Output: 0
Explanation: There is no such common subsequence, so the result is 0.

 

Constraints:

• 1 <= text1.length, text2.length <= 1000
• text1 and text2 consist of only lowercase English characters.

Solution

/**
 * @param {string} text1
 * @param {string} text2
 * @return {number}
 */
var longestCommonSubsequence = function(text1, text2) {
    let dp = Array(text1.length + 1)
        .fill(null)
        .map(() => Array(text2.length + 1).fill(0));

    for (let i = 1; i <= text1.length; i++) {
        for (let j = 1; j <= text2.length; j++) {
            if (text1[i - 1] === text2[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[text1.length][text2.length];
};

We will implement a DP solution. Let dp[i][j] be the length of the longest common subsequence between text1[0:i] and text2[0:j].

• For the base case:
  • If i = 0, then dp[0][j] = 0, since text1[0:0] is the empty string.
  • If j = 0, then dp[i][0] = 0, since text2[0:0] is the empty string.
• For the recursive case, there are three possible outcomes at any pair of indices: either include the character in both strings (ie. both characters match), include the character in text1, or include the character in text2.
  • If the characters match, take the longest subsequence without the current character and add 1.
  • Otherwise, take the longest subsequence of either including the character from text1 or including the character from text2.