1143. Longest Common Subsequence

1. Description

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.

2. Example

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.

3. Constraints

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

4. Solutions

Dynamic Programming

m = long_text.size(), n = short_text.size()
Time complexity: O(mn)
Space complexity: O(n)

class Solution {
public:
    int longestCommonSubsequence(const string &text1, const string &text2) {
        const string &long_text = text1.size() > text2.size() ? text1 : text2;
        const string &short_text = text1.size() > text2.size() ? text2 : text1;

        const int m = long_text.size(), n = short_text.size();
        vector<int> max_length(n + 1, 0);
        for (int i = 0; i < m; ++i) {
            int prev_diagonal = 0;
            for (int j = 0; j < n; ++j) {
                int backup = max_length[j + 1];
                if (long_text[i] == short_text[j]) {
                    max_length[j + 1] = prev_diagonal + 1;
                } else {
                    max_length[j + 1] = max(max_length[j], max_length[j + 1]);
                }
                prev_diagonal = backup;
            }
        }

        return max_length.back();
    }
};