10.Longest Common Subsequence

Given two strings text1 and text2, return the length of their longest common subsequence.

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. (eg, "ace" is a subsequence of "abcde" while "aec" is not). 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.

Soution : (DP)

class Solution
{
public:
    int longestCommonSubsequence(string text1, string text2)
    {
        int n = text1.length();
        int m = text2.length();

        vector<vector<int>> arr(n + 1, vector<int>(m + 1, 0));

        for (int i = 1; i <= n; i++)
        {

            for (int j = 1; j <= m; j++)
            {

                if (text1[i - 1] == text2[j - 1])
                {
                    arr[i][j] = arr[i - 1][j - 1] + 1;
                }
                else
                {
                    arr[i][j] = max(arr[i - 1][j], arr[i][j - 1]);
                }
            }
        }

        return arr[n][m];
    }
};