Longest Common Subsequence

 

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.

 

If there is no common subsequence, return 0.

 

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.

 

 

class Solution {
public:
    int longestCommonSubsequence(string text1, string text2) {
        int n=text1.size(),m=text2.size();
        vector<vector<int> > v(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])
                {
                    v[i][j]=v[i-1][j-1]+1;
                }else
                {
                    v[i][j]=max(v[i-1][j],v[i][j-1]);
                }
            }
        }
        return v[n][m];
    }
};