Day 25 Uncrossed Lines.cpp

PROBLEM:



We write the integers of A and B (in the order they are given) on two separate horizontal lines.

Now, we may draw connecting lines: a straight line connecting two numbers A[i] and B[j] such that:

A[i] == B[j];
The line we draw does not intersect any other connecting (non-horizontal) line.
Note that a connecting lines cannot intersect even at the endpoints: each number can only belong to one connecting line.

Return the maximum number of connecting lines we can draw in this way.

 

Example 1:
Input: A = [1,4,2], B = [1,2,4]
Output: 2
Explanation: We can draw 2 uncrossed lines as in the diagram.
We cannot draw 3 uncrossed lines, because the line from A[1]=4 to B[2]=4 will intersect the line from A[2]=2 to B[1]=2.


Example 2:
Input: A = [2,5,1,2,5], B = [10,5,2,1,5,2]
Output: 3


Example 3:
Input: A = [1,3,7,1,7,5], B = [1,9,2,5,1]
Output: 2
 

Note:

1. 1 <= A.length <= 500
2. 1 <= B.length <= 500
3. 1 <= A[i], B[i] <= 2000




SOLUTION:



class Solution {
public:
    int maxUncrossedLines(vector<int>& A, vector<int>& B) {
        
        int i,j,n,m;
        n = A.size();
        m = B.size();
        
        vector<vector<int>> dp(n+1,vector<int>(m+1,0));
        
        for(i=1;i<=n;i++)
        {
            for(j=1;j<=m;j++)
            {
                if(A[i-1]==B[j-1])
                {
                    dp[i][j] = 1 + dp[i-1][j-1];
                }
                else
                    dp[i][j]=max(dp[i-1][j],dp[i][j-1]);
            }
        }
        
        return dp[n][m];
        
    }
};