25. Uncrossed Lines.cpp

/*

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

*/

class Solution {
public:
    int maxUncrossedLines(vector<int>& A, vector<int>& B) 
    {
        int n1 = A.size();
        int n2 = B.size();
        
        int dp[n1+1][n2+1];
        
        memset(dp,0,sizeof(dp));
        
        for(int i=1;i<=n1;i++)
        {
            for(int j=1;j<=n2;j++)
            {
                if(B[j-1]==A[i-1])
                {
                    dp[i][j]=dp[i-1][j-1]+1;
                }
                else
                {
                    dp[i][j]=max( dp[i-1][j], dp[i][j-1] );
                }
            }
        }
    return dp[n1][n2];
    }
};