Uncrossed Lines

Uncrossed Lines

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

 class Solution {

public:

    int maxUncrossedLines(vector<int>& A, vector<int>& B) {

      int n=A.size(),m=B.size();

        int dp[n+1][m+1];

        memset(dp,0,sizeof(dp));

        

        for(int i=1;i<=n;++i)

        {

            for(int j=1;j<=m;++j)

            {

                if(A[i-1]==B[j-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[n][m];

    }

};