20. 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

Solution: (DP)

class Solution
{
public:
    int maxUncrossedLines(vector<int> &A, vector<int> &B)
    {

        int n = A.size();
        int m = B.size();
        vector<vector<int>> v(n + 1, vector<int>(m + 1, 0));

        for (int i = 1; i <= A.size(); i++)
        {
            for (int j = 1; j <= B.size(); j++)
            {
                if (A[i - 1] == B[j - 1])
                {

                    v[i][j] = 1+v[i - 1][j - 1];
                }
                else
                {
                    v[i][j] = max(v[i][j - 1], v[i - 1][j]);
                }
            }
        }

        return v[n][m];
    }
};

Time Complexity: O(nm) Space Complexity: O(nm)