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 <= A.length <= 500
1 <= B.length <= 500
1 <= A[i], B[i] <= 2000
class Solution:
    def maxUncrossedLines(self, A: List[int], B: List[int]) -> int:
        a = len(A)
        b = len(B)
        memo = {}
        for i in range(a):
            for j in range(b):
                if A[i] == B[j]:
                    memo[(i,j)] = memo.get((i-1, j-1), 0) + 1
                else:
                    memo[(i,j)] = max(memo.get((i-1,j), 0), memo.get((i,j-1), 0))
        return memo.get((a-1, b-1), 0)
                    

class Solution:
    def maxUncrossedLines(self, A: List[int], B: List[int]) -> int:
        a = len(A)
        b = len(B)
        memo = {}
        for i in range(a):
            for j in range(b):
                if A[i] == B[j]:
                    memo[(i,j)] = memo.get((i-1, j-1), 0) + 1
                else:
                    memo[(i,j)] = max(memo.get((i-1,j), 0), memo.get((i,j-1), 0))
        return memo.get((a-1, b-1), 0)
                    
