1

Code

Python3

def maxUncrossedLines(self, nums1: List[int], nums2: List[int]) -> int:
 
    def helper(n1, n2, i, j, memo):
        if (i, j) in memo: return memo[(i,j)]
 
        if i >= len(n1) or j >= len(n2):
            return 0
 
        result = 1 if n1[i] == n2[j] else 0
 
        if n1[i] == n2[j]:
            result += helper(n1, n2, i+1, j+1, memo)
        else:
            left = helper(n1, n2, i, j+1, memo)
            right = helper(n1, n2, i+1, j, memo)
            result += max(left,right)
 
        memo[(i, j)] = result
 
        return result
 
    memo = defaultdict(int)
 
    return helper(nums1, nums2, 0, 0, memo)

Big O Analysis

• Runtime

  The runtime complexity here is $O(N^2)$ after memoizing. Before memoizing it’s $O(2^N)$ since there are two functions calls for every call. After memoizing, since we store a pair (i, j).

• Memory

  The memory usage is $O(N)$ since we use the collections.defaultdict object to store memoized results.

— A

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