Published: Sep 20, 2022
This problem can be solved by multiple approaches. A naive solution would be to create a character map and check subarray equality. However, the naive approach runs slow. If we look at the problem carefully, the comparison should be done at each index while extending the range. The next comparison is an extension of previous comparison. This means the dynamic programing is among multiple approaches.
Given two integer arrays
nums2, return the maximum length of a subarray that appears in both arrays.
1 <= nums1.length, nums2.length <= 1000
0 <= nums1[i], nums2[i] <= 100
Example 1 Input: nums1 = [1,2,3,2,1], nums2 = [3,2,1,4,7] Output: 3 Explanation: The repeated subarray with maximum length is [3,2,1].
Example 2 Input: nums1 = [0,0,0,0,0], nums2 = [0,0,0,0,0] Output: 5
The DP solution is the approach taken here. The 2 dimensional auxiliary array is used to save the state so far. If the array values are the same at index i of nums1 and j of nums2, extend the length by one. Then compare the maximum value. In the end, we get the answer.
class MaximumLengthOfRepeatedSubarray: def findLength(self, nums1: List[int], nums2: List[int]) -> int: m, n = len(nums1), len(nums2) memo = [[0 for _ in range(n + 1)] for _ in range(m + 1)] max_v = 0 for i in range(1, m + 1): for j in range(1, n + 1): if nums1[i - 1] == nums2[j - 1]: memo[i][j] = memo[i - 1][j - 1] + 1 max_v = max(max_v, memo[i][j]) return max_v
O(mn)– m, n: length of nums1 and nums2