Introduction

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.

Problem Description

Given two integer arrays nums1 and nums2, return the maximum length of a subarray that appears in both arrays.

Constraints:

• 1 <= nums1.length, nums2.length <= 1000
• 0 <= nums1[i], nums2[i] <= 100

https://leetcode.com/problems/maximum-length-of-repeated-subarray/

Examples

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

Analysis

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.

Solution

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

Complexities

• Time: O(mn) – m, n: length of nums1 and nums2
• Space: O(mn)