Introduction

In this blog post, we will explore how to solve the LeetCode problem "1477" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

You are given an array of integers arr and an integer target. You have to find two non-overlapping sub-arrays of arr each with a sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum. Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays. Example 1: Input: arr = [3,2,2,4,3], target = 3 Output: 2 Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2. Example 2: Input: arr = [7,3,4,7], target = 7 Output: 2 Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2. Example 3: Input: arr = [4,3,2,6,2,3,4], target = 6 Output: -1 Explanation: We have only one sub-array of sum = 6. Constraints: 1 <= arr.length <= 105 1 <= arr[i] <= 1000 1 <= target <= 108

Explanation

Here's a breakdown of the solution, followed by the Python code:

• Sliding Window & Prefix Minimum: Use a sliding window to find all sub-arrays that sum to the target. Store the lengths of these sub-arrays. Employ a prefix minimum array to efficiently find the minimum length of a sub-array ending before a certain index.

• Iteration & Minimum Sum: Iterate through the sub-array lengths found, using the prefix minimum to find the minimum length of a non-overlapping sub-array preceding the current one. Update the overall minimum sum of lengths.

• Return Result: If no two such sub-arrays are found, return -1; otherwise, return the minimum sum of their lengths.

• Complexity:

  • Runtime: O(n)
  • Storage: O(n)

Code

    def minSumOfLengths(arr, target):
    n = len(arr)
    min_len = float('inf')
    lengths = []

    # Find all sub-arrays with sum equal to target
    for i in range(n):
        curr_sum = 0
        for j in range(i, n):
            curr_sum += arr[j]
            if curr_sum == target:
                lengths.append((i, j))
                break
            elif curr_sum > target:
                break

    # Calculate prefix minimum lengths
    prefix_min = [float('inf')] * n
    last_end = -1
    min_so_far = float('inf')
    for i in range(n):
        prefix_min[i] = min_so_far
        for start, end in lengths:
            if end == i:
                min_so_far = min(min_so_far, end - start + 1)

    ans = float('inf')
    for start, end in lengths:
        length = end - start + 1
        if start > 0:
            ans = min(ans, length + prefix_min[start - 1])

    if ans == float('inf'):
        return -1
    else:
        return ans