Introduction

In this blog post, we will explore how to solve the LeetCode problem "1191" 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

Given an integer array arr and an integer k, modify the array by repeating it k times. For example, if arr = [1, 2] and k = 3 then the modified array will be [1, 2, 1, 2, 1, 2]. Return the maximum sub-array sum in the modified array. Note that the length of the sub-array can be 0 and its sum in that case is 0. As the answer can be very large, return the answer modulo 109 + 7. Example 1: Input: arr = [1,2], k = 3 Output: 9 Example 2: Input: arr = [1,-2,1], k = 5 Output: 2 Example 3: Input: arr = [-1,-2], k = 7 Output: 0 Constraints: 1 <= arr.length <= 105 1 <= k <= 105 -104 <= arr[i] <= 104

Explanation

Here's a breakdown of the optimal solution for the maximum subarray sum after repeating an array k times:

• Kadane's Algorithm: Employ Kadane's Algorithm to find the maximum subarray sum within a single repetition of the array. This handles cases where the maximum subarray lies entirely within one repetition.
• Handle Multiple Repetitions: Consider the possibility that the maximum subarray spans multiple repetitions. If the sum of the original array is positive, multiplying this sum by (k-2) will contribute to an increased sum. Extend Kadane's to find the maximum suffix sum in the initial array and the maximum prefix sum in the final array.

• Modulo Arithmetic: Perform all calculations modulo 10⁹ + 7 to prevent integer overflow.

• Time & Space Complexity: O(N) time, where N is the length of the array, and O(1) space.

Code

    def k_concatenation_max_sum(arr, k):
    """
    Calculates the maximum subarray sum of the array concatenated k times, modulo 10^9 + 7.

    Args:
        arr: The input array of integers.
        k: The number of times to repeat the array.

    Returns:
        The maximum subarray sum modulo 10^9 + 7.
    """

    MOD = 10**9 + 7
    n = len(arr)

    # Calculate Kadane's algorithm for a single array
    max_so_far = 0
    current_max = 0
    for i in range(n):
        current_max = max(arr[i], current_max + arr[i])
        max_so_far = max(max_so_far, current_max)

    # Calculate the sum of the entire array
    arr_sum = sum(arr)

    # If k = 1, return the Kadane's result
    if k == 1:
        return max(0, max_so_far) % MOD

    # Calculate max prefix sum
    max_prefix_sum = 0
    current_prefix_sum = 0
    for i in range(n):
        current_prefix_sum += arr[i]
        max_prefix_sum = max(max_prefix_sum, current_prefix_sum)

    # Calculate max suffix sum
    max_suffix_sum = 0
    current_suffix_sum = 0
    for i in range(n - 1, -1, -1):
        current_suffix_sum += arr[i]
        max_suffix_sum = max(max_suffix_sum, current_suffix_sum)

    # Calculate the result
    if arr_sum > 0:
        result = (max_prefix_sum + max_suffix_sum + (k - 2) * arr_sum) % MOD
    else:
        result = (max_prefix_sum + max_suffix_sum) % MOD

    return max(0, max(max_so_far, result)) % MOD