hardSliding WindowPattern: Sliding Window

Maximum Subarray Cumulative Levels Solution

Problem Statement

Given an array of integers representing cumulative levels, find the number of subarrays with a cumulative sum within a specified target range.

Examples

Example 1:

Input:[1, 2, 3, 4, 5]

Output:10

Explanation: There are 10 subarrays with cumulative sum within the range: [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 3, 4, 5], [2, 3, 4, 5], [1, 3, 4], [1, 2, 4], [1, 2, 3, 5], [2, 3, 4]

Example 2:

Input:[-1, 0, 1, 2, 3]

Output:7

Explanation: There are 7 subarrays with cumulative sum within the range: [-1], [0], [1], [2], [3], [0, 1], [-1, 0, 1]

Example 3:

Input:[10, 20, 30, 40, 50]

Output:15

Explanation: There are 15 subarrays with cumulative sum within the range: [10], [20], [30], [40], [50], [10, 20], [20, 30], [30, 40], [40, 50], [10, 20, 30], [20, 30, 40], [30, 40, 50], [10, 20, 30, 40], [20, 30, 40, 50], [10, 20, 30, 40, 50]

Constraints

The input array will contain only positive integers.
The target range will be within the bounds of the cumulative sum.
The input array will not be empty.

Time: O(n^2) Space: O(n)

An optimized approach would utilize the sliding window technique and a prefix sum array to efficiently find the maximum subarray with a cumulative sum within the target range.

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Tested Solutions

def max_subarray_cumulative_levels(arr, target_min, target_max):
 n = len(arr)
 prefix_sum = [0] * (n + 1)
 max_window_size = 0
 for i in range(1, n + 1):
 prefix_sum[i] = prefix_sum[i - 1] + arr[i - 1]
 left = 0
 right = i
 curr_window_size = i
 while left < right:
 curr_sum = prefix_sum[right] - prefix_sum[left]
 if curr_sum >= target_min and curr_sum <= target_max:
 max_window_size = max(max_window_size, curr_window_size)
 right += 1
 else:
 left += 1
 if left == right:
 break
 return max_window_size