Maximum Number of Non-Overlapping Subarrays With Sum Equals Target

Problem Description

Given an array nums and an integer target, return the maximum number of non-empty non-overlapping subarrays such that the sum of values in each subarray is equal to target.

Key Insights

• We need to find subarrays whose sums equal the target.
• The subarrays must be non-overlapping, meaning if one subarray is chosen, elements from it cannot be part of another subarray.
• Utilizing a hash map (or dictionary) can help track the cumulative sums and their indices to efficiently identify valid subarrays.
• A greedy approach can be applied to maximize the number of non-overlapping subarrays.

Space and Time Complexity

Time Complexity: O(n), where n is the length of the nums array, since we traverse the array once. Space Complexity: O(n), in the worst case, for storing the cumulative sums in the hash map.

Solution

To solve this problem, we can use a prefix sum approach combined with a hash map. The main idea is to keep track of the cumulative sum as we iterate through the array. When the cumulative sum minus the target is found in the hash map, it indicates that a subarray summing to the target has been found. We will also keep track of the last ending index of the previously found subarray to ensure non-overlapping.

1. Initialize a hash map to store the cumulative sums and their indices.
2. Traverse through the array while maintaining the cumulative sum.
3. For each cumulative sum, check if subtracting the target exists in the hash map.
4. If it does, it means we found a valid subarray. Check if it overlaps with the previously found subarray.
5. Update the count of valid subarrays accordingly.

Code Solutions