Minimum Operations to Reduce X to Zero

Problem Description

You are given an integer array nums and an integer x. In one operation, you can either remove the leftmost or the rightmost element from the array nums and subtract its value from x. Return the minimum number of operations to reduce x to exactly 0 if it is possible, otherwise, return -1.

Key Insights

• The problem can be thought of as finding a subarray whose sum is equal to total_sum - x, where total_sum is the sum of all elements in the array.
• If total_sum is less than x, it is impossible to reduce x to zero.
• We can use a sliding window approach to find the longest subarray that sums to total_sum - x.
• The minimum number of operations will then be len(nums) - length_of_longest_subarray.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve this problem, we can utilize a sliding window technique along with a hash map (or dictionary) to track the prefix sums. The idea is to find the longest contiguous subarray with a sum equal to total_sum - x. By maintaining two pointers, we can efficiently calculate the sum of elements in the current window and adjust the window size based on whether the current sum is greater than or less than the target.

Code Solutions