1658. Minimum Operations to Reduce X to Zero

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. Note that this modifies the array for future operations.

Return the minimum number of operations to reduce x to exactly 0 if it is possible, otherwise, return -1.

 

Example 1:

Input: nums = [1,1,4,2,3], x = 5
Output: 2
Explanation: The optimal solution is to remove the last two elements to reduce x to zero.

Example 2:

Input: nums = [5,6,7,8,9], x = 4
Output: -1

Example 3:

Input: nums = [3,2,20,1,1,3], x = 10
Output: 5
Explanation: The optimal solution is to remove the last three elements and the first two elements (5 operations in total) to reduce x to zero.

 

Constraints:

• 1 <= nums.length <= 105
• 1 <= nums[i] <= 104
• 1 <= x <= 109

 

Solutions

Solution: Prefix Sum

• Time complexity: O(n)
• Space complexity: O(n)

 

JavaScript

/**
 * @param {number[]} nums
 * @param {number} x
 * @return {number}
 */
const minOperations = function (nums, x) {
  const sum = nums.reduce((result, num) => result + num);
  const size = nums.length;

  if (sum === x) return size;
  const prefixSumMap = new Map([[0, -1]]);
  const target = sum - x;
  let currentSum = 0;
  let result = -1;

  for (let index = 0; index < size; index++) {
    currentSum += nums[index];
    prefixSumMap.set(currentSum, index);

    if (prefixSumMap.has(currentSum - target)) {
      const position = prefixSumMap.get(currentSum - target);

      result = Math.max(result, index - position);
    }
  }
  return result > -1 ? size - result : -1;
};