Minimum Elements to Add to Form a Given Sum

Problem Description

You are given an integer array nums and two integers limit and goal. The array nums has an interesting property that abs(nums[i]) <= limit. Return the minimum number of elements you need to add to make the sum of the array equal to goal. The array must maintain its property that abs(nums[i]) <= limit.

Key Insights

• Calculate the current sum of the array.
• Determine the difference between the current sum and the goal.
• The absolute value of this difference gives the total amount we need to add to the current sum.
• Each element we add can have a maximum absolute value of limit.
• The minimum number of elements required can be computed using the formula:
  • ceil(abs(difference) / limit), where difference is the difference between the current sum and the goal.

Space and Time Complexity

Time Complexity: O(n), where n is the length of the nums array (to calculate the sum). Space Complexity: O(1), since we are using a constant amount of space.

Solution

To solve this problem, we will follow these steps:

1. Compute the sum of the elements in the array.
2. Calculate the difference between the current sum and the goal.
3. Use the limit to determine how many elements are needed to bridge this difference.

The approach primarily uses basic arithmetic operations and requires no additional data structures beyond simple variables for tracking the sum and difference.

Code Solutions