How do you solve Minimum Elements to Add to Form a Given Sum on LeetCode?

Minimum Elements to Add to Form a Given Sum (LeetCode #1785) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Understanding the relationship between the current sum and the goal is crucial.

What is the brute force solution for Minimum Elements to Add to Form a Given Sum?

The brute force approach for Minimum Elements to Add to Form a Given Sum is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute force approach, we can try to add elements one by one to reach the goal. This method checks all possible combinations of elements that can be added to see if we can achieve the desired sum. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Minimum Elements to Add to Form a Given Sum?

Minimum Elements to Add to Form a Given Sum uses the following concepts: Array, Greedy. The recommended patterns to study are: Greedy, Mathematical reasoning.

What are the interview tips for Minimum Elements to Add to Form a Given Sum?

Always clarify the constraints and properties of the input data. Think about edge cases, such as when the current sum is already equal to the goal. Practice explaining your thought process clearly as you work through the problem.

What are common mistakes when solving Minimum Elements to Add to Form a Given Sum?

Failing to account for the absolute value when calculating the difference. Not using the ceiling function correctly when determining the number of elements needed.

#1785

Minimum Elements to Add to Form a Given Sum

Medium

ArrayGreedyGreedyMathematical reasoning

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

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Intuition

Time O(n)Space O(1)

The optimal solution leverages the fact that we can add elements with absolute values up to the limit. By calculating how many such elements are needed to cover the difference to the goal, we can efficiently find the minimum number of additions required.

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Algorithm

3 steps

1Step 1: Calculate the current sum of the array.
2Step 2: Compute the difference between the current sum and the goal.
3Step 3: Calculate the minimum number of elements needed by using ceil(abs(difference) / limit).

solution.py10 lines

1# Full working Python code
2import math
3
4def minElements(nums, limit, goal):
5    current_sum = sum(nums)
6    difference = abs(goal - current_sum)
7    return math.ceil(difference / limit)
8
9# Example usage
10print(minElements([1, -1, 1], 3, -4))  # Output: 2

ℹ

Complexity note: This solution runs in linear time since we only need to iterate through the array once to compute the sum, making it much more efficient than the brute force approach.

1Understanding the relationship between the current sum and the goal is crucial.
2Using the properties of the limits allows for a more efficient solution.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.