#2357

Easy

auto_awesomeArray scanning plus hash lookup

LeetCode Problem Workspace

Make Array Zero by Subtracting Equal Amounts

Minimize operations to make all array elements zero by subtracting equal amounts in each operation.

array hash table greedy sorting heap priority queue

Problem Statement

You are given a non-negative integer array nums. In one operation, you subtract the same amount from each element of the array. Your task is to return the minimum number of operations required to make every element in the array equal to 0.

For example, with nums = [1,5,0,3,5], the minimal number of operations is 3. The process involves subtracting from all elements using the smallest non-zero values sequentially until all elements become zero.

Examples

Example 1

Input: nums = [1,5,0,3,5]

Output: 3

In the first operation, choose x = 1. Now, nums = [0,4,0,2,4]. In the second operation, choose x = 2. Now, nums = [0,2,0,0,2]. In the third operation, choose x = 2. Now, nums = [0,0,0,0,0].

Example 2

Input: nums = [0]

Output: 0

Each element in nums is already 0 so no operations are needed.

Constraints

1 <= nums.length <= 100
0 <= nums[i] <= 100

Solution Approach

Identify distinct non-zero elements

To minimize operations, first identify all distinct non-zero values in the array. The minimum number of operations corresponds to the number of unique non-zero values.

Sort or use a hash table for distinct values

By sorting or using a hash table, you can efficiently track the distinct non-zero elements in the array, ensuring that you subtract the smallest available values to minimize operations.

Repeat until all elements are zero

For each operation, subtract the smallest remaining non-zero number from all elements. Continue this process until the array is filled with zeroes.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time and space complexity depend on the approach used. Sorting the array has a time complexity of O(n log n), while using a hash table or set to track unique elements can be more efficient with O(n) time and space complexity.

What Interviewers Usually Probe

Look for efficient handling of unique elements in the array.
Test the ability to minimize operations by choosing the smallest non-zero value.
Evaluate how well the candidate can implement array manipulation using sorting or hash tables.

Common Pitfalls or Variants

Common pitfalls

Failing to track all unique non-zero values efficiently.
Not properly updating the array after each operation.
Misunderstanding the pattern of subtracting the smallest values first.

Follow-up variants

Handling arrays with many repeated elements efficiently.
Working with larger arrays or more complex constraints.
Exploring more optimized algorithms or approaches for minimal operation counting.

FAQ

What is the key to minimizing the number of operations in this problem?

The key is to repeatedly subtract the smallest non-zero value from all elements, ensuring that each operation reduces multiple values towards zero.

How does using a hash table or set help in this problem?

A hash table or set helps track the distinct non-zero elements, allowing you to efficiently determine the number of operations needed.

What is the time complexity of sorting the array in this problem?

Sorting the array takes O(n log n) time, which is one of the simplest ways to identify distinct non-zero elements.

Why should I always subtract the smallest non-zero value?

Subtracting the smallest non-zero value minimizes the number of operations, as it reduces the largest number of elements in each operation.

What happens if the array contains many repeated elements?

Even with many repeated elements, tracking unique non-zero values ensures that the number of operations remains minimal.

terminal

Solution

Solution 1: Hash Table or Array

We observe that in each operation, all identical nonzero elements in the array $\textit{nums}$ can be reduced to $0$. Therefore, we only need to count the number of distinct nonzero elements in $\textit{nums}$, which is the minimum number of operations required. To count the distinct nonzero elements, we can use a hash table or an array.

1

2

3

class Solution:
    def minimumOperations(self, nums: List[int]) -> int:
        return len({x for x in nums if x})

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