How to Move Zeros in an Array?

Moving zeros in an array is a common problem faced during coding interviews. This task usually involves rearranging the elements in an array so that all zeros are moved to the end while preserving the order of the non-zero elements. It might seem simple, but this problem can test your ability to write efficient code and handle edge cases.

Why is this Topic Important?

This topic is significant in technical interviews because it demonstrates a candidate's problem-solving skills, their understanding of array manipulation, and their ability to write clean and efficient code. It also reveals how a candidate handles edge cases and optimizes performance.

Example Interview Question

A typical interview question might be:

“Write a function that takes an array of integers and moves all the zeros to the end of the array without changing the order of the non-zero elements.”

Analyzing the Problem

Before jumping to the code, it’s vital to clarify the problem. Here are some points to consider:

1. Input: An array of integers which may contain zeros.
2. Output: The same array with zeros moved to the end.
3. Order Preservation: Non-zero numbers should maintain their original relative order in the final output.

Example Input and Output

Input: [0, 1, 0, 3, 12]

Output: [1, 3, 12, 0, 0]

Ensuring Edge Cases

Consider various scenarios:

• An array composed entirely of zeros: [0, 0, 0]
• An empty array: []
• An array with no zeros: [1, 2, 3]

Solution Approach

A straightforward approach to solve this problem is to use two pointers: one for iterating through the array and another to track the position of the last non-zero element.

Coding the Solution

Here’s how you might implement this in Python:

PythonCopy code
def move_zeros(arr):
    # Pointer for the position of the last non-zero element
    last_non_zero_index = 0

    # Loop through the array
    for i in range(len(arr)):
        # When a non-zero element is found, we swap it with the last non-zero element's position
        if arr[i] != 0:
            arr[last_non_zero_index], arr[i] = arr[i], arr[last_non_zero_index]
            last_non_zero_index += 1

    return arr

Code Explanation

1. Initialization: Start with last_non_zero_index pointing to the beginning.
2. Loop through the array: For every element:
   • If it is non-zero, swap it with the element at last_non_zero_index.
   • Increment last_non_zero_index.
3. Return the modified array.

Complexity Analysis

The time complexity of this solution is O(n), where n is the number of elements in the array. This is because we only pass through the array once. The space complexity is O(1) since we are not using any additional data structures that grow with input size.

Additional Interview Questions

1. “What would you do if the array could contain negative numbers?”

   A: The solution remains the same since the requirement is to only move zeros, regardless of whether numbers are positive or negative.

2. “Can you provide a solution without using extra space?”

   A: The provided solution already does not use any extra space, as it rearranges the elements in place.

3. “How would you handle a very large array?”

   A: The same approach works efficiently for large arrays. As long as the space complexity is O(1) and we maintain a time complexity of O(n), the algorithm will perform well.

This problem not only tests algorithmic skills but also encourages a candidate to communicate their thought process and handle technical discussions confidently.