Mastering the Move Zeroes Problem in Python – LeetCode 75 Explained

Move Zeroes is a classic array manipulation problem from the LeetCode 75 challenge list. It evaluates your grasp of in-place updates, the two-pointer approach, and efficient iteration techniques. While the objective—moving all zeroes to the end of the list—might appear straightforward, performing the operation in-place, without disrupting the order of non-zero elements, adds a layer of complexity.

In this blog post, we’ll break down the Move Zeroes problem in Python step-by-step. We’ll explain how the code works, outline the logic behind each operation, and help you strengthen your understanding of a frequently asked coding interview question.

Problem Statement

Given an integer array nums, move all 0‘s to the end of the array while maintaining the relative order of the non-zero elements.

Important Conditions:

• Modify the input array in-place.
• Don’t return a new array.
• Aim for minimal operations.

What does “Move Zeroes” mean?

• All non-zero elements must retain their original order.
• All zeroes must be moved to the end.
• The modification must be done without using extra space for another array.

Examples

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

Input:  [1, 0, 2, 0, 3]
Output: [1, 2, 3, 0, 0]

Python Solution – Step-by-Step Explanation

Let’s look at the optimal solution using the two-pointer technique and explain it in detail:

class Solution:
    def moveZeroes(self, nums: List[int]) -> None:
        """
        Do not return anything, modify nums in-place instead.
        """
        non_zero_index = 0

        for i in range(len(nums)):
            if nums[i] != 0:
                nums[non_zero_index], nums[i] = nums[i], nums[non_zero_index]
                non_zero_index += 1

        for i in range(non_zero_index, len(nums)):
            nums[i] = 0

Step 1: Initialize Pointer

non_zero_index = 0

• This pointer tracks the position where the next non-zero value should be placed.
• It also represents the boundary between processed non-zero values and the rest of the array.

Step 2: Traverse the Array and Swap

for i in range(len(nums)):
    if nums[i] != 0:
        nums[non_zero_index], nums[i] = nums[i], nums[non_zero_index]
        non_zero_index += 1

• Loop through each element.
• If you find a non-zero, swap it with the element at non_zero_index.
• Move the pointer forward to prepare for the next non-zero placement.
• This effectively pushes all non-zero elements to the beginning, preserving their order.

Step 3: Fill the Remaining Positions with Zeroes

for i in range(non_zero_index, len(nums)):
    nums[i] = 0

• Once all non-zero elements are at the beginning, fill the rest of the array with 0.
• This finalizes the in-place transformation.

Why This Solution Works

This solution is:

• ✅ Efficient: Only makes one full pass through the array.
• ✅ In-place: Doesn’t use any extra memory.
• ✅ Stable: Maintains the order of all non-zero elements.

It’s a textbook example of applying the two-pointer technique to solve array problems with optimal space and time efficiency.

Time and Space Complexity

Metric	Value
Time Complexity	O(n)
Space Complexity	O(1) – in-place

• The function scans the array twice at most—once for placing non-zeroes and once for appending zeroes.
• No extra space is used, which is critical for performance-sensitive tasks.

Edge Cases to Consider

Case	Output	Explanation
[0, 0, 0]	[0, 0, 0]	All elements are zero; nothing moves.
[1, 2, 3]	[1, 2, 3]	No zero present; original order maintained.
[0, 1]	[1, 0]	A simple case with one zero.
[4, 0, 5, 0, 6]	[4, 5, 6, 0, 0]	Mixed zero and non-zero elements.

Real-World Relevance

This problem is more than just an academic exercise. Here’s how the pattern shows up in practice:

• Data Cleaning: Removing or shifting invalid/missing values in data pipelines.
• Gaming Engines: Managing player states or scores where inactive entities (represented by 0) are shifted.
• Sparse Matrix Optimization: Moving non-zero values for efficient computation.
• Real-time Systems: Reducing memory writes by modifying data structures in-place.

Conclusion

The Move Zeroes problem in Python is a fundamental coding challenge that prepares you for a wide variety of real-world and interview scenarios. It helps you master in-place operations, optimal pointer movement, and efficient list processing.

By solving this, you strengthen your command over array manipulation and gain insights into writing memory-conscious, performance-optimized code. Whether you’re preparing for technical interviews or building high-performance apps, this problem—and its solution—should be part of your core toolkit.

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