Single Number Leetcode Problem 136 [Python Solution]

Welcome to another Python coding tutorial!

In this guide, we will tackle the Single Number problem from LeetCode.

This problem falls under the category of Bit Manipulation and is classified as “Easy” on difficulty level.

The problem statement is as follows:

Problem Overview
Given a non-empty array of integers nums, every element appears twice except for one.

Our task is to find that single unique number.

Importantly, we must implement a solution with linear runtime complexity (O(n)) and use only constant extra space (O(1)).

You can access the problem directly on LeetCode by following this link.

Problem Overview

In this problem, we are given an array of integers, and our goal is to find the one number that appears only once in the array, while all other numbers appear twice.

We are required to solve this problem with linear runtime complexity and without using any additional memory.

Let’s start with an example:

Example 1:

Input: nums = [2,2,1]
Output: 1

In this example, the number 1 appears only once, while 2 appears twice.

Therefore, our task is to find and return the single number, which is 1. Now, let’s move on to understanding the constraints of the problem.

Understanding Constraints

It’s essential to understand the constraints provided in the problem, as they guide us in designing an efficient solution.

• The length of the input array nums is between 1 and 30,000.
• The values of elements in the array nums range from -30,000 to 30,000.
• Every element in the array appears twice, except for one element, which appears only once.

These constraints are crucial in ensuring that our solution is both efficient and can handle large inputs.

We need to devise an algorithm that works within these limits.

Efficient Python Code Solution

Now, let’s dive into the Python solution for this problem.

To find the single number, we will utilize the concept of bitwise XOR (exclusive OR).

Here’s the code solution:

def singleNumber(nums):
    result = 0
    for n in nums:
        result ^= n
    return result

In this code, we start with result initialized to 0. We iterate through each element n in the array nums and perform a bitwise XOR operation with result.

The key idea behind using XOR is that it cancels out duplicate elements and leaves us with the unique number.

We return the result at the end of the loop, which contains the single number.

How XOR Works

• If two bits are the same, the XOR operation results in 0.
• If two bits are different, the XOR operation results in 1. This property allows us to cancel out all the duplicates in the array efficiently.

The order in which the XOR operation is performed doesn’t matter, so we can use this approach to find the unique number.

Time and Space Complexity

Let’s analyze the time and space complexity of our solution:

Time Complexity: O(n)
– We iterate through the entire array of length n once, making this a linear time complexity solution.

Space Complexity: O(1)
– We use a constant amount of extra space, as we only need a single variable (result) to store the XOR result.

This satisfies the constraint of not using additional memory.

Reasoning Behind Our Approach

Our approach is based on the properties of the XOR operation.

We exploit the fact that XORing a value with itself results in 0, and XORing a value with 0 results in the same value.

By iteratively XORing all elements in the array, we effectively cancel out duplicates, leaving us with the unique number.

This approach is efficient and adheres to the problem’s constraints of linear runtime complexity and constant extra space.

Edge Cases a Valid Solution Must Consider

When implementing a solution for this problem, it’s essential to consider edge cases to ensure the correctness of our algorithm.

Here are some scenarios to keep in mind:

1. The array contains a single element.

   • In this case, the single element is the answer, as there are no duplicates.

2. The array contains only negative numbers.

   • The solution should work for negative numbers as well, as the XOR operation is bitwise and works for all integers.

3. The array contains a mix of positive and negative numbers.

   • The solution should handle arrays with both positive and negative integers.

The XOR operation is bitwise and is not affected by the sign of the numbers.

1. The array contains a large number of elements.
   • The algorithm should efficiently handle arrays with a large number of elements, as specified in the problem’s constraints.

Related Interview Questions By Company:

• Climbing Stairs LeetCode
• Verifying An Alien Dictionary LeetCode
• Diameter Of Binary Tree LeetCode

Related Interview Questions By Difficulty:

• Missing Number LeetCode
• Reverse Integer LeetCode
• Number Of 1 Bits LeetCode

Related Interview Questions By Category:

• Find The Duplicate Number LeetCode
• Simplify Path LeetCode
• Is Subsequence LeetCode

Conclusion

In this blog post, we tackled the Single Number problem from LeetCode, which involves finding a unique number in an array of integers.

We discussed the problem’s constraints, provided an efficient Python code solution using bitwise XOR, and explained the reasoning behind our approach.

We also emphasized the importance of considering edge cases to ensure a robust solution.

By following this approach, you can solve the Single Number problem with linear runtime complexity and constant extra space.

This solution is optimized for efficiency and satisfies the problem’s requirements.

If you found this guide helpful, please consider liking, subscribing, and sharing the content.

We encourage you to ask questions, make suggestions, and leave comments to foster a supportive learning community.

Happy coding!

Access the problem on LeetCode.