Single Number

Problem Statement

Given a non-empty array of integers where every element appears twice except for one, find that single element.

You need to solve this problem efficiently.

What to notice first

• Key insight 1 for Single Number
• Key insight 2 for solving this problem
• Key insight 3 specific to the approach

Examples

Input	Output	Explanation
Example 1	Result 1	Explanation for example 1
Example 2	Result 2	Explanation for example 2

Constraints

• Constraint 1 for Single Number
• Constraint 2
• Constraint 3

Real-World Applications

Where this pattern appears

• Database indexing and query optimization
• Buffer management in system memory
• Time-series data analysis and sliding windows
• Image pixel manipulation and batch processing

Complexity Comparison

Approach	Time	Space	Best When
Xor	O(n)	O(1)	When applicable
Hashmap	O(n)	O(1)	When applicable
Math	O(n)	O(1)	When applicable

Approach 1: Xor

★ Recommended

This approach provides an efficient solution for single number.

⏱ Time O(n) Single pass 💾 Space O(1) Minimal storage

Solution Code

Python

single_number_xor.py

from typing import List

def single_number_xor(nums: List[int]) -> int:
    """Find single number using XOR operation."""
    result = 0
    for num in nums:
        result ^= num
    return result

# Test cases
print(single_number_xor([2, 2, 1]))  # 1
print(single_number_xor([4, 1, 2, 1, 2]))  # 4

C++

single_number_xor.cpp

#include <vector>
using namespace std;

int singleNumberXor(vector<int>& nums) {
    int result = 0;
    for (int num : nums) {
        result ^= num;
    }
    return result;
}

int main() {
    vector<int> nums1 = {2, 2, 1};
    cout << singleNumberXor(nums1) << endl;  // 1
    return 0;
}

Java

single_number_xor.java

public class SingleNumberXor {
    public static int singleNumberXor(int[] nums) {
        int result = 0;
        for (int num : nums) {
            result ^= num;
        }
        return result;
    }

    public static void main(String[] args) {
        int[] nums = {2, 2, 1};
        System.out.println(singleNumberXor(nums));  // 1
    }
}

JavaScript

single_number_xor.js

function singleNumberXor(nums) {
    let result = 0;
    for (const num of nums) {
        result ^= num;
    }
    return result;
}

console.log(singleNumberXor([2, 2, 1]));  // 1
console.log(singleNumberXor([4, 1, 2, 1, 2]));  // 4

Rust

single_number_xor.rs

fn single_number_xor(nums: Vec<i32>) -> i32 {
    let mut result = 0;
    for num in nums {
        result ^= num;
    }
    result
}

fn main() {
    println!("{}", single_number_xor(vec![2, 2, 1]));  // 1
    println!("{}", single_number_xor(vec![4, 1, 2, 1, 2]));  // 4
}

Go

single_number_xor.go

package main

import "fmt"

func singleNumberXor(nums []int) int {
  result := 0
  for _, num := range nums {
    result ^= num
  }
  return result
}

func main() {
  fmt.Println(singleNumberXor([]int{2, 2, 1}))  // 1
  fmt.Println(singleNumberXor([]int{4, 1, 2, 1, 2}))  // 4
}

Approach 2: Hashmap

🎯 Interview Favourite

This approach provides an efficient solution for single number.

⏱ Time O(n) Single pass 💾 Space O(1) Minimal storage

Solution Code

Python

single_number_hashmap.py

# Python Solution
# Problem: single-number
# Approach: hashmap

# Implementation placeholder for single_number_hashmap
# This file is auto-generated and should contain the solution code.

def single_number_hashmap():
    pass

if __name__ == "__main__":
    pass

C++

single_number_hashmap.cpp

# C++ Solution
# Problem: single-number
# Approach: hashmap

# Implementation placeholder for single_number_hashmap
# This file is auto-generated and should contain the solution code.

def single_number_hashmap():
    pass

if __name__ == "__main__":
    pass

Java

single_number_hashmap.java

# Java Solution
# Problem: single-number
# Approach: hashmap

# Implementation placeholder for single_number_hashmap
# This file is auto-generated and should contain the solution code.

def single_number_hashmap():
    pass

if __name__ == "__main__":
    pass

JavaScript

single_number_hashmap.js

# JavaScript Solution
# Problem: single-number
# Approach: hashmap

# Implementation placeholder for single_number_hashmap
# This file is auto-generated and should contain the solution code.

def single_number_hashmap():
    pass

if __name__ == "__main__":
    pass

Rust

single_number_hashmap.rs

# Rust Solution
# Problem: single-number
# Approach: hashmap

# Implementation placeholder for single_number_hashmap
# This file is auto-generated and should contain the solution code.

def single_number_hashmap():
    pass

if __name__ == "__main__":
    pass

Go

single_number_hashmap.go

# Golang Solution
# Problem: single-number
# Approach: hashmap

# Implementation placeholder for single_number_hashmap
# This file is auto-generated and should contain the solution code.

def single_number_hashmap():
    pass

if __name__ == "__main__":
    pass

Approach 3: Math

✓ Simple

This approach provides an efficient solution for single number.

⏱ Time O(n) Single pass 💾 Space O(1) Minimal storage

Solution Code

Python

single_number_math.py

# Python Solution
# Problem: single-number
# Approach: math

# Implementation placeholder for single_number_math
# This file is auto-generated and should contain the solution code.

def single_number_math():
    pass

if __name__ == "__main__":
    pass

C++

single_number_math.cpp

# C++ Solution
# Problem: single-number
# Approach: math

# Implementation placeholder for single_number_math
# This file is auto-generated and should contain the solution code.

def single_number_math():
    pass

if __name__ == "__main__":
    pass

Java

single_number_math.java

# Java Solution
# Problem: single-number
# Approach: math

# Implementation placeholder for single_number_math
# This file is auto-generated and should contain the solution code.

def single_number_math():
    pass

if __name__ == "__main__":
    pass

JavaScript

single_number_math.js

# JavaScript Solution
# Problem: single-number
# Approach: math

# Implementation placeholder for single_number_math
# This file is auto-generated and should contain the solution code.

def single_number_math():
    pass

if __name__ == "__main__":
    pass

Rust

single_number_math.rs

# Rust Solution
# Problem: single-number
# Approach: math

# Implementation placeholder for single_number_math
# This file is auto-generated and should contain the solution code.

def single_number_math():
    pass

if __name__ == "__main__":
    pass

Go

single_number_math.go

# Golang Solution
# Problem: single-number
# Approach: math

# Implementation placeholder for single_number_math
# This file is auto-generated and should contain the solution code.

def single_number_math():
    pass

if __name__ == "__main__":
    pass

Related Problems

• Two Sum ↗ Easy #1
• Palindrome Number ↗ Easy #9

Interview Tips

Key trade-offs to discuss

• Time vs. space trade-offs between approaches
• Handling edge cases (empty inputs, single elements, duplicates)
• Optimization opportunities and when they matter
• Follow-up variations and constraint changes

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