Find the Missing Number

(Coding Clutch Challenge Series 101) – Coding Challenge #1

Imagine you’re playing detective and trying to find a missing piece of a puzzle. That’s precisely what we do in the “Find the Missing Number” challenge. It’s a fun yet practical problem that helps build problem-solving skills. Let’s dive in!

Coding Clutch Challenge Series 101 – All Coding Challenges

Approach to Solving the Problem

Understanding the Problem Statement

You’re given an array of n unique integers ranging from 1 to n+1. One number is missing. Your job is to find that missing number efficiently.

Methods to Solve the Problem

1. Sum Formula: Use the mathematical formula for the sum of the first n natural numbers.
2. XOR Approach: Leverage the properties of XOR for a neat and efficient solution.
3. Iterative Search: Check each number systematically (less efficient).

Coding Clutch Challenge Series 101 – All Coding Challenges

Implementation in Different Languages

Python Solution

def find_missing_number(arr):
    n = len(arr) + 1
    total_sum = n * (n + 1) // 2
    return total_sum - sum(arr)

# Example
numbers = [1, 2, 4, 5, 6]
print("Missing number is:", find_missing_number(numbers))

Explanation:

• Calculate the total sum of numbers from 1 to n.
• Subtract the sum of the array from the total sum.

Output:
Missing number is: 3

C Solution

#include <stdio.h>

int findMissingNumber(int arr[], int n) {
    int total = (n + 1) * (n + 2) / 2;
    int sum = 0;
    for (int i = 0; i < n; i++) {
        sum += arr[i];
    }
    return total - sum;
}

int main() {
    int arr[] = {1, 2, 4, 5, 6};
    int n = sizeof(arr) / sizeof(arr[0]);
    printf("Missing number is: %d\n", findMissingNumber(arr, n));
    return 0;
}

Explanation:

• Use a loop to calculate the array sum.
• Find the difference between the total and array sums.

Output:
Missing number is: 3

C++ Solution

#include <iostream>
using namespace std;

int findMissingNumber(int arr[], int n) {
    int total = (n + 1) * (n + 2) / 2;
    int sum = 0;
    for (int i = 0; i < n; i++) {
        sum += arr[i];
    }
    return total - sum;
}

int main() {
    int arr[] = {1, 2, 4, 5, 6};
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << "Missing number is: " << findMissingNumber(arr, n) << endl;
    return 0;
}

Output:
Missing number is: 3

Coding Clutch Challenge Series 101 – All Coding Challenges

Java Solution

public class MissingNumber {
    public static int findMissingNumber(int[] arr, int n) {
        int total = (n + 1) * (n + 2) / 2;
        int sum = 0;
        for (int num : arr) {
            sum += num;
        }
        return total - sum;
    }

    public static void main(String[] args) {
        int[] arr = {1, 2, 4, 5, 6};
        System.out.println("Missing number is: " + findMissingNumber(arr, arr.length));
    }
}

Output:
Missing number is: 3

Coding Clutch Challenge Series 101 – All Coding Challenges

Optimizing the Code

Using the Sum Formula

The formula n(n+1)/2 reduces time complexity to O(n).

Using the XOR Approach

This method involves XORing all elements in the array and numbers from 1 to n+1.

Comparative Analysis of Solutions

Time Complexity

• Sum Formula: O(n)
• XOR Approach: O(n)

Space Complexity

• All methods: O(1)

Common Mistakes and Debugging Tips

1. Forgetting to include all numbers in the range.
2. Miscalculating the total sum.
3. Errors in loop indexing.

Coding Clutch Challenge Series 101 – All Coding Challenges

FAQs

1. Can this be solved with recursion?
   Yes, but it might not be as efficient due to stack overhead.
2. How does the XOR approach work?
   It cancels out all paired numbers, leaving only the missing number.
3. Is there a difference in runtime between the languages?
   No, the algorithm dictates the runtime, not the language.
4. What happens if the input array is unsorted?
   The solution still works as the order doesn’t matter.
5. Can we use libraries to simplify the task?
   Yes, libraries like NumPy in Python can help, but it’s good to understand the core logic.

Coding Clutch Challenge Series 101 – All Coding Challenges