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Day 4 - Challenge 1 - Find the Missing Number

Solving the Missing Number Problem using JavaScript

Have you ever encountered a situation where you had a list of numbers in a sequence, but one number seemed to be missing? Don't worry, it's a common problem that can be solved using a simple approach in JavaScript. In this blog post, we'll explore the "Missing Number" problem, understand its essence, and walk through a step-by-step solution using JavaScript.

Understanding the Problem:

Imagine you have an array of n-1 distinct numbers, taken from the range 1 to n. However, one number is missing from this sequence, and your task is to identify that missing number.

Approach:

We can approach this problem by exploiting the mathematical properties of the sum of consecutive natural numbers. The sum of the first n natural numbers can be calculated using the formula: sum = n * (n + 1) / 2. We will use this formula to find the sum of the entire sequence of numbers.

Here's the plan:

  1. Calculate the sum of the first n natural numbers.
  2. Iterate through the given array and calculate the sum of its elements.
  3. The difference between the sum of the entire sequence and the sum of the given array will be the missing number.

Let's implement this solution step by step in JavaScript:

Code Implementation:


function findMissingNumber(arr, n) {
  // Calculate the sum of the first n natural numbers
  const totalSum = (n * (n + 1)) / 2;

  // Calculate the sum of the elements in the given array
  const arraySum = arr.reduce((sum, num) => sum + num, 0);

  // The missing number is the difference between totalSum and arraySum
  const missingNumber = totalSum - arraySum;

  return missingNumber;
}

// Example usage
const sequence = [1, 2, 4, 5, 6]; // Missing number: 3
const n = sequence.length + 1; // Since there are n-1 elements in the sequence

const missingNumber = findMissingNumber(sequence, n);
console.log("The missing number is:", missingNumber);

Explanation:

In the above code, we define a function findMissingNumber that takes an array arr and the length of the original sequence n as parameters. We calculate the sum of the first n natural numbers and the sum of the given array elements. Subtracting the array sum from the total sum gives us the missing number.

 Demo:

Missing Number Problem

Given an array of n-1 distinct numbers taken from the range 1 to n, find the missing number.


Conclusion:

Solving the "Missing Number" problem is straightforward when you understand the underlying concept of the sum of natural numbers. By leveraging the mathematical formula and some basic JavaScript operations, we can efficiently find the missing number in a given sequence. This problem showcases the power of combining mathematics and programming to solve real-world challenges.

Now write the same program in your favorite language in comment section. 

Other Challenges: 

  1. Day 1 Challenges
  2. Day 2 Challenges
  3. Day 3 Challenges

 

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