JavaScript Puzzle: The Lost Number

Welcome to the world of JavaScript puzzles, where your coding prowess will be put to the test. In this challenge, you'll embark on a journey to find the lost number in an array. Get ready to showcase your problem-solving skills and JavaScript expertise.

Challenge:

You are given an array of integers containing numbers from 1 to N, where N is the length of the array. However, one number is missing from the sequence. Your task is to write a JavaScript function to find and return the missing number.

Function Signature:

function findMissingNumber(arr) {
    // Your code goes here
}

Example:

const inputArray = [1, 2, 4, 6, 3, 7, 8];
console.log(findMissingNumber(inputArray)); // Output: 5

Rules:

1. The input array will have at least one element and at most 10^5 elements.
2. The array will contain unique integers from 1 to N (inclusive), where N is the length of the array.
3. Only one number is missing from the sequence.

Feel free to explain your approach, optimizations, and any edge cases considered in your solution in the comments section above. Happy coding!

hints:

Here are some hints to help you solve the "JavaScript Puzzle: The Lost Number":

1. Mathematical Approach:

   • Think about the mathematical properties of a complete sequence of consecutive numbers.
   • Consider the sum of the first N natural numbers and the sum of the given array.

2. Summation Formula:

   • Recall the formula for the sum of the first N natural numbers: sum = N * (N + 1) / 2.
   • Calculate the expected sum for the given array length.

3. Difference Calculation:

   • Find the difference between the expected sum and the sum of the elements in the array.
   • The result will be the missing number.

4. Array Traversal:

   • Alternatively, you can iterate through the array and keep track of the cumulative sum.
   • The difference between the expected sum and the cumulative sum at the end will give you the missing number.

5. Edge Cases:

   • Consider edge cases, such as an array with only one element or an array with the maximum possible length.
   • Ensure your solution handles these cases gracefully.

Remember, the key is to think logically about the problem, leverage mathematical properties, and implement an efficient solution. Good luck!