. Day 7 - Challenge 3 - Finding Duplicate Numbers in Array Skip to main content

Day 7 - Challenge 3 - Finding Duplicate Numbers in Array

Solving the Duplicate Number Dilemma: Unearthing Hidden Duplicates in JavaScript

Introduction: 

Have you ever been faced with a perplexing puzzle involving an array of numbers, where one number seems to have duplicated itself? Fear not, for today we embark on a journey to decipher this mystery using the power of JavaScript! In this blog post, we'll unravel the enigma of finding a duplicate number in an array, utilizing a simple yet effective approach that leverages the characteristics of the given integers.

The Problem: 

Imagine you're presented with an array of n+1 integers, where each integer falls between the range of 1 and n. Hidden within this array is a single duplicate number, and your task is to unveil its identity.

The Solution: 

Fear not, for the solution is closer than you think. We'll use a technique known as the "tortoise and hare" algorithm, which is based on Floyd's cycle-finding algorithm. This approach is highly efficient with a time complexity of O(n) and a space complexity of O(1), making it a powerful tool in our arsenal.

function findDuplicate(nums) {
    let tortoise = nums[0];
    let hare = nums[0];
    
    // Phase 1: Detect the point of intersection within the cycle
    do {
        tortoise = nums[tortoise];
        hare = nums[nums[hare]];
    } while (tortoise !== hare);
    
    // Phase 2: Find the entrance to the cycle (duplicate number)
    tortoise = nums[0];
    while (tortoise !== hare) {
        tortoise = nums[tortoise];
        hare = nums[hare];
    }
    return hare;
}

// Example usage
const nums = [1, 3, 4, 2, 2];
const duplicate = findDuplicate(nums);
console.log(`The duplicate number is: ${duplicate}`);

Explanation:

  1. Phase 1: In this phase, we move the tortoise one step at a time and the hare two steps at a time. This way, they will eventually meet inside the cycle formed by the duplicate number and the indices it points to.

  2. Phase 2: After identifying the point of intersection in the cycle, we reset the tortoise to the beginning while keeping the hare at the intersection point. Moving both the tortoise and hare one step at a time will inevitably lead them to the entrance of the cycle, which is the duplicate number.

Demo:

Duplicate Number Finder

Enter an array of numbers separated by commas:

Conclusion: 

The journey to uncovering the duplicate number concealed within an array has come to an end. With the power of the "tortoise and hare" algorithm, we've navigated through the intricacies of cycle detection and emerged victorious in our quest. Armed with JavaScript, we've turned a complex problem into an elegant solution with an optimal runtime complexity.

Remember, the next time you encounter an array of numbers shrouded in mystery, you can confidently apply this algorithm to unearth the hidden duplicate and conquer the challenge! Happy coding!

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

Other Challenges:

  1. Day 5 Challenges
  2. Day 6 Challenges 
  3. Day 7 Challenges

 

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