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[LeetCode 287] Find the Duplicate Number

Problem

Given an array of integers nums containing n + 1 integers where each integer is in the range [1, n] inclusive.

There is only one repeated number in nums, return this repeated number.

You must solve the problem without modifying the array nums and uses only constant extra space.

Example 1:

Input: nums = [1,3,4,2,2]
Output: 2

Example 2:

Input: nums = [3,1,3,4,2]
Output: 3

Constraints:

  • 1 <= n <= 105
  • nums.length == n + 1
  • 1 <= nums[i] <= n
  • All the integers in nums appear only once except for precisely one integer which appears two or more times.

Follow up:

  • How can we prove that at least one duplicate number must exist in nums?
  • Can you solve the problem in linear runtime complexity?

Thoughts

  • Let's use slow & fast pointer to find the start of cycle

TypeScript

function findDuplicate(nums: number[]): number {
    let slow: number = 0, fast: number = 0;
    
    // find intersection of slow & fast
    while(true){
        slow = nums[slow]
        fast = nums[nums[fast]]
        if (slow === fast){
            break;
        }
    }
    
    // find the start of cycle
    let slow2: number = 0;
    while(true){
        slow = nums[slow]
        slow2 = nums[slow2]
        if(slow === slow2) {
            return slow;
        }
    }
};

Reference