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    [LeetCode 287] Find the Duplicate Number

    Published May 30, 2022 [  Array  ]

    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