287. Find the Duplicate Number (Medium)

https://leetcode.com/problems/find-the-duplicate-number/

Given an array nums containing n + 1 integers where each integer is between 1 and n (inclusive), prove that at least one duplicate number must exist. Assume that there is only one duplicate number, find the duplicate one.

Example 1:

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

Example 2:

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

Note:

1. You must not modify the array (assume the array is read only).
2. You must use only constant, O(1) extra space.
3. Your runtime complexity should be less than O(n²).
4. There is only one duplicate number in the array, but it could be repeated more than once.

Solutions

class Solution {

    // This solution is too difficult to think of, ignore it.

    // This solution is similar with 142. Linked List Cycle II (Medium), see also
    // https://leetcode.com/problems/linked-list-cycle-ii/

    public int findDuplicate(int[] nums) {
        int fast = nums[0];
        int slow = nums[0];

        do {
            fast = nums[nums[fast]];
            slow = nums[slow];
        } while (fast != slow);

        slow = nums[0];
        while (fast != slow) {
            fast = nums[fast];
            slow = nums[slow];
        }

        return fast;
    }
}

Incorrect Solutions

References