Find the Duplicate Number

Problem

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.

Note:

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

Solution

Floyd's Circle Finding Algorithm: O(n) time

public class Solution {
    public int findDuplicate(int[] nums) {
        int slow = 0, fast = 0;
        do {
            slow = nums[slow];
            fast = nums[nums[fast]];
        } while (slow != fast);
        slow = 0;
        while (slow != fast) {
            slow = nums[slow];
            fast = nums[fast];
        }
        return slow;
    }
}

Analysis

Same algorithm we used in Linked List Cycle
The difference is that there is no next in the array
Instead, we use slow as slower index and fast as faster index