LeetCode 287: 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.
*/

namespace CsharpSolutions.Problems.LeetCode.Array.FindTheDuplicateNumber_287
{
    public class Solution
    {
        /// <summary>
        ///     Finds duplicate in an array of integers.
        ///     Uses Floyds Tortoise and Hare Algorithm.
        ///     Time complexity : O(n)
        ///     Space complexity : O(1)
        /// </summary>
        /// <param name="nums">An array of integers.</param>
        public int FindDuplicate(int[] nums)
        {
            var tortoise = nums[nums[0]];
            var hare = nums[nums[nums[0]]];

            while (tortoise != hare)
            {
                tortoise = nums[tortoise];
                hare = nums[nums[hare]];
            }

            hare = nums[0];

            while (tortoise != hare)
            {
                tortoise = nums[tortoise];
                hare = nums[hare];
            }

            return hare;
        }

        /// <summary>
        ///     Finds duplicate in an array of integers.
        ///     Uses HashSet to record previously seen integers.
        ///     Time complexity : O(n)
        ///     Space complexity : O(n)
        /// </summary>
        /// <param name="nums">An array of integers.</param>
        public int FindDuplicate2(int[] nums)
        {
            var seenIntegers = new System.Collections.Generic.HashSet<int>();

            foreach (var num in nums)
            {
                if (seenIntegers.Contains(num))
                    return num;
                seenIntegers.Add(num);
            }

            return -1;
        }

        /// <summary>
        ///     Finds duplicate in an array of integers.
        ///     Sorts the array first, then applies linear search.
        ///     Time complexity : O(nlgn)
        ///     Space complexity : If source is mutable, O(1) / Otherwise, O(n)
        /// </summary>
        /// <param name="nums">An array of integers.</param>
        public int FindDuplicate3(int[] nums)
        {
            System.Array.Sort(nums);

            for (var i = 1; i < nums.Length; i++)
                if (nums[i] == nums[i - 1])
                    return nums[i];

            return -1;
        }
    }
}