问题描述：

Find the Duplicate Number

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Total Accepted: 11017  Total Submissions: 31520  Difficulty: Hard

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:

  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.

Credits:
Special thanks to @jianchao.li.fighter for adding this problem and creating all test cases.

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算法

数组也是一种映射，将index映射为对应元素。
分析题目，发现所有重复元素都是在1至N的整数，这些整数完全可以作为数组的索引，由此想到龟兔赛跑算法，寻找循环。
具体的龟兔赛跑算法，在维基百科有讲解。
https://en.wikipedia.org/wiki/Cycle_detection 


#!usr/bin/env python
#-*- coding:utf-8 -*-

class Solution(object):
    def findDuplicate(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        hare = nums[nums[0]]
        turtle = nums[0]
        while hare != turtle:
            hare = nums[nums[hare]]
            turtle = nums[turtle]
        
        turtle = 0
        while hare != turtle:
            turtle = nums[turtle]
            hare = nums[hare]
        return hare