数组和矩阵（1）——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.

Note:

You must not modify the array (assume the array is read only). //不能排序

You must use only constant, O(1) extra space. // 不能用哈希表

Your runtime complexity should be less than O(n²). //不能暴力求解

There is only one duplicate number in the array, but it could be repeated more than once.

https://segmentfault.com/a/1190000003817671#articleHeader4

考虑：

暴力求解，选择一个数，看有没有重复的；
哈希表
排序后遍历
二分法
设置快慢指针，映射找环法

 1 public class Solution {
 2     public int findDuplicate(int[] nums) { //映射找环
 3         int n = nums.length - 1;
 4         int pre = 0;
 5         int last = 0;
 6         do {
 7             pre = nums[pre];
 8             last = nums[nums[last]];
 9         } while(nums[pre] != nums[last]);
10         last = 0;
11         while(nums[pre] != nums[last]) {
12             pre = nums[pre];
13             last = nums[last];
14         }
15         return nums[last];
16     }
17 }