Leetcode () 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 are only one duplicate number, find the duplicate one.

Note:

2. You must the Modify the array (assume the array was read only).
4. You must use only constant, O(1) Extra space.
6. Your runtime complexity should is less than O(n2) .
7. There is a duplicate number in the array, but it could was repeated more than once

   Class Solution {public:    int findduplicate (vector<int>& nums) {        int min=1,max=nums.size ();        while (Min<=max)        {            int mid= (MIN+MAX)/2;            int cnt=0;            for (int i=0;i<nums.size (); i++)                if (nums[i]<=mid)                    cnt++;            if (cnt>mid)                max=mid-1;            else                min=mid+1;        }        return min;    }};

   Binary search ideas, how 1 to N/2 there are duplicates, then 1 to n/2 number of numbers must be greater than N/2 this number itself. The following is the network of other people's ideas, can not understand.

   Class Solution {Public:int findduplicate (vector<int>& nums) {    int slow = 0;    int fast = 0;    int finder = 0;    while (true)    {        slow = Nums[slow];        Fast = Nums[nums[fast]];        if (slow = = fast) break            ;    }    while (true)    {        slow = Nums[slow];        Finder = Nums[finder];        if (slow = = Finder)            return slow;}    }

   If the first number is 0, does it have a dead loop? It seems to be a special case of special thinking.

Leetcode () Find the Duplicate number