Leetcode 287. Find the Duplicate number (Find duplicates)

Original title URL: https://leetcode.com/problems/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 D Uplicate number must exist. Assume that there are only one duplicate number, find the duplicate one.

Note:
You must the Modify the array (assume the array was read only). You must use only constant, O (1) Extra space. Your runtime complexity should is less than O (N2). There is a duplicate number in the array, but it could was repeated more than once.

Method One: Apply the pigeon cage principle to find the binary method.

Because you can place up to n different numbers in the range of 1~n, the array now has n+1 numbers, so there is at least one repetition.

For a number m in the 1~n range, the number of the array that is less than or equal to M is at least m, and when it is just M, there is no repetition between the 1~m. We separate to prove.

public class Solution {public
    int findduplicate (int[] nums) {
        int. = 1, high = nums.length-1;
        while (Low
 

Method Two: Cyclic chain detection method. This method I did not think out, found on the Internet, the use of technology and the circular link list detection method exactly the same.



public class Solution {public
    int findduplicate (int[] nums) {
        int slow = 0, fast = 0;
        Do {
            slow = Nums[slow];
            Fast = Nums[nums[fast]];
        } while (Nums[slow]! = Nums[fast]);
        int restart = 0;
        while (Nums[restart]! = Nums[slow]) {
            restart = Nums[restart];
            slow = Nums[slow];
        }
        return Nums[restart];
    }
}
Reference article:

http://bookshadow.com/weblog/2015/09/28/leetcode-find-duplicate-number/
https://segmentfault.com/a/1190000003817671