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.

source ： Power button （LeetCode）
link ：https://leetcode-cn.com/problems/find-the-duplicate-number

Ring detection algorithm

Using two pointers , One of them moves twice as fast as the other

When we met , You know where the ring starts

Take the array value as a pointer to the array index （1-n）

int findDuplicate(int* a, int l){
    
    int x=a[0],y=a[0];
	while(1)
	{
    
		x=a[x];
		y=a[a[y]];
		if(x==y)break;
	}
    int xx=a[0];
	int yy=x;
	while(xx!=yy)
	{
    
		xx=a[xx];
		yy=a[yy];
	}
	return xx;
}