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.

来源：力扣（LeetCode）
链接：https://leetcode-cn.com/problems/find-the-duplicate-number

环检测算法

利用两个指针，其中一个移动比另一个快一倍

相遇时，就知道环开始的地方

把数组值当作指向数组索引的指针（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;
}