LeetCode287. Find the Duplicate Number

一、题目

Given an array of integers nums containing n + 1 integers where each integer is in the range [1, n] inclusive.

There is only one repeated number in nums, return this repeated number.

You must solve the problem without modifying the array nums and uses only constant extra space.

Example 1:

Input: nums = [1,3,4,2,2]
Output: 2
Example 2:

Input: nums = [3,1,3,4,2]
Output: 3

Constraints:

1 <= n <= 105
nums.length == n + 1
1 <= nums[i] <= n
All the integers in nums appear only once except for precisely one integer which appears two or more times.

Follow up:

How can we prove that at least one duplicate number must exist in nums?
Can you solve the problem in linear runtime complexity?

二、题解

class Solution {
public:
    int findDuplicate(vector<int>& nums) {
        if(nums.size() == 1) return -1;
        int slow = nums[0],fast = nums[nums[0]];
        while(fast != slow){
            slow = nums[slow];
            fast = nums[nums[fast]];
        }
        fast = 0;
        while(fast != slow){
            fast = nums[fast];
            slow = nums[slow];
        }
        return slow;
    }
};