LeetCode 287. Find the Duplicate Number

题意：

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.

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

思路： 二分+抽屉原理。

二分1~n, 如果nums中比mid小的数目大于mid，那么在左边， 否则在右边。

AC代码：

class Solution {
public:
    int findDuplicate(vector<int>& nums) {
        int n = nums.size()-1;
        int left = 1, right = n, mid = -1;
        while(left<=right)
        {
            mid = (left+right)/2;
            int count_litt = 0, count_eque = 0;
            for(int i=0; i<nums.size(); i++)
            {
                if (nums[i] == mid) count_eque++;
                if (nums[i] <= mid) count_litt++;
            }
            if(count_eque>1) return mid;
            if(count_litt>mid) right = mid-1;
            else left = mid+1;
        }
    }
};