Leetcode 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.

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.

Solution 1: Use binary search for number count. Give a range, [lo,hi], if the duplicate number is within the range, counter>hi-lo. It is O(nlogn) complexity

 public class Solution {  
   public int findDuplicate(int[] nums) {  
     int n=nums.length-1;  
     int lo=1, hi=n;  
     while (lo<hi) {  
       int mid=lo+(hi-lo)/2;  
       if (count(nums,lo,mid)>mid-lo+1) hi=mid;  
       else lo=mid+1;  
     }  
     return lo;  
   }  
   private int count(int[] nums, int lo, int hi) {  
     int res=0;  
     for (int x: nums) {  
       if (x>=lo && x<=hi) res++;  
     }  
     return res;  
   }  
 }