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:

You must not modify the array (assume the array is read only).
You must use only constant, O(1) extra space.
Your runtime complexity should be less than

O(n2)

.
There is only one duplicate number in the array, but it could be repeated more than once.

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

if (count <= mid)
{
left = mid;
}
else
{
right = mid;
}
}

int count = 0;
for (int i = 0; i < n; i++)
{
if (nums[i] == left)
{
count++;
}
}
if (count > 1)
{
return left;
}

return right;
}
};