Problem

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.

Solution

class Solution {    public int findDuplicate(int[] nums) {        int start = 0, end = nums.length-1;        while (start <= end) {            int mid = start + (end-start)/2;            if (count(nums, mid) <= mid) {                start = mid+1; //numbers no larger than mid <= mid, so mid is safe, search second half            } else end = mid-1; //numbers less than mid > mid, so there is duplicate in first half        }        return start; //when start > end,     }    private int count(int[] nums, int k) {        int count = 0;        for (int num: nums) {            if (num <= k) count++;        }        return count;    }}