Leetcode: Find the Duplicate Number

Difficulty: Hard

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.

Credits:
Special thanks to @jianchao.li.fighter for adding this problem and creating all test cases.

Subscribe to see which companies asked this question

Hide Tags

 Array Two Pointers Binary Search

Show Similar Problems

--------------------------------------------------------------------------

-------------------------------------------------------------------------

Binary search:

turn left or right based on the index instead of the data. See following procedure:

when m=1, we count the # of value in data who is <=m; if the count less than m, turn left, otherwise turn right. Returned value is L in index, not in data!

//////////////////////////////////////////////

//////codes

class Solution {

 public:

        int findDuplicate(vector<int>& nums) {

               int low = 1, high = nums.size() - 1;

               while (low <= high) {

                      int mid = low + (high - low) * 0.5;

                      int cnt = 0;

                      for (auto a : nums) {

                            if (a <= mid) ++cnt;

                      }

                      if (cnt <= mid) low = mid + 1;

                      else high = mid - 1;

               }

               return low;

        }

 };