Find the Duplicate Number

Desicription

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.

Example 1:

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Input: [1,3,4,2,2]
Output: 2

Example 2:

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Input: [3,1,3,4,2]
Output: 3

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(n^2).
  4. There is only one duplicate number in the array, but it could be repeated more than once.

Solution

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class Solution {
public:
int findDuplicate(vector<int>& nums) {
if(nums.size() <= 1) {
return 0;
}
int slow = nums[0];
int first = nums[nums[0]];
while(slow != first) {
slow = nums[slow];
first = nums[nums[first]];
}
first = 0;
while(first != slow) {
slow = nums[slow];
first = nums[first];
}
return slow;
}
};