287. Find the Duplicate Number

Given an array of integers nums containing n + 1 integers where each integer is in the range [1, n] inclusive.

There is only one repeated number in nums, return this repeated number.

You must solve the problem without modifying the array nums and uses only constant extra space.

Example 1:

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

Example 2:

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

/*
TC: O(nlogn) Arrays.sort() is merge sort
SC: O(logn) Java 13's Arrays.sort() uses a dual-pivot quicksort, which uses log n additional space  
*/

class Solution {
    public int findDuplicate(int[] nums) {
        Arrays.sort(nums); // TC: O(nlog(n)) modified mergesort
        int len = nums.length;
        for (int i = 1; i < len; i++) {
            if (nums[i] == nums[i - 1]) {
                return nums[i];
            }
        }

        return len;
}

/*
TC: O(n)
SC: O(n) 
*/

import java.util.HashSet;

class Solution {
    public int findDuplicate(int[] nums) {
        HashSet<Integer> set = new HashSet<>();
        for(int i=0;i<nums.length;i++){ // O(n)
            if(set.contains(nums[i])) 
                return nums[i]; // contains O(1)
            else
                set.add(nums[i]); // add O(1)
        }
        return -1;
    }
}

/*
TC: O(n)
SC: O(1) 
Floyd Algorithm  
*/
class Solution {
    public int findDuplicate(int[] nums) {
        int slow = 0;
        int fast = 0;
        
        do {
            slow = nums[slow];
            fast = nums[nums[fast]];
        } while (slow != fast);

        slow = 0;
        while (slow != fast) {
            slow = nums[slow];
            fast = nums[fast];
        }
        
        return slow;
    }
}

ref: 142. Linked List Cycle II

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