Detect the Only Duplicate in a List - Amazon Top Interview Questions

Problem Statement :

You are given a list nums of length n + 1 picked from the range 1, 2, ..., n. By the pigeonhole principle, there must be a duplicate. Find and return it. There is guaranteed to be exactly one duplicate.

Bonus: Can you do this in O(n) time and O(1) space?


n ≤ 10,000

Example 1

nums = [1, 2, 3, 1]


Example 2

nums = [4, 2, 1, 3, 2]


Solution :


                        Solution in C++ :

int solve(vector<int>& nums) {
    int tortoise = nums[0], hare = nums[0];

    do {
        tortoise = nums[tortoise];
        hare = nums[nums[hare]];
    } while (tortoise != hare);

    tortoise = nums[0];

    while (tortoise != hare) {
        tortoise = nums[tortoise];
        hare = nums[hare];

    return hare;

                        Solution in Java :

import java.util.*;

class Solution {
    public int solve(int[] nums) {
        int res = 0;
        for (int i = 0; i < nums.length; i++) res ^= i ^ nums[i];
        return res;

                        Solution in Python : 
class Solution:
    def solve(self, nums):
        q = sum(nums)
        n = len(nums)
        v = (n - 1) * (n) // 2
        return q - v

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