**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? Constraints n ≤ 10,000 Example 1 Input nums = [1, 2, 3, 1] Output 1 Example 2 Input nums = [4, 2, 1, 3, 2] Output 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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