# Kth Smallest Element - Amazon Top Interview Questions

### Problem Statement :

Given a list of unsorted integers nums, and an integer k, return the kth (0-indexed) smallest element in the list.

This should be done in \mathcal{O}(n)O(n) time on average.

Constraints

0 ≤ k < n ≤ 100,000 where n is the length of nums

Example 1

Input

nums = [5, 3, 8, 2, 0]
k = 2

Output

3

Explanation

When sorted the numbers are [0, 2, 3, 5, 8] and index 2's value is 3.

### Solution :

                        Solution in C++ :

int partition(vector<int>& nums, int start, int end) {
int pivot = nums[start], j = end;
for (int i = start + 1; i <= j;) {
if (nums[i] >= pivot)
swap(nums[i], nums[j--]);
else
i++;
}
swap(nums[start], nums[j]);
return j;
}

int solve(vector<int>& nums, int k) {
int l = 0, r = nums.size() - 1;
while (l < r) {
int m = partition(nums, l, r);
if (m == k)
return nums[m];
else if (m < k)
l = m + 1;
else
r = m - 1;
}
return nums[l];
}


                        Solution in Python :

class Solution:
def solve(self, nums, k):
hp = []
heapq.heapify(hp)
for num in nums:
heapq.heappush(hp, num)

while k >= 0:
num = heapq.heappop(hp)
k -= 1
return num


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