Merge pull request #4246 from Ishitamukherjee2004/main

Kth Smallest problem from gfg is added

Author: ajay-dhangar

dsa-solutions/gfg-solutions/Easy problems/KthSmallest.md

@@ -0,0 +1,128 @@
+---
+id: kth-smallest
+title: Kth Smallest
+sidebar_label: Kth-Smallest
+tags:
+  - Sorting
+  - Algorithms
+  - Arrays
+  - Searching
+description: "This tutorial covers the solution to the Kth Smallest problem from the GeeksforGeeks."
+---
+## Problem Description
+
+Given an array `arr[]` and an integer `k` where `k` is smaller than the size of the array, the task is to find the `kth` smallest element in the given array. It is given that all array elements are distinct.
+
+Note:-  `l` and `r` denotes the starting and ending index of the array.
+
+## Examples
+
+**Example 1:**
+
+```
+Input:
+n = 6
+arr[] = 7 10 4 3 20 15
+k = 3
+l=0 r=5
+
+Output : 
+7
+
+Explanation :
+3rd smallest element in the given 
+array is 7.
+```
+
+**Example 2:**
+```
+Input:
+n = 5
+arr[] = 7 10 4 20 15
+k = 4 
+l=0 r=4
+
+Output : 
+15
+
+Explanation :
+4th smallest element in the given 
+array is 15.
+```
+
+### Your Task
+You don't have to read input or print anything. Your task is to complete the function kthSmallest() which takes the array arr[], integers l and r denoting the starting and ending index of the array and an integer k as input and returns the kth smallest element.
+
+Expected Time Complexity: O(n*log(n))
+
+Expected Auxiliary Space: O(1)
+
+## Constraints
+
+* `1 ≤ N ≤ 10^5`
+
+## Problem Explanation
+
+Given an array `arr[]` and an integer `k` where `k` is smaller than the size of the array, the task is to find the `kth` smallest element in the given array. It is given that all array elements are distinct.
+
+Note:-  `l` and `r` denotes the starting and ending index of the array.
+
+## Code Implementation
+
+### C++ Solution
+
+```cpp
+int kthSmallest(int arr[], int l, int r, int k) {
+  sort(arr + l, arr + r + 1);
+  return arr[l + k - 1];
+}
+
+
+```
+
+```java
+
+int kthSmallest(int arr[], int l, int r, int k) {
+  Arrays.sort(arr, l, r + 1);
+  return arr[l + k - 1];
+}
+
+
+```
+
+```python
+def kthSmallest(arr, l, r, k):
+  arr.sort()
+  return arr[l + k - 1]
+
+
+```
+
+```javascript
+function kthSmallest(arr, l, r, k) {
+  arr.sort((a, b) => a - b);
+  return arr[l + k - 1];
+}
+
+
+```
+
+## Solution Logic:
+
+1. sort(arr + l, arr + r + 1) (C++), arr.sort() (Python, JavaScript, TypeScript):
+    - Sort the array in ascending order.
+    - This step is necessary to ensure that the array is in a sorted state, allowing us to easily access the kth smallest element.
+2. return arr[l + k - 1]:
+    - Return the element at the index l + k - 1.
+    - l is the starting index of the array, k is the position of the element to be found, and -1 is to adjust for zero-based indexing.
+    - Since the array is sorted in ascending order, the element at this index will be the kth smallest element.
+
+
+
+## Time Complexity
+
+* The time complexity is $O(n*log(n))$ due to the sorting step, where n is the length of the array.
+
+## Space Complexity
+
+* The auxiliary space complexity is $O(1)$ due to the only extra memory used is for temporary variables while swapping two values in Array.