Add KthElementFinder algorithm (#5836)

Author: Hardvan

DIRECTORY.md

@@ -174,6 +174,7 @@
               * [GenericHeap](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/GenericHeap.java)
               * [Heap](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/Heap.java)
               * [HeapElement](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/HeapElement.java)
+              * [KthElementFinder](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/KthElementFinder.java)
               * [LeftistHeap](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/LeftistHeap.java)
               * [MaxHeap](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/MaxHeap.java)
               * [MinHeap](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/MinHeap.java)
@@ -848,6 +849,7 @@
             * heaps
               * [FibonacciHeapTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/heaps/FibonacciHeapTest.java)
               * [GenericHeapTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/heaps/GenericHeapTest.java)
+              * [KthElementFinderTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/heaps/KthElementFinderTest.java)
               * [LeftistHeapTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/heaps/LeftistHeapTest.java)
               * [MinPriorityQueueTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/heaps/MinPriorityQueueTest.java)
             * lists

src/main/java/com/thealgorithms/datastructures/heaps/KthElementFinder.java

@@ -0,0 +1,60 @@
+
+package com.thealgorithms.datastructures.heaps;
+
+import java.util.PriorityQueue;
+
+/**
+ * This class provides methods to find the Kth largest or Kth smallest element
+ * in an array using heaps. It leverages a min-heap to find the Kth largest element
+ * and a max-heap to find the Kth smallest element efficiently.
+ *
+ * @author Hardvan
+ */
+public final class KthElementFinder {
+    private KthElementFinder() {
+    }
+
+    /**
+     * Finds the Kth largest element in the given array.
+     * Uses a min-heap of size K to track the largest K elements.
+     *
+     * Time Complexity: O(n * log(k)), where n is the size of the input array.
+     * Space Complexity: O(k), as we maintain a heap of size K.
+     *
+     * @param nums the input array of integers
+     * @param k the desired Kth position (1-indexed, i.e., 1 means the largest element)
+     * @return the Kth largest element in the array
+     */
+    public static int findKthLargest(int[] nums, int k) {
+        PriorityQueue<Integer> minHeap = new PriorityQueue<>(k);
+        for (int num : nums) {
+            minHeap.offer(num);
+            if (minHeap.size() > k) {
+                minHeap.poll();
+            }
+        }
+        return minHeap.peek();
+    }
+
+    /**
+     * Finds the Kth smallest element in the given array.
+     * Uses a max-heap of size K to track the smallest K elements.
+     *
+     * Time Complexity: O(n * log(k)), where n is the size of the input array.
+     * Space Complexity: O(k), as we maintain a heap of size K.
+     *
+     * @param nums the input array of integers
+     * @param k the desired Kth position (1-indexed, i.e., 1 means the smallest element)
+     * @return the Kth smallest element in the array
+     */
+    public static int findKthSmallest(int[] nums, int k) {
+        PriorityQueue<Integer> maxHeap = new PriorityQueue<>((a, b) -> b - a);
+        for (int num : nums) {
+            maxHeap.offer(num);
+            if (maxHeap.size() > k) {
+                maxHeap.poll();
+            }
+        }
+        return maxHeap.peek();
+    }
+}

src/test/java/com/thealgorithms/datastructures/heaps/KthElementFinderTest.java

@@ -0,0 +1,19 @@
+package com.thealgorithms.datastructures.heaps;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import org.junit.jupiter.api.Test;
+
+public class KthElementFinderTest {
+    @Test
+    public void testFindKthLargest() {
+        int[] nums = {3, 2, 1, 5, 6, 4};
+        assertEquals(5, KthElementFinder.findKthLargest(nums, 2));
+    }
+
+    @Test
+    public void testFindKthSmallest() {
+        int[] nums = {7, 10, 4, 3, 20, 15};
+        assertEquals(7, KthElementFinder.findKthSmallest(nums, 3));
+    }
+}