Add KthElementFinder algorithm (#5836)

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();
+    }
+}