Add MedianFinder algorithm (#5837)

Author: Hardvan

DIRECTORY.md

@@ -177,6 +177,7 @@
               * [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)
+              * [MedianFinder](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/MedianFinder.java)
               * [MinHeap](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/MinHeap.java)
               * [MinPriorityQueue](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/heaps/MinPriorityQueue.java)
             * lists
@@ -851,6 +852,7 @@
               * [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)
+              * [MedianFinderTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/heaps/MedianFinderTest.java)
               * [MinPriorityQueueTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/heaps/MinPriorityQueueTest.java)
             * lists
               * [CircleLinkedListTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/lists/CircleLinkedListTest.java)

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

@@ -0,0 +1,59 @@
+package com.thealgorithms.datastructures.heaps;
+
+import java.util.PriorityQueue;
+
+/**
+ * This class maintains the median of a dynamically changing data stream using
+ * two heaps: a max-heap and a min-heap. The max-heap stores the smaller half
+ * of the numbers, and the min-heap stores the larger half.
+ * This data structure ensures that retrieving the median is efficient.
+ *
+ * Time Complexity:
+ * - Adding a number: O(log n) due to heap insertion.
+ * - Finding the median: O(1).
+ *
+ * Space Complexity: O(n), where n is the total number of elements added.
+ *
+ * @author Hardvan
+ */
+public final class MedianFinder {
+    MedianFinder() {
+    }
+
+    private PriorityQueue<Integer> minHeap = new PriorityQueue<>();
+    private PriorityQueue<Integer> maxHeap = new PriorityQueue<>((a, b) -> b - a);
+
+    /**
+     * Adds a new number to the data stream. The number is placed in the appropriate
+     * heap to maintain the balance between the two heaps.
+     *
+     * @param num the number to be added to the data stream
+     */
+    public void addNum(int num) {
+        if (maxHeap.isEmpty() || num <= maxHeap.peek()) {
+            maxHeap.offer(num);
+        } else {
+            minHeap.offer(num);
+        }
+
+        if (maxHeap.size() > minHeap.size() + 1) {
+            minHeap.offer(maxHeap.poll());
+        } else if (minHeap.size() > maxHeap.size()) {
+            maxHeap.offer(minHeap.poll());
+        }
+    }
+
+    /**
+     * Finds the median of the numbers added so far. If the total number of elements
+     * is even, the median is the average of the two middle elements. If odd, the
+     * median is the middle element from the max-heap.
+     *
+     * @return the median of the numbers in the data stream
+     */
+    public double findMedian() {
+        if (maxHeap.size() == minHeap.size()) {
+            return (maxHeap.peek() + minHeap.peek()) / 2.0;
+        }
+        return maxHeap.peek();
+    }
+}

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

@@ -0,0 +1,17 @@
+package com.thealgorithms.datastructures.heaps;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import org.junit.jupiter.api.Test;
+
+public class MedianFinderTest {
+    @Test
+    public void testMedianMaintenance() {
+        MedianFinder mf = new MedianFinder();
+        mf.addNum(1);
+        mf.addNum(2);
+        assertEquals(1.5, mf.findMedian());
+        mf.addNum(3);
+        assertEquals(2.0, mf.findMedian());
+    }
+}