Add OptimalFileMerging algorithm (#5805)

src/main/java/com/thealgorithms/greedyalgorithms/OptimalFileMerging.java

@@ -0,0 +1,52 @@
+package com.thealgorithms.greedyalgorithms;
+
+import java.util.PriorityQueue;
+
+/**
+ * Class to solve the Optimal File Merging Problem.
+ * The goal is to minimize the cost of merging files, where the cost of merging two files is the sum of their sizes.
+ * The cost of merging all files is the sum of the costs of merging each pair of files.
+ * Example:
+ * files = [4, 3, 2, 6]
+ * The minimum cost to merge all files is 29.
+ * Steps:
+ * 1. Merge files 2 and 3 (cost = 2 + 3 = 5). New files = [4, 5, 6]
+ * 2. Merge files 4 and 5 (cost = 4 + 5 = 9). New files = [6, 9]
+ * 3. Merge files 6 and 9 (cost = 6 + 9 = 15). New files = [15]
+ * Total cost = 5 + 9 + 15 = 29
+ *
+ * @author Hardvan
+ */
+public final class OptimalFileMerging {
+    private OptimalFileMerging() {
+    }
+
+    /**
+     * Calculates the minimum cost to merge all files.
+     * Steps:
+     * 1. Add all files to a min heap.
+     * 2. Remove the two smallest files from the heap, merge them, and add the result back to the heap.
+     * 3. Repeat step 2 until there is only one file left in the heap.
+     * 4. The total cost is the sum of all the costs of merging the files.
+     *
+     * @param files array of file sizes
+     * @return the minimum cost to merge the files
+     */
+    public static int minMergeCost(int[] files) {
+        PriorityQueue<Integer> minHeap = new PriorityQueue<>();
+        for (int file : files) {
+            minHeap.add(file);
+        }
+
+        int totalCost = 0;
+        while (minHeap.size() > 1) {
+            int first = minHeap.poll();
+            int second = minHeap.poll();
+            int cost = first + second;
+            totalCost += cost;
+
+            minHeap.add(cost);
+        }
+        return totalCost;
+    }
+}