Optimal File Merge Patterns

Given n number of sorted files, the task is to find the minimum computations done to reach Optimal Merge Pattern.

When two or more sorted files are to be merged all together to form a single file, the minimum computations done to reach this file are known as Optimal Merge Pattern.

If more than 2 files need to be merged then it can be done in pairs. For example, if need to merge 4 files A, B, C, D. First Merge A with B to get X1, merge X1 with C to get X2, merge X2 with D to get X3 as the output file.



If we have two files of sizes m and n, the total computation time will be m+n. Here, we use greedy strategy by merging two smallest size files among all the files present.

Examples:
Given 3 files with size 2, 3, 4 units.Find optimal way to combine these files

Input: n = 3, size = {2, 3, 4}
Output: 14
Explanation: There are different ways to combine these files:
Method 1: Optimal method

Method 2:

Method 3:

Input: n = 6, size = {2, 3, 4, 5, 6, 7}
Output: 68
Explanation: Optimal way to combine these files

Approach:

Node represents a file with a given size also given nodes are greater than 2

  1. Add all the nodes in a priority queue (Min Heap).{node.weight = file size}
  2. Initialize count = 0 // variable to store file computations.
  3. Repeat while (size of priority Queue is greater than 1)
    1. create a new node
    2. new node = pq.poll().weight+pq.poll().weight;//pq denotes priority queue, remove 1st smallest and 2nd smallest element and add their weights to get a new node
    3. count += node.wight
    4. add this new node to priority queue;
  4. count is the final answer

Below is the implementation of the above approach:

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// Java program to implement
// Optimal File Merge Pattern
  
import java.util.Scanner;
import java.util.PriorityQueue;
  
public class OptimalMergePatterns {
  
    // Function to find minimum computation
    static int minComputation(int size, int files[])
    {
  
        // create a min heap
        PriorityQueue<Integer> pq
            = new PriorityQueue<>();
  
        for (int i = 0; i < size; i++) {
  
            // add sizes to priorityQueue
            pq.add(files[i]);
        }
  
        // variable to count total computations
        int count = 0;
  
        while (pq.size() > 1) {
  
            // pop two smallest size element
            // from the min heap
            int temp = pq.poll() + pq.poll();
  
            // add the current computations
            // with the previous one's
            count += temp;
  
            // add new combined file size
            // to priority queue or min heap
            pq.add(temp);
        }
  
        return count;
    }
  
    public static void main(String[] args)
    {
  
        // no of files
        int size = 6;
  
        // 6 files with their sizes
        int files[] = new int[] { 2, 3, 4, 5, 6, 7 };
  
        // total no of computations
        // do be done final answer
        System.out.println("Minimum Computations = "
                           + minComputation(size, files));
    }
}

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Output:

Minimum Computations = 68


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