Optimal File Merge Patterns | Algorithms - Computer Science Engineering (CSE) PDF Download

Optimal File Merge Patterns

The Optimal Merge Pattern refers to a strategy for merging multiple sorted files into a single file with the minimum computational effort. 

Concept

When you have several sorted files and you want to merge them into one single file, you can do this using the Optimal Merge Pattern to minimize the total computations needed.

Strategy

1. Merge in Pairs: Start by merging the smallest files first.
2. Greedy Approach: At each step, merge the two smallest available files. This ensures that the size of the files being merged remains as small as possible at each stage of the process.
3. Repeat: Continue merging pairs of files until all files are merged into a single file.

Example: Given 3 files with sizes 2, 3, 4 units. Find an 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 
Cost = 5 + 9 = 14

Method 2: 
Cost = 7 + 9 = 16

Method 3:

Cost = 6 + 9 = 15

Observations

From the observations made, it becomes clear that to minimize the computation cost effectively, it's essential to always prioritize merging the smallest possible files first and continuously reduce the number of files in consideration. This optimal strategy can be efficiently implemented using a min-heap (priority queue) data structure.

Code Implementation

// C++ program to implement

// Optimal File Merge Pattern

#include <bits/stdc++.h>

using namespace std; 

// Function to find minimum computation

int minComputation(int size, int files[])

{ 

    // Create a min heap

    priority_queue<int, vector<int>, greater<int> > pq; 

    for (int i = 0; i < size; i++) { 

        // Add sizes to priorityQueue

        pq.push(files[i]);

    }

    // Variable to count total Computation

    int count = 0; 

    while (pq.size() > 1) {

        // pop two smallest size element

        // from the min heap

        int first_smallest = pq.top();

        pq.pop();

        int second_smallest = pq.top();

        pq.pop(); 

        int temp = first_smallest + second_smallest; 

        // Add the current computations

        // with the previous one's

        count += temp;

        // Add new combined file size

        // to priority queue or min heap

        pq.push(temp);

    }

    return count;

} 

// Driver code

int main()

{

    // No of files

    int n = 6;

    // 6 files with their sizes

    int files[] = { 2, 3, 4, 5, 6, 7 };

    // Total no of computations

    // do be done final answer

    cout << "Minimum Computations = "

         << minComputation(n, files);

    return 0;

}

Output:
Minimum Computations = 68

Time Complexity: O(nlogn)
Auxiliary Space: O(n)