Optimal File Merge Patterns
Given n number of sorted files, the task is to find the minimum computations done to reach the Optimal Merge Pattern.
When two or more sorted files are to be merged altogether to form a single file, the minimum computations are 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.
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If we have two files of sizes m and n, the total computation time will be m+n. Here, we use the greedy strategy by merging the two smallest size files among all the files present.
Examples:
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
Method 2:
Method 3:
Input: n = 6, size = {2, 3, 4, 5, 6, 7}
Output: 68
Explanation: Optimal way to combine these files
Input: n = 5, size = {5,10,20,30,30}
Output: 205Input: n = 5, size = {8,8,8,8,8}
Output: 96
Approach:
Node represents a file with a given size also given nodes are greater than 2
- Add all the nodes in a priority queue (Min Heap).{node.weight = file size}
- Initialize count = 0 // variable to store file computations.
- Repeat while (size of priority Queue is greater than 1)
- create a new node
- 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
- count += node.weight
- add this new node to priority queue;
- count is the final answer
Below is the implementation of the above approach:
C++
// C++ program to implement// Optimal File Merge Pattern#include <bits/stdc++.h>using namespace std;// Function to find minimum computationint 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 codeint 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;}// This code is contributed by jaigoyal1328 |
Java
// Java program to implement// Optimal File Merge Patternimport java.util.PriorityQueue;import java.util.Scanner;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)); }} |
Python3
# Python Program to implement# Optimal File Merge Patternclass Heap(): # Building own implementation of Min Heap def __init__(self): self.h = [] def parent(self, index): # Returns parent index for given index if index > 0: return (index - 1) // 2 def lchild(self, index): # Returns left child index for given index return (2 * index) + 1 def rchild(self, index): # Returns right child index for given index return (2 * index) + 2 def addItem(self, item): # Function to add an item to heap self.h.append(item) if len(self.h) == 1: # If heap has only one item no need to heapify return index = len(self.h) - 1 parent = self.parent(index) # Moves the item up if it is smaller than the parent while index > 0 and item < self.h[parent]: self.h[index], self.h[parent] = self.h[parent], self.h[parent] index = parent parent = self.parent(index) def deleteItem(self): # Function to add an item to heap length = len(self.h) self.h[0], self.h[length-1] = self.h[length-1], self.h[0] deleted = self.h.pop() # Since root will be violating heap property # Call moveDownHeapify() to restore heap property self.moveDownHeapify(0) return deleted def moveDownHeapify(self, index): # Function to make the items follow Heap property # Compares the value with the children and moves item down lc, rc = self.lchild(index), self.rchild(index) length, smallest = len(self.h), index if lc < length and self.h[lc] <= self.h[smallest]: smallest = lc if rc < length and self.h[rc] <= self.h[smallest]: smallest = rc if smallest != index: # Swaps the parent node with the smaller child self.h[smallest], self.h[index] = self.h[index], self.h[smallest] # Recursive call to compare next subtree self.moveDownHeapify(smallest) def increaseItem(self, index, value): # Increase the value of 'index' to 'value' if value <= self.h[index]: return self.h[index] = value self.moveDownHeapify(index)class OptimalMergePattern(): def __init__(self, n, items): self.n = n self.items = items self.heap = Heap() def optimalMerge(self): # Corner cases if list has no more than 1 item if self.n <= 0: return 0 if self.n == 1: return self.items[0] # Insert items into min heap for _ in self.items: self.heap.addItem(_) count = 0 while len(self.heap.h) != 1: tmp = self.heap.deleteItem() count += (tmp + self.heap.h[0]) self.heap.increaseItem(0, tmp + self.heap.h[0]) return count# Driver Codeif __name__ == '__main__': OMP = OptimalMergePattern(6, [2, 3, 4, 5, 6, 7]) ans = OMP.optimalMerge() print(ans)# This code is contributed by Rajat Gupta |
Minimum Computations = 68
