Design and Analysis of Algorithms
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Basics of Algorithms
DAA - Introduction
DAA - Analysis of Algorithms
DAA - Methodology of Analysis
Asymptotic Notations & Apriori Analysis
Time Complexity
Master’s Theorem
DAA - Space Complexities
Divide & Conquer
DAA - Divide & Conquer
DAA - Max-Min Problem
DAA - Merge Sort
DAA - Binary Search
Strassen’s Matrix Multiplication
Karatsuba Algorithm
Towers of Hanoi
Greedy Algorithms
DAA - Greedy Method
Travelling Salesman Problem
Prim's Minimal Spanning Tree
Kruskal’s Minimal Spanning Tree
Dijkstra’s Shortest Path Algorithm
Map Colouring Algorithm
DAA - Fractional Knapsack
DAA - Job Sequencing with Deadline
DAA - Optimal Merge Pattern
Dynamic Programming
DAA - Dynamic Programming
Matrix Chain Multiplication
Floyd Warshall Algorithm
DAA - 0-1 Knapsack
Longest Common Subsequence
Travelling Salesman Problem | Dynamic Programming
Randomized Algorithms
Randomized Algorithms
Randomized Quick Sort
Karger’s Minimum Cut
Fisher-Yates Shuffle
Approximation Algorithms
Approximation Algorithms
Vertex Cover Problem
Set Cover Problem
Travelling Salesperson Approximation Algorithm
Graph Theory
DAA - Spanning Tree
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DAA - Multistage Graph
Optimal Cost Binary Search Trees
Heap Algorithms
DAA - Binary Heap
DAA - Insert Method
DAA - Heapify Method
DAA - Extract Method
Sorting Techniques
DAA - Bubble Sort
DAA - Insertion Sort
DAA - Selection Sort
DAA - Shell Sort
DAA - Heap Sort
DAA - Bucket Sort
DAA - Counting Sort
DAA - Radix Sort
Searching Techniques
Searching Techniques Introduction
DAA - Linear Search
DAA - Binary Search
DAA - Interpolation Search
DAA - Jump Search
DAA - Exponential Search
DAA - Fibonacci Search
DAA - Sublist Search
Complexity Theory
Deterministic vs. Nondeterministic Computations
DAA - Max Cliques
DAA - Vertex Cover
DAA - P and NP Class
DAA - Cook’s Theorem
NP Hard & NP-Complete Classes
DAA - Hill Climbing Algorithm
DAA Useful Resources
DAA - Quick Guide
DAA - Useful Resources
DAA - Discussion

Design and Analysis Optimal Merge Pattern

Merge a set of sorted files of different length into a single sorted file. We need to find an optimal solution, where the resultant file will be generated in minimum time.

If the number of sorted files are given, there are many ways to merge them into a single sorted file. This merge can be performed pair wise. Hence, this type of merging is called as 2-way merge patterns.

As, different pairings require different amounts of time, in this strategy we want to determine an optimal way of merging many files together. At each step, two shortest sequences are merged.

To merge a p-record file and a q-record file requires possibly p + q record moves, the obvious choice being, merge the two smallest files together at each step.

Two-way merge patterns can be represented by binary merge trees. Let us consider a set of n sorted files {f₁, f₂, f₃, …, f_n}. Initially, each element of this is considered as a single node binary tree. To find this optimal solution, the following algorithm is used.

Algorithm: TREE (n)  
for i := 1 to n – 1 do  
   declare new node  
   node.leftchild := least (list) 
   node.rightchild := least (list) 
   node.weight) := ((node.leftchild).weight) + ((node.rightchild).weight)  
   insert (list, node);  
return least (list);

At the end of this algorithm, the weight of the root node represents the optimal cost.