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Questions and Answers
Two main measures for the efficiency of an algorithm are
Which of the following case does not exist in complexity theory
The time factor when determining the efficiency of an algorithm is measured by
The Knapsack problem where the objective function is to minimize the profit is ______
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What is the type of the algorithm used in solving the 8 Queens problem?
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Sorting is not possible by using which of the following methods?
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Choose the correct answer for the following statements: I. The theory of NP–completeness provides a method of obtaining a polynomial time for NP algorithms. II. All NP-complete problem are NP-Hard.
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The worst case time complexity of the nondeterministic dynamic knapsack algorithm is
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The upper bound on the time complexity of the nondeterministic sorting algorithm is
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Dijkstra’s algorithm bears some similarity to
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Study Notes
Algorithm Efficiency
- Two main measures for the efficiency of an algorithm are time and space complexity
- Time complexity is measured by counting the number of key operations
- Space complexity is measured by counting the maximum memory needed by the algorithm
Complexity Theory
- Cases that exist in complexity theory: best case, worst case, and average case
- There is no null case in complexity theory
Problem Solving Strategies
- Dynamic programming is used to solve the 0/1 Knapsack problem
- Backtracking is a strategy that stops execution when it finds a solution, otherwise starts the problem from the top
- Divide and Conquer is a strategy used in algorithms like Merge Sort
- Greedy algorithms are used to solve problems like the Knapsack problem and Huffman Coding
Sorting Algorithms
- Sorting is not possible using the deletion method
- Insertion, Selection, and Exchange are all methods of sorting
Graph Algorithms
- Dijkstra's algorithm bears some similarity to BFS and Prim's algorithm
- Breadth-First Search scans all incident nodes along with their children
- BFS is often used to find the shortest path in unweighted graphs
- DFS is often used to find the shortest path in weighted graphs
Asymptotic Notation
- Big O notation is used to measure the upper bound of an algorithm's time complexity
- Omega (Ω) notation is used to measure the lower bound of an algorithm's time complexity
- Theta (Θ) notation is used to measure the tight bound of an algorithm's time complexity
Algorithm Design Techniques
- Dynamic programming is used to find all pairs of shortest distances in a graph
- Divide and Conquer is used to solve problems like Merge Sort
- Greedy algorithms are used to solve problems like Huffman Coding
Tree Data Structures
- A Binary Search Tree (BST) is a tree where each node has a value greater than every value in its left subtree and less than every value in its right subtree
- A Heap is a complete binary tree where each node is at least as large as its children
- A Binary Tree is a tree where each node has at most two children
Huffman Coding
- Huffman Coding is a method of encoding characters using variable-length codes
- The optimal Huffman code is determined by the frequencies of the characters in the alphabet
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Description
Test your understanding of algorithms with these objective type questions on efficiency and time complexity measures. Evaluate your knowledge of algorithm design and analysis.
