Algorithms and Data Structures

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Questions and Answers

Which of the following characteristics is NOT a fundamental requirement of an algorithm?

  • Effectiveness: Each step must be executable in a finite amount of time with finite resources.
  • Finiteness: The algorithm must terminate after a finite number of steps.
  • Definiteness: Each step must be precisely defined and unambiguous.
  • Optimality: The algorithm must produce the most efficient solution possible. (correct)

Which algorithm design technique involves breaking down a problem into smaller, overlapping subproblems, solving each subproblem only once, and storing the solutions to avoid redundant computations?

  • Divide and Conquer
  • Dynamic Programming (correct)
  • Greedy Algorithms
  • Backtracking

When analyzing the efficiency of an algorithm, Big O notation is used to describe its time complexity. What aspect of the algorithm's growth rate does Big O notation primarily focus on?

  • The upper bound of the growth rate (correct)
  • The lower bound of the growth rate
  • The exact running time for specific inputs
  • The average case running time

Which sorting algorithm has an average time complexity of $O(n \log n)$ and utilizes a divide-and-conquer approach?

<p>Merge Sort (B)</p> Signup and view all the answers

In the context of graph algorithms, what is the primary purpose of Dijkstra's algorithm?

<p>To find the shortest paths from a single source vertex to all other vertices in a weighted graph with non-negative edge weights. (A)</p> Signup and view all the answers

Which tree traversal algorithm visits the root node after traversing the left and right subtrees?

<p>Postorder Traversal (A)</p> Signup and view all the answers

Which string matching algorithm uses a precomputed table to avoid redundant comparisons and improve efficiency when searching for a pattern within a text?

<p>Knuth-Morris-Pratt (KMP) Algorithm (D)</p> Signup and view all the answers

In hashing, what is the primary purpose of collision resolution techniques?

<p>To handle the situation when two different keys map to the same index in the hash table. (C)</p> Signup and view all the answers

Which of the following probing techniques is used in open addressing for collision resolution?

<p>All of the above (D)</p> Signup and view all the answers

If a hash table uses the division method $h(k) = k \mod m$ as the hash function, where k is the key and m is the size of the hash table, what is a potential drawback of choosing a value for m that is a power of 2?

<p>It may not distribute keys uniformly across the table if the keys have certain patterns, leading to more collisions. (C)</p> Signup and view all the answers

Flashcards

Algorithms

Step-by-step procedures to solve a specific problem.

Finiteness

Terminate after a finite number of steps.

Definiteness

Each step is precisely defined and unambiguous.

Sequence Construct

Steps executed in order, one after the other.

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Selection Construct

Making decisions based on certain conditions.

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Iteration Construct

Repeating a block of code until a condition is met.

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Divide and Conquer

Breaking down a problem into smaller subproblems.

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Dynamic Programming

Solve each subproblem only once, storing solutions to avoid recomputation.

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Time Complexity

Measures how long an algorithm takes to run.

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Space Complexity

Measures the memory space required by an algorithm.

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