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Algorithm Design Techniques

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Algorithm design techniques are general strategies, like divide and conquer, greedy choice and dynamic programming, for building efficient solutions. Questions ask you to identify the paradigm behind merge sort, binary search or Huffman coding, and to explain the properties each relies on: optimal substructure, overlapping subproblems and the greedy-choice property, sometimes justified through matroid theory. Classic dynamic programming examples include memoised Fibonacci, rod cutting, longest common subsequence and edit distance in O(mn) time. The fractional knapsack, solvable greedily, is contrasted with 0/1 knapsack, which needs DP, and backtracking and branch-and-bound also appear.

Below are 30 practice questions from a pool of 210 Algorithm Design Techniques MCQs, one of 12 topics in Data Structures & Algorithms. Each shows the correct answer with an explanation; when you are ready, take a timed quiz to test recall under exam conditions.

Practice Questions

Each question below shows the correct answer with a full explanation. Use these to build conceptual understanding before attempting a timed quiz.

Algorithm Design TechniquesEasy

Q1. What is the divide and conquer strategy?

  1. A.Breaking into subproblems, solving, and combining✓ Correct
  2. B.Solving all problems using bottom-up iteration
  3. C.Using a greedy approach at each step
  4. D.Solving problems by trying all possibilities

Explanation

Divide and conquer breaks a problem into smaller subproblems, solves each recursively, and combines their solutions to solve the original problem.

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Algorithm Design TechniquesEasy

Q2. What is a greedy algorithm?

  1. A.An algorithm making locally optimal choices each step✓ Correct
  2. B.An algorithm that solves all subproblems first
  3. C.An algorithm that uses backtracking for search
  4. D.An algorithm that tries all possible combinations

Explanation

A greedy algorithm makes the best choice available at each step without reconsidering previous choices, hoping to reach a globally optimal solution.

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Algorithm Design TechniquesEasy

Q3. What is memoization?

  1. A.Writing memos about code documentation
  2. B.A type of sorting with memory optimization
  3. C.Memorizing the algorithm steps by heart
  4. D.Caching results of function calls for reuse✓ Correct

Explanation

Memoization stores the results of expensive function calls and returns the cached result when the same inputs occur again, avoiding redundant computation.

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Algorithm Design TechniquesEasy

Q4. Which of the following is an example of divide and conquer?

  1. A.Merge sort✓ Correct
  2. B.Linear search
  3. C.Insertion sort
  4. D.Bubble sort

Explanation

Merge sort is a classic divide and conquer algorithm: it divides the array in half, sorts each half, and merges the results.

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Algorithm Design TechniquesEasy

Q5. What is backtracking?

  1. A.Sorting data elements in reverse descending order
  2. B.Trying solutions and abandoning invalid paths early✓ Correct
  3. C.Going back to the start of an algorithm run
  4. D.Reversing the input data before processing

Explanation

Backtracking explores all potential solutions by building them incrementally and abandoning (backtracking from) paths that cannot lead to valid solutions.

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Algorithm Design TechniquesEasy

Q6. What is dynamic programming?

  1. A.A type of greedy algorithm with memoization
  2. B.Solving problems by storing overlapping subproblem results✓ Correct
  3. C.Programming that changes dynamically at runtime
  4. D.An algorithm that uses only recursion for solving

Explanation

Dynamic programming solves problems by dividing them into overlapping subproblems, solving each once, and storing results to avoid redundant computation.

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Algorithm Design TechniquesEasy

Q7. What is brute force in algorithm design?

  1. A.An optimized search using heuristics
  2. B.Trying all possible solutions exhaustively✓ Correct
  3. C.The most efficient approach available
  4. D.A divide and conquer optimization

Explanation

Brute force tries every possible solution systematically, checking each one until the correct answer is found. It is simple but often inefficient.

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Algorithm Design TechniquesEasy

Q8. What two properties must a problem have to be solvable by dynamic programming?

  1. A.Optimal substructure and overlapping subproblems✓ Correct
  2. B.Linear structure and constant time operations
  3. C.Greedy choice property and unique solution
  4. D.Sorting and searching capabilities

Explanation

Dynamic programming requires optimal substructure (optimal solution uses optimal solutions to subproblems) and overlapping subproblems (same subproblems are solved multiple times).

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Algorithm Design TechniquesEasy

Q9. Which approach builds solutions from smallest subproblems to larger ones?

  1. A.Greedy approach
  2. B.Top-down approach
  3. C.Bottom-up (tabulation)✓ Correct
  4. D.Brute force approach

Explanation

Bottom-up (tabulation) starts by solving the smallest subproblems first and iteratively builds up to the solution of the original problem.

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Algorithm Design TechniquesEasy

Q10. Which algorithm design paradigm does the activity selection problem use?

  1. A.Backtracking search approach
  2. B.Dynamic programming approach
  3. C.Divide and conquer approach
  4. D.Greedy algorithm approach✓ Correct

Explanation

The activity selection problem is optimally solved using a greedy approach: always select the activity that finishes earliest.

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Algorithm Design TechniquesMedium

Q11. What is the time complexity of the dynamic programming solution for the 0/1 knapsack problem with n items and capacity W?

  1. A.O(n log n)
  2. B.O(2^n)
  3. C.O(n × W)✓ Correct
  4. D.O(n)

Explanation

The 0/1 knapsack DP solution fills an n × W table, where each cell is computed in O(1), giving O(n × W) time (pseudo-polynomial).

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Algorithm Design TechniquesMedium

Q12. What is the coin change problem (minimum coins)?

  1. A.Finding minimum coins to make a target amount✓ Correct
  2. B.Sorting coins by their face value order
  3. C.Counting total coins in a collection
  4. D.Finding the maximum number of coins used

Explanation

The coin change problem asks for the minimum number of coins from given denominations to make a target amount. It is solved using DP.

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Algorithm Design TechniquesMedium

Q13. What is the time complexity of the recursive Fibonacci without memoization?

  1. A.O(n)
  2. B.O(log n)
  3. C.O(n^2)
  4. D.O(2^n)✓ Correct

Explanation

Without memoization, the recursive Fibonacci has O(2^n) time complexity due to redundant computation of the same subproblems.

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Algorithm Design TechniquesMedium

Q14. What is the greedy choice property?

  1. A.Always choosing the most expensive option first
  2. B.A locally optimal choice leads to global optimum✓ Correct
  3. C.A property that all algorithms must have
  4. D.A property unique to dynamic programming only

Explanation

The greedy choice property means that a locally optimal choice at each step will lead to a globally optimal solution.

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Algorithm Design TechniquesMedium

Q15. What is the Longest Common Subsequence (LCS) problem?

  1. A.Finding the longest subsequence present in both sequences✓ Correct
  2. B.Finding the longest increasing subsequence in an array
  3. C.Finding the longest common substring between two strings
  4. D.Finding the longest common prefix of two strings

Explanation

LCS finds the longest subsequence (not necessarily contiguous) that appears in both sequences. It is solved using DP in O(m × n) time.

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Algorithm Design TechniquesMedium

Q16. How does memoization improve the Fibonacci computation?

  1. A.It reduces time from O(2^n) to O(n) by caching✓ Correct
  2. B.It makes the computation run in O(log n) time
  3. C.It does not improve it at all
  4. D.It makes the computation run in O(1) time

Explanation

Memoization caches the result of each Fibonacci number, ensuring each is computed only once, reducing time from O(2^n) to O(n).

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Algorithm Design TechniquesMedium

Q17. What is the difference between top-down and bottom-up dynamic programming?

  1. A.Top-down is always faster in practice than the bottom-up approach overall
  2. B.Top-down uses recursion with memoization; bottom-up uses tabulation✓ Correct
  3. C.Bottom-up always uses significantly more memory than the top-down approach
  4. D.They are exactly the same fundamental approach overall

Explanation

Top-down (memoization) uses recursion and caches results. Bottom-up (tabulation) iteratively fills a table from smallest subproblems upward.

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Algorithm Design TechniquesMedium

Q18. What is the N-Queens problem?

  1. A.A graph traversal problem with N vertices
  2. B.Sorting N queens by their rank and position
  3. C.Finding N queens in a given dataset collection
  4. D.Placing N queens so no two attack each other✓ Correct

Explanation

The N-Queens problem asks to place N queens on an N×N chessboard so that no two queens share the same row, column, or diagonal. It is typically solved using backtracking.

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Algorithm Design TechniquesHard

Q19. What is a randomized algorithm?

  1. A.An algorithm with random bugs in code
  2. B.An algorithm using random numbers in its decisions✓ Correct
  3. C.An algorithm that shuffles input before sorting
  4. D.An algorithm that produces random wrong output

Explanation

A randomized algorithm uses random numbers in its logic, often achieving good expected performance (e.g., randomized quicksort, randomized primality testing).

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Algorithm Design TechniquesHard

Q20. What is the meet-in-the-middle technique?

  1. A.A two-pointer approach for sorted arrays
  2. B.A median-finding technique using partitioning
  3. C.Dividing the array in half for sorting
  4. D.Splitting input in half and combining to reduce complexity✓ Correct

Explanation

Meet-in-the-middle splits the input in half, independently computes results for each half, and combines them. It reduces O(2^n) to O(2^(n/2)) for problems like subset sum.

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Algorithm Design TechniquesHard

Q21. What is the edit distance (Levenshtein distance) problem?

  1. A.The minimum single-character edits between two strings✓ Correct
  2. B.The difference in the lengths of two strings
  3. C.The number of common characters in two strings
  4. D.The distance between two arrays in memory

Explanation

Edit distance measures the minimum number of insertions, deletions, and substitutions needed to transform one string into another. Solved using DP in O(m × n).

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Algorithm Design TechniquesHard

Q22. What is branch and bound?

  1. A.A hashing technique for collision resolution
  2. B.A type of comparison-based sorting method
  3. C.An optimization technique pruning suboptimal branches✓ Correct
  4. D.A graph traversal method for shortest paths

Explanation

Branch and bound explores a tree of solutions, using bounds to prune branches that cannot lead to a better solution than the best found so far.

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Algorithm Design TechniquesHard

Q23. What is the difference between the 0/1 knapsack and fractional knapsack?

  1. A.0/1 uses greedy approach; fractional uses DP approach
  2. B.Fractional knapsack is computationally harder overall
  3. C.They are exactly the same problem formulation
  4. D.0/1 requires whole items (DP); fractional allows fractions (greedy)✓ Correct

Explanation

In 0/1 knapsack, items must be taken whole (solved by DP). In fractional knapsack, items can be divided (solved greedily by value-to-weight ratio).

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Algorithm Design TechniquesHard

Q24. What is the subset sum problem?

  1. A.Finding the sum of all array elements
  2. B.Summing consecutive elements in an array
  3. C.Finding the maximum valued subset overall
  4. D.Determining if a subset sums to a target value✓ Correct

Explanation

The subset sum problem asks whether any subset of a given set of integers sums to a target value. It is NP-complete but solvable in pseudo-polynomial time using DP.

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Algorithm Design TechniquesMedium

Q25. What is Huffman coding an example of?

  1. A.Greedy algorithm✓ Correct
  2. B.Backtracking
  3. C.Dynamic programming
  4. D.Divide and conquer

Explanation

Huffman coding is a greedy algorithm for constructing optimal prefix-free codes, always merging the two least frequent nodes first.

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Algorithm Design TechniquesHard

Q26. What is the time complexity of solving TSP using dynamic programming (Held-Karp)?

  1. A.O(n^3)
  2. B.O(n^2 × 2^n)✓ Correct
  3. C.O(n!)
  4. D.O(2^n)

Explanation

The Held-Karp DP algorithm solves TSP in O(n^2 × 2^n) time, much better than the brute-force O(n!) approach.

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Algorithm Design TechniquesMedium

Q27. What is the Longest Increasing Subsequence (LIS) problem's time complexity with DP?

  1. A.O(n)
  2. B.O(2^n)
  3. C.O(n log n)
  4. D.O(n^2)✓ Correct

Explanation

The standard DP solution for LIS runs in O(n^2) time. An optimized approach using binary search achieves O(n log n).

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Algorithm Design TechniquesHard

Q28. What is the Traveling Salesman Problem (TSP)?

  1. A.Finding the shortest path between two specific cities
  2. B.Finding the fastest route avoiding all toll roads
  3. C.Finding minimum cost Hamiltonian cycle visiting all cities✓ Correct
  4. D.A minimum spanning tree problem for city networks

Explanation

TSP asks for the shortest possible route that visits each city exactly once and returns to the starting city. It is NP-hard.

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Algorithm Design TechniquesHard

Q29. What is an approximation algorithm?

  1. A.An algorithm that gives approximate time complexity
  2. B.An algorithm finding near-optimal solutions in polynomial time✓ Correct
  3. C.An imprecise algorithm with unreliable output
  4. D.An algorithm that estimates the input data size

Explanation

An approximation algorithm finds solutions within a provable factor of the optimal for NP-hard problems, running in polynomial time.

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Algorithm Design TechniquesHard

Q30. What is the matrix chain multiplication problem's time complexity using DP?

  1. A.O(n^3)✓ Correct
  2. B.O(n!)
  3. C.O(2^n)
  4. D.O(n^2)

Explanation

The matrix chain multiplication DP solution has O(n^3) time complexity and O(n^2) space, where n is the number of matrices.

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