dynamic programming

Dynamic Programming Introduction Dynamic programming (DP) is a powerful algorithmic technique used for solving complex problems by breaking them down into simpler subproblems and solving each subproblem just once, storing the results for future reference. This method significantly optimizes computational efficiency, making it a crucial concept in computer science, particularly in fields like ...

Quiz Type

Practice

Subject

Computer Science

Level

Level 600

Questions

10 questions

Created By

Akotia Louis

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Time limit: 5 minutes
Multiple attempts are not allowed
All questions must be answered to submit

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Question 1 of 10

Question 1

Multiple choice

In the context of dynamic programming, which of the following statements best defines the principle of optimality?

Optimal solutions to subproblems can be ignored in finding the overall solution.

An optimal solution can be composed of solutions that may not be optimal.

An optimal solution can be derived by re-evaluating subproblems multiple times.

An optimal solution to any instance is composed of optimal solutions to its subproblems.

Correct

Explanation

The principle of optimality states that an optimal solution can be constructed from optimal solutions to its subproblems.

Question 2

Multiple choice

Which dynamic programming approach is most suitable when the problem requires immediate feedback from previously computed subproblems?

Memoization

Correct

Tabulation

Greedy algorithms

Backtracking

Explanation

Memoization allows for a top-down approach where results of previously computed subproblems are reused immediately.

Question 3

Multiple choice

In solving the 0/1 Knapsack Problem using dynamic programming, which of the following approaches correctly captures the maximum value for a given weight limit?

Store the values in a list and incrementally build the solution based on sorted weights.

Create a binary tree to represent the decisions of including or excluding items.

Use a single array and iterate backward to update the values for the current weight.

Use a 2D array where dp[i][w] represents the maximum value of the first i items with weight limit w.

Correct

Explanation

In the 0/1 Knapsack Problem, a 2D array is utilized to keep track of the maximum value at each combination of items and weight.

Question 4

Multiple choice

Given the choice between memoization and tabulation for a specific dynamic programming problem, which situation would favor a tabulation approach?

When the problem has a small number of subproblems.

When the maximum depth of recursion is limited.

When the problem requires immediately resolving and accessing previously computed results.

When optimizing for space by avoiding recursive call overhead.

Correct

Explanation

Tabulation is a bottom-up approach that avoids recursive overhead, making it space-efficient for certain problems.

Question 5

Multiple choice

When solving a problem using dynamic programming, which of the following properties must be present to ensure efficiency?

Overlapping subproblems and optimal substructure

Correct

A large number of states to search

Complex error handling

Single-pass evaluation of all elements

Explanation

Dynamic programming is effective when both overlapping subproblems and optimal substructure properties are present.

Question 6

Multiple choice

In a case study where a dynamic programming approach is applied to find the longest common subsequence (LCS) between two sequences, what would be a critical step in ensuring correct implementation?

Using a recursive method without memoization.

Comparing characters and building the solution from the end of both sequences.

Correct

Storing only the lengths of subsequences in a 1D array.

Directly manipulating the original sequences for updates.

Explanation

Building the solution from the end allows retrieval of the optimal LCS while maintaining an efficient structure.

Question 7

Multiple choice

What is a significant risk of using dynamic programming to solve optimization problems without fully understanding their constraints?

Inefficient time complexity due to unnecessary recalculations.

Reduced adaptability to real-time data updates.

Potentially incorrect results due to inappropriate subproblem definitions.

Correct

Increased memory usage without improving performance.

Explanation

Defining improper subproblems can lead to incorrect results even when a dynamic programming approach is theoretically sound.

Question 8

Multiple choice

When considering dynamic programming for a new problem, which combination of characteristics most strongly indicates suitability for this technique?

Complexity in state transitions and non-linear relationships

Presence of unique solutions and constant space requirements

Recurrent patterns in subproblem solutions with overlapping states

Correct

High dimensional inputs with no repeated computations

Explanation

The combination of recurrent patterns in solutions with overlapping states signifies the potential benefit of using dynamic programming.

Question 9

Multiple choice

How does the time complexity of the naive recursive approach to the Fibonacci sequence compare to the dynamic programming approaches of memoization and tabulation?

Both dynamic programming variations have linear time complexity, while the recursive approach has exponential.

Correct

All approaches have exponential time complexity.

The recursive approach is faster than both dynamic programming methods.

Memoization has quadratic complexity while tabulation stays linear.

Explanation

The naive approach has exponential time complexity (O(2^n)), whereas both memoization and tabulation reduce it to linear time (O(n)).

Question 10

Multiple choice

What is the primary computational advantage of using dynamic programming over simple recursion in large search spaces?

Inherent parallelizability in solving subproblems

Reduction in repeated calculations by storing intermediate results

Correct

Ability to solve every instance of a problem using a single pass

Dependence on external memory resources for larger computations

Explanation

Dynamic programming significantly reduces repeated calculations by storing and reusing already computed results.