We use dynamic programming approach when

The solution has optimal substructure and overlapping subproblems

The given problem can be reduced to the 3-SAT problem

An algorithm to find the length of the longest monotonically increasing sequence of numbers in an array A[0 :n-1] is given below. Let Li denote the length of the longest monotonically increasing sequence starting at index i in the array. EquationWhich of the following statements is TRUE?

The algorithm uses dynamic programming paradigm

The algorithm has a linear complexity and uses branch and bound paradigm

The algorithm has a non-linear polynomial complexity and uses branch and bound paradigm

The algorithm uses divide and conquer paradigm.

Which of the following is NOT a characteristic of dynamic programming?

Solving problems in a sequential manner.

Memoization, which involves storing the results of expensive function calls and reusing them.

Breaking a problem into smaller overlapping subproblems.

Dynamic programming can be used for problems where the solution has an optimal substructure.

What happens when a top-down approach of dynamic programming is applied to any problem?

It increases the space complexity and decreases the time complexity.

It increases both, the time complexity and the space complexity

It increases the time complexity and decreases the space complexity

It decreases both, the time complexity and the space complexity

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Top MCQs on Dynamic Programming with Answers

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Question 1

Consider the weights and values of items listed below. Note that there is only one unit of each item.

The task is to pick a subset of these items such that their total weight is no more than 11 Kgs and their total value is maximized. Moreover, no item may be split. The total value of items picked by an optimal algorithm is denoted by V_opt. A greedy algorithm sorts the items by their value-to-weight ratios in descending order and packs them greedily, starting from the first item in the ordered list. The total value of items picked by the greedy algorithm is denoted by V_greedy. The value of V_opt − V_greedy is ______ .

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Question 2

In dynamic programming, the time complexity of solving a problem with overlapping subproblems using memoization is:

O(1)
O(log n)
O(n)
O(n^2)

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Question 3

What is the main goal of the Word Break Problem?

To break a given string into individual characters.
To determine if a string can be segmented into a sequence of words from a dictionary.
To find the longest subsequence of a string.
To reverse a given string.

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Question 4

The Partition Problem can be reduced to which well-known problem?

Knapsack Problem
Traveling Salesman Problem
Subset Sum Problem
Graph Coloring Problem

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Question 5

The "Egg Dropping Puzzle" involves determining the minimum number of attempts needed to find the critical floor from which an egg will break when dropped. What is the time complexity of the dynamic programming approach for solving the Egg Dropping Puzzle for K eggs and N floors?

O(K * N)
O(K + N)
O(K * N^2)
O(K^2 * N)

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Question 6

The "Longest Increasing Subsequence" problem involves finding the length of the longest subsequence of an array in which the elements are in increasing order. What is the time complexity of the dynamic programming approach for solving the LIS problem for an array of length n?

O(n)
O(n log n)
O(n^2)
O(2^n)

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Question 7

Which of the following problems is closely related to the Subsets Sum problem and can also be solved using dynamic programming?

Longest Common Subsequence Problem
Longest Palindromic Subsequence Problem
Coin Change Problem
Optimal Binary Search Tree Problem

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Question 8

Which of the following problems is closely related to the LPS problem and can also be solved using dynamic programming?

Longest Common Subsequence Problem
Longest Increasing Subsequence Problem
Edit Distance Problem
Subset Sum Problem

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Question 9

In the 0-1 Knapsack Problem, if an item's weight is greater than the remaining capacity of the knapsack, what action is typically taken?

Ignore the item and move to the next one
Remove the least valuable item from the knapsack to make space
Add the fractional part of the item that can fit into the knapsack
Remove the most valuable item from the knapsack to make space

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Question 10

The time complexity of solving the 0-1 Knapsack Problem using dynamic programming with a bottom-up approach (tabulation) is:

O(n)
O(n log n)
O(n * capacity)
O(n * capacity^2)

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