MCQs on backtracking

Backtracking is an algorithmic approach to problem-solving that involves progressively solving by experimenting with many possibilities and reversing them if they result in a dead end. It is frequently employed in scenarios where you must consider several options to find a solution, such as when figuring out Sudoku puzzles or finding a way around mazes. When an algorithm encounters a dead end, it returns to the original decision point. It continues searching for a different route until a solution is discovered or all options have been considered.

Backtracking can be defined as a general algorithmic technique that considers searching every possible combination to solve a computational problem.

Here are some MCQs(Multiple Choice Questions):

Question 1: What is backtracking?

A search algorithm that finds the shortest path in a graph.
An algorithmic paradigm that tries different solutions until the correct one is found.
An algorithm for sorting elements in an array.
A dynamic programming technique.

Answer: b) An algorithmic paradigm that tries different solutions until the correct one is found.

Explanation:

Generally, backtracking is an algorithmic approach to resolving computational issues. Gradually, it constructs candidates for a solution and "backtracks"-quits-a candidate as soon as it realizes it cannot potentially lead to a workable solution.

Question 2: In backtracking, what is pruning?

Trimming unwanted branches in the search space.
The process of selecting the best solution
reversing the steps taken.
The process of finding the optimal solution.

Answer: a) Trimming unwanted branches in the search space.

Explanation:

Pruning, as used in backtracking, is the act of removing or trimming undesirable branches from the search area. Pruning assists in the algorithm's selective removal of branches that are judged unlikely to result in a workable or ideal solution as it searches through various avenues in search of a solution. By eliminating certain paths, the method becomes more efficient and requires less computing.

Question 3: Which of the following problems can be solved efficiently using backtracking?

Sorting an array.
Finding the shortest path in a graph.
Traveling Salesman Problem.
Calculating factorial.

Answer: c) Traveling Salesman Problem.

Explanation:

The Traveling Salesman Problem (TSP) is a problem that can be effectively resolved by going back and evaluating the options that have been provided. The traveling salesman problem aims to determine the quickest path that passes through several locations and returns to the beginning point. Because it systematically investigates various orderings in which cities can be visited and looks for the quickest route, backtracking is a good solution for this problem.

Question 4: What is the key feature of a problem that makes it suitable for a backtracking solution?

The problem has overlapping subproblems.
The problem has an optimal substructure.
The problem can be divided into smaller independent subproblems.
The problem exhibits a recursive structure and can be solved by trying out different possibilities.

Answer: d) The problem exhibits a recursive structure and can be solved by trying out different possibilities.

Explanation:

Recursive problems, in which solutions are discovered by methodically exploring various options, are good possibilities for backtracking. Backtracking is making decisions at crucial moments, pursuing paths until a solution is discovered, or deciding it isn't practical. In contrast, optimum substructure and overlapping subproblems are the foundation of dynamic programming.

Question 5: In backtracking, what is a solution candidate?

The final solution to the problem.
A partial solution that may or may not lead to a valid solution.
A solution obtained through dynamic programming.
The optimal solution.

Answer: b) A partial solution that may or may not lead to a valid solution.

Explanation:

A solution candidate in backtracking is a partial solution that may or may not end in an acceptable final solution. By exploring paths through the solution space and making decisions at decision points, the algorithm gradually constructs these possibilities. It assesses if the current option can lead to a comprehensive and realistic solution at each stage.

Question 6: What is the main purpose of backtracking?

To find the maximum element in an array.
To explore all possible solutions to a problem.
To perform sorting on a list of elements.
To calculate the average of a set of numbers.

Answer: b) To explore all possible solutions to a problem.

Explanation:

Backtracking is mostly used for exploring every potential solution for a certain issue. Backtracking is a wide algorithmic strategy that iteratively explores the solution space, experimenting at decision points with many options and reverting as required. It is beneficial for issues where solutions must be developed gradually and when considering every option is necessary to arrive at the best or most acceptable solution.

Question 7: What is the term used to describe a situation in backtracking where all possible choices have been explored, and the algorithm backtracks to the previous decision point?

Reversal.
Retreat.
Backstep.
Backtrack.

Answer: d) Backtrack.

Explanation:

"Backtrack" is the term that describes a backtracking situation in which the algorithm returns to the prior decision point after exhausting all potential options. When an algorithm encounters an impasse or runs out of possibilities at a given decision point, it reverts to the last viable option and investigates further options. Until a solution is found or every option has been explored, this process keeps going.

Question 8: In backtracking, what is a constraint?

A condition that a solution must satisfy.
A mathematical equation.
A decision point.
A variable in the algorithm.

Answer: a) A condition that a solution must satisfy.

Explanation:

A constraint in the context of backtracking is a requirement that a solution needs to meet. The standards or guidelines that direct the hunt for a workable solution in the solution space are known as constraints. The backtracking algorithm makes decisions at each decision point, and the algorithm is responsible for ensuring the selected path complies with these limitations. The algorithm reverses its course and reverses the previous decision if a choice violates a constraint.

Question 9: What is the term for the process of accepting a solution candidate as the final solution?

Confirmation.
Validation.
Acceptance.
Pruning.

Answer: b) Validation.

Explanation:

In the context of backtracking, the process of accepting a solution candidate as the ultimate solution is known as "validation." Validation entails determining whether a certain candidate for a solution satisfies the requirements and limitations given by the problem. Upon exploring various paths inside the solution space and gradually constructing solution candidates, the backtracking algorithm eventually arrives at a point when a candidate is deemed a credible ultimate solution.

Question 10: How does backtracking differ from brute force?

Backtracking is a more efficient form of brute force.
Backtracking uses pruning, while brute force does not.
Backtracking always finds the optimal solution, while brute force may not.
Backtracking and brute force are synonymous terms.

Answer: b) Backtracking uses pruning, while brute force does not.

Explanation:

Though both backtracking and brute force are methodical approaches to issue solving that involve exploring possible fixes, they differ in terms of strategy and efficiency. Using a brute force approach usually means exploring every potential option without taking optimality or practicality into account. It can be computationally expensive because it thoroughly examines the whole solution space. Conversely, backtracking includes pruning, which is the process of removing some pathways from the solution space if it is thought that they are not likely to result in a workable or ideal solution.

Question 11: What is the role of the base case in a recursive backtracking algorithm?

It defines the initial state of the problem.
It defines the stopping condition for the recursion.
It represents the optimal solution.
It is used for input validation.

Answer: b) It defines the stopping condition for the recursion.

Explanation:

The base case of a recursive backtracking algorithm is essential in determining the recursion's preventing condition. A condition known as the "base case" tells the algorithm to halt the recursive operation and produce a result when it is satisfied. It acts as the recursion's endpoint, guaranteeing that the process converges to a solution and avoiding an infinite loop.

Question 12: Which data structure is commonly used to implement backtracking algorithms?

Linked list.
Stack.
Queue.
Hash table.

Answer: b) Stack.

Explanation:

A stack is a frequently utilized data structure in the implementation of backtracking algorithms. The stack is utilized in a backtracking algorithm to record the decisions and selections made at each stage of the solution space analysis. Choices are pushed onto the stack by the algorithm as it goes along, and when reversing course is necessary, it pops them off.

Next TopicDesign a data structure that supports insert, delete, search, and getRandom in constant time

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