Challenging Algorithms and Puzzles

What is the Traveling Salesman Problem (TSP)?

• An algorithm to optimize network traffic

• The Traveling Salesman Problem (TSP) is an optimization problem to find the shortest possible route that visits each city once and returns to the origin.

• A method for scheduling flights efficiently

• A problem to find the fastest delivery service

Explain the concept of a Hamiltonian cycle.

• A Hamiltonian cycle is a cycle in a graph that visits every vertex exactly once and returns to the starting vertex.

• A Hamiltonian cycle is a cycle that can visit some vertices multiple times.

• A Hamiltonian cycle is a path that visits every edge in a graph.

• A Hamiltonian cycle is a cycle that does not return to the starting vertex.

What is the main goal of the Shortest Path problem?

• To identify all possible routes between two points in a graph.

• To determine the longest path between two points in a graph.

• To calculate the total weight of all edges in a graph.

• To find the shortest route or minimum distance between two points in a graph.

Describe the branch and bound technique in optimization.

• Branch and bound is used exclusively for linear programming problems.

• Branch and bound is an optimization technique that explores and prunes solution spaces to find the optimal solution.

• Branch and bound is a technique that only finds local minima.

• Branch and bound is a method that guarantees finding all possible solutions.

How does the n-queen problem work?

• The n-queen problem is a combinatorial problem of placing n queens on an n x n chessboard so that no two queens threaten each other.

• The n-queen problem requires placing n queens on a 2 x 2 chessboard.

• The n-queen problem is about arranging n queens in a straight line.

• The n-queen problem involves placing n knights on a chessboard.

What is the significance of the sum of subsets problem?

• It simplifies linear programming problems.

• It helps in combinatorial optimization and decision-making.

• It is used for sorting algorithms.

• It determines the maximum value in a dataset.

Can you provide an example of a greedy algorithm?

• Sorting an array using bubble sort.

• Using a depth-first search for graph traversal.

• Dynamic programming approach to the knapsack problem.

• Coin change problem using the largest denomination first.

What are the differences between TSP and the Shortest Path problem?

• TSP finds the shortest route between all nodes without returning to the start.

• TSP only considers direct connections between two nodes.

• The Shortest Path problem requires visiting all nodes exactly once.

• TSP requires visiting all nodes exactly once and returning to the start, while the Shortest Path problem finds the shortest route between two specific nodes.

How can backtracking be used to solve the n-queen problem?

• Backtracking only allows placing queens in the first row.

• Backtracking randomly places queens without checking for threats.

• Backtracking solves the problem by placing all queens in one column.

• Backtracking can systematically explore all possible placements of queens on the board, ensuring that no two queens threaten each other.

What is the time complexity of finding a Hamiltonian cycle?

• O(n log n)

• O(2^n)

• O(n!)

• O(n^2)