Shortest Paths Quiz

Question 1: Finding the shortest path - What is the shortest path from A to B in a graph?

• The shortest path is the one with the highest weight on the edges

• It depends on the specific graph and the algorithm used to find the shortest path.

• The shortest path is always the direct path from A to B

• The shortest path is the one with the most number of edges

Tags

CCSS.8.EE.C.8C

Question 2: Finding the shortest path - How do you find the shortest path between two points on a map?

• Guessing and randomly choosing a path

• Using algorithms such as Dijkstra's algorithm or A* algorithm

• Asking for directions from strangers

• Using a compass and drawing a straight line

Question 3: Using Dijkstra's algorithm - Explain how Dijkstra's algorithm finds the shortest path in a graph.

• It always selects the node with the highest total distance from the initial node

• It randomly selects nodes and checks if it leads to the shortest path

• It iteratively selects the next node with the lowest total distance from the initial node, updating the distances of adjacent nodes as it progresses.

• It only considers the distance between adjacent nodes and ignores the total distance

Tags

CCSS.8.EE.C.8C

Question 4: Using Dijkstra's algorithm - Solve the following problem using Dijkstra's algorithm: Find the shortest path from node A to node D in a weighted graph.

• Use Prim's algorithm to find the shortest path

• Use Bellman-Ford algorithm to find the shortest path

• Use Kruskal's algorithm to find the shortest path

• Apply Dijkstra's algorithm to find the shortest path from node A to node D.

Question 5: Understanding weighted graphs - What is a weighted graph and how is it different from an unweighted graph?

• A weighted graph has no edges, while an unweighted graph has edges

• A weighted graph has numerical values associated with its edges, while an unweighted graph does not.

• A weighted graph has no vertices, while an unweighted graph has vertices

• A weighted graph has colors associated with its edges, while an unweighted graph does not

Question 6: Understanding weighted graphs - How are weights represented in a weighted graph?

• Shapes assigned to the edges or vertices

• Numerical values assigned to the edges or vertices

• Letters assigned to the edges or vertices

• Colors assigned to the edges or vertices

Question 7: Applying breadth-first search - Describe how breadth-first search can be used to find the shortest path in a graph.

• Starting from the farthest node and working backwards

• Traversing the graph in a random order

• Only considering the nodes with the highest degree

• Exploration of neighboring nodes level by level to find the shortest path

Question 8: Applying breadth-first search - Use breadth-first search to find the shortest path from node A to node D in a given graph.

• Use breadth-first search algorithm to find the shortest path from node A to node D.

• Use Dijkstra's algorithm to find the shortest path from node A to node D.

• Use depth-first search algorithm to find the shortest path from node A to node D.

• Use A* search algorithm to find the shortest path from node A to node D.

Question 9: Analyzing time complexity of algorithms - What is time complexity and how is it important in analyzing algorithms?

• Time complexity is the amount of space an algorithm takes to run as a function of the length of its input. It is important in analyzing algorithms because it helps in understanding how the algorithm will perform in terms of memory usage.

• Time complexity is the amount of time an algorithm takes to run as a function of the length of its input. It is important in analyzing algorithms because it helps in understanding how the algorithm will perform as the input size grows.

• Time complexity is the number of steps an algorithm takes to run as a function of the length of its input. It is important in analyzing algorithms because it helps in understanding how the algorithm will perform in terms of speed.

• Time complexity is the amount of time an algorithm takes to run as a function of the length of its output. It is important in analyzing algorithms because it helps in understanding how the algorithm will perform as the output size grows.

Question 10: Analyzing time complexity of algorithms - Compare the time complexity of Dijkstra's algorithm and breadth-first search.

• Breadth-first search has a time complexity of O(E^2) using a priority queue

• Dijkstra's algorithm has a time complexity of O(ElogV) using a queue

• Dijkstra's algorithm has a time complexity of O((V+E)logV) using a priority queue, while breadth-first search has a time complexity of O(V+E) using a queue.

• Dijkstra's algorithm has a time complexity of O(V^2) using a stack