Which of the following algorithms uses dynamic programming to solve the problem of finding the shortest path in a weighted graph?
Practice Questions
1 question
Q1
Which of the following algorithms uses dynamic programming to solve the problem of finding the shortest path in a weighted graph?
Dijkstra's Algorithm
Bellman-Ford Algorithm
A* Search
Depth-First Search
The Bellman-Ford Algorithm uses dynamic programming to find the shortest path in a weighted graph, especially when negative weights are present.
Questions & Step-by-step Solutions
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Q
Q: Which of the following algorithms uses dynamic programming to solve the problem of finding the shortest path in a weighted graph?
Solution: The Bellman-Ford Algorithm uses dynamic programming to find the shortest path in a weighted graph, especially when negative weights are present.
Steps: 5
Step 1: Understand what a weighted graph is. A weighted graph is a graph where each edge has a numerical value (weight) that represents the cost to travel from one vertex to another.
Step 2: Learn about the shortest path problem. This problem involves finding the path between two vertices in a graph that has the smallest total weight.
Step 3: Know that there are different algorithms to solve the shortest path problem. Some of these algorithms can handle graphs with negative weights.
Step 4: Identify the Bellman-Ford Algorithm. This algorithm is specifically designed to find the shortest path in graphs that may have negative weights.
Step 5: Recognize that the Bellman-Ford Algorithm uses dynamic programming. This means it breaks the problem down into smaller subproblems and solves each one to build up the solution to the overall problem.
