Which of the following algorithms is an example of dynamic programming?

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Q: Which of the following algorithms is an example of dynamic programming?

Solution: The Floyd-Warshall Algorithm is an example of dynamic programming, used to find shortest paths in a weighted graph.

Steps: 6

Step 1: Understand what dynamic programming is. It is a method for solving complex problems by breaking them down into simpler subproblems.
Step 2: Identify the characteristics of dynamic programming. It typically involves overlapping subproblems and optimal substructure.
Step 3: Look at the algorithms provided in the question. Check if any of them use dynamic programming principles.
Step 4: Recognize that the Floyd-Warshall Algorithm is designed to find the shortest paths between all pairs of vertices in a weighted graph.
Step 5: Confirm that the Floyd-Warshall Algorithm uses dynamic programming by storing the results of subproblems (shortest paths) to avoid redundant calculations.
Step 6: Conclude that since the Floyd-Warshall Algorithm meets the criteria of dynamic programming, it is indeed an example of this technique.