Summary

In this chapter, we explored the key concepts and differences among these algorithmic strategies, highlighting how each approach solves problems with optimal substructure. We discussed how divide-and-conquer algorithms break problems into smaller, non-overlapping subproblems, and how dynamic programming efficiently handles overlapping subproblems by storing and reusing their solutions. This chapter also covered greedy algorithms, emphasizing their reliance on heuristics to make locally optimal choices at each step, even though this may not always lead to a globally optimal solution.

Throughout the chapter, we provided examples such as the 0/1 knapsack problem and the TSP to illustrate the strengths and limitations of each approach. We also examined the role of heuristics in greedy algorithms, noting how they enable quick, approximate solutions but can sometimes lead to suboptimal results. As we concluded the discussion, we acknowledged the importance of choosing the right...