19. Greedy algorithms: Interval scheduling
Greedy algorithms focus on achieving a global optimum through a series of local choices. These algorithms make decisions based on immediate benefit without revising past decisions. The discussion includes specific algorithms like Dijkstra’s, Prim’s, and Kruskal’s, culminating in a comprehensive interval scheduling problem that illustrates the principles of greedy strategies effectively.
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What we have learnt
- Greedy algorithms make decisions by selecting the most beneficial option at each step without reconsideration.
- Dijkstra's algorithm finds the shortest path in a network based on a greedy approach.
- Evaluating optimality is essential when implementing greedy strategies, as they do not always yield the best solution.
Key Concepts
- -- Greedy Algorithm
- An algorithmic paradigm that builds up a solution piece by piece, choosing the next piece with the most immediate benefit.
- -- Dijkstra's Algorithm
- A greedy algorithm that finds the shortest paths from a single source vertex to all other vertices in a graph.
- -- Interval Scheduling
- A classic optimization problem where the objective is to select the largest subset of mutually compatible intervals.
- -- Prim's Algorithm
- A greedy algorithm that finds a minimum spanning tree for a weighted undirected graph.
- -- Kruskal's Algorithm
- A greedy algorithm that finds a minimum spanning tree by considering edges in order of weight.
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