Greedy Introduction
A greedy algorithm makes the locally optimal choice at each step, hoping to find a global optimum. It's like climbing a hill: at each point, you choose the steepest upward path, hoping it leads to the top. Greedy algorithms are often simpler and faster than DP, but they only work when the problem has the greedy-choice property (a local optimum leads to a global optimum).
Greedy algorithms are used for problems like:
- Minimum spanning tree (Prim's, Kruskal's)
- Shortest path (Dijkstra's)
- Huffman coding
- Activity selection
- Fractional knapsack
Key properties for greedy:
- Greedy choice property – A global optimum can be reached by choosing a local optimum.
- Optimal substructure – An optimal solution contains optimal solutions to subproblems.
Two Minute Drill
- Greedy algorithms make locally optimal choices at each step.
- They are simpler and often faster than DP.
- Works only for problems with greedy-choice property.
- Examples: Dijkstra, Prim, Kruskal, Huffman, activity selection.
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