Greedy Algorithm is an algorithm strategy for solving optimization problems. In a greedy algorithm, each step chooses the best option in the current situation without considering future consequences.
The basic idea of the greedy algorithm is to achieve the global optimum through local optimal selection. It does not guarantee that the global optimal solution will be obtained, but in some cases it can obtain an approximately optimal solution or a solution that meets the requirements.
The applicable conditions for the greedy algorithm are that the problem has "optimal substructure" and "greedy selection properties". Optimal substructure means that the optimal solution to the problem can be derived from the optimal solutions to the subproblems. The greedy selection property means that the optimal choice at each step can lead to the final global optimal solution.
Common applications of greedy algorithms include:
- Huffman coding: used for data compression, constructing a coding scheme based on the frequency of character occurrences.
- Minimum spanning tree: such as Prim's algorithm and Kruskal's algorithm, used to find a connected subgraph containing all nodes in the graph with the smallest sum of weights.
- Partial solution to the knapsack problem: When the knapsack capacity is limited, choose the most cost-effective items to put into the knapsack.
However, not all problems are suitable to be solved by greedy algorithms. In some cases, greedy algorithms may obtain suboptimal solutions or fail to obtain feasible solutions. When designing a greedy algorithm, you need to carefully analyze the nature and conditions of the problem to ensure the correctness of the greedy choice and perform appropriate proofs.