# Greedy Algorithms

Greedy Algorithms follow a problem solving approach wherein they make the locally optimal choice at each stage, with the hope of finding a global optimum.

The focus is, however, on finding the local optimums at each step, regardless of whether a global optimum is ever obtained.

The image below depicts the result of a greedy algorithm that needed to find the largest possible sum, starting from the root. It focused on choosing the maximum value at each step, leading to a solution that wasn't globally optimal.

The image below depicts the globally optimal solution (in green).

**Pros of Greedy Algorithms**:

- simple
- easy to implement
- reasonable complexity

**Cons of Greedy Algorithms**:

- may not result in a globally optimal solution for any given problem

**Where do we use Greedy Algorithms?**

Problems that can be solved using Greedy Algorithms satisfy the following properties:

**Greedy choice property**: from a local optimum we can reach a global optimum, without having to reconsider the decisions already taken**Optimal Substructure**: an optimal solution can be constructed efficiently from the optimal solutions of its subproblems

*A Greedy Algorithm never reconsiders its choices!*

Some common problems solved using the greedy approach include:

- Activity Selection problem
- Fractional Knapsack Problem
- Minimum Number of Coins
- Huffman Coding
- Job Sequencing problem
- Kruskal's Minimum Spanning Tree
- Prim's Minimum Spanning Tree
- Dijkstra's Shortest Path problem