# Greedy Approach

A greedy approach, huh? Well, imagine you’re at a party and there’s a buffet full of all sorts of delicious dishes. But there’s a catch - you’ve only got one plate, and you can’t stack your food, everything has to sit on the plate without any mounding up.

Now, you’re really hungry and you want to get the most satisfying plate of food that you can. What do you do? You could try and calculate all the possible combinations of food, weigh their pros and cons, but by the time you’re done figuring it out, the party might be over!

A greedy approach to this problem would be to always pick the best-looking dish that fits on your plate, each time you have room for more. You’d start with the biggest, most delicious-looking item that fits, then choose the next best thing that still fits alongside what you’ve already got, and so on, until your plate is full.

You’re not worried about whether you might have to pass up something even better later on - you just take the best option available each time. That’s the greedy approach.

Now, this strategy doesn’t always get you the absolute best possible outcome - maybe if you’d taken a smaller piece of chicken at the start, you’d have had room for that big chunk of lasagna later on. But the greedy approach is simple, and it often gets you a pretty good result without needing to do a lot of complicated calculations.

In computer science, we use greedy algorithms when we want to solve a problem by always making the choice that looks best at the moment, even if it might not guarantee the best overall solution. It’s a method of problem-solving that’s quick, easy to understand, and often pretty effective, even if it’s not always perfect.

## When to Apply

Determining whether a problem can be solved with a greedy algorithm can often be challenging. Here are some indicators that a greedy approach might be suitable:

**Optimization Problems:**Greedy algorithms are often used in optimization problems where you’re asked to find the maximum or minimum of something. These can be problems like “Find the maximum number of activities that don’t overlap” or “Find the minimum spanning tree of a graph.”**Local Optima Leads to Global Optima:**Greedy algorithms work by making the locally optimal choice at each step in the hope that these local choices will lead to a global optimum. However, this property doesn’t hold true for all problems. It requires what’s called an optimal substructure. An optimal solution to the problem contains within it optimal solutions to subproblems.**Greedy Choice Property:**The problem exhibits the property of greedy choice, i.e., a global optimum can be arrived at by selecting a local optimum.**No need for Backtracking:**In problems where backtracking or looking ahead is needed to determine the optimal solution, greedy algorithms usually fail.**Sorting helps solving the problem:**In some problems, sorting the input data might lead to easier solutions. This might be an indicator that a greedy algorithm could be used.

Even when a problem seems like it could be solved with a greedy algorithm, it’s crucial to prove that the greedy approach will always lead to the optimal solution. Many problems can seem like they would lend themselves to a greedy approach but actually require a more sophisticated method like dynamic programming.

## Greedy Problems

Here are some problems that can be commonly solved using a greedy approach:

**Activity Selection Problem:**Given a set of activities with start and end times, the goal is to select the maximum number of activities that don’t overlap.**Huffman Coding:**This is a lossless data compression algorithm. The idea is to assign variable-length codes to input characters, lengths of the assigned codes are based on the frequencies of corresponding characters.**Job Sequencing Problem:**Given an array of jobs where every job has a deadline and associated profit if the job is finished before the deadline. It is also given that every job takes a single unit of time, so the minimum possible deadline for any job is 1. The goal is to maximize total profit if only one job can be scheduled at a time.**Fractional Knapsack Problem:**Given weights and values of n items, the goal is to put these items in a knapsack of capacity W to get the maximum total value in the knapsack. In Fractional Knapsack, we can break items for maximizing the total value of the knapsack.**Dijkstra’s Shortest Path Algorithm:**This is a graph algorithm for finding the shortest paths from a single source vertex to all other vertices in a weighted graph.**Kruskal’s Minimum Spanning Tree Algorithm:**This is a graph algorithm for finding the Minimum Spanning Tree (MST) of a graph. It falls under a class of algorithms called greedy algorithms.**Prim’s Minimum Spanning Tree Algorithm:**Similar to Kruskal’s algorithm, this algorithm also falls under the greedy paradigm and is used to find MSTs.**Traveling Salesman Problem (heuristic):**A heuristic solution to the Traveling Salesman Problem can be constructed using a greedy approach, though it does not guarantee the optimal solution.**Coin change problem:**If the denominations of coins have a certain property (like in US currency), the problem of giving change can be solved with a greedy algorithm.**Interval Scheduling:**Scheduling multiple intervals of time so that the maximum number are non-overlapping.

While the greedy approach is intuitive and works well for these problems, it’s crucial to ensure that a greedy approach is valid for the problem you’re trying to solve, as it does not work for all problems. It might not provide the most optimized solution in all cases.