# Data Structures – Greedy Algorithms

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(Last Updated On: May 27, 2018)

## In this DSA tutorial, you will learn what is Greedy Algorithms and how to use it.

An algorithm is designed to achieve the optimum solution for a given problem. In Data Structures Greedy Algorithms approach, decisions are made from the given solution domain. As being greedy, the closest solution that seems to provide an optimum solution is chosen.
Data structures Greedy algorithms try to find a localized optimum solution, which may eventually lead to globally optimized solutions. However, generally greedy algorithms do not provide globally optimized solutions.

#### Counting Coins

This problem is to count to a desired value by choosing the least possible coins and the greedy approach forces the algorithm to pick the largest possible coin. If we are provided coins of ₹ 1, 2, 5 and 10 and we are asked to count ₹ 18 then the greedy procedure will be −

• Select one ₹ 10 coins, the remaining count is 8
• Then select one ₹ 5 coin, the remaining count is 3
• Then select one ₹ 2 coin, the remaining count is 1
• And finally, the selection of one ₹ 1 coins solves the problem

Though, it seems to be working fine, for this count we need to pick only 4 coins. But if we slightly change the problem then the same approach may not be able to produce the same optimum result.

For the currency system, where we have coins of 1, 7, 10 value, counting coins for value 18 will be absolutely optimum but for count like 15, it may use more coins than necessary. For example, the greedy approach will use 10 + 1 + 1 + 1 + 1 + 1, total 6 coins. Whereas the same problem could be solved by using only 3 coins (7 + 7 + 1)

Hence, we may conclude that the greedy approach picks an immediate optimized solution and may fail where global optimization is a major concern.

#### Examples

Most networking algorithms use the greedy approach. Here is a list of few of them −

• Travelling Salesman Problem
• Prim’s Minimal Spanning Tree Algorithm
• Kruskal’s Minimal Spanning Tree Algorithm
• Dijkstra’s Minimal Spanning Tree Algorithm
• Graph – Map Coloring
• Graph – Vertex Cover
• Knapsack Problem
• Job Scheduling Problem

There are lots of similar problems that uses the greedy approach to find an optimum solution.

Data Structures Algorithms Books: Algorithms Plus Data Structures

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