Greedy Algorithms

Table of content

Among all the algorithmic approaches, the simplest and straightforward approach is the Greedy method. In this approach, the decision is taken on the basis of current available information without worrying about the effect of the current decision in future.

Greedy algorithms build a solution part by part, choosing the next part in such a way, that it gives an immediate benefit. This approach never reconsiders the choices taken previously. This approach is mainly used to solve optimization problems. Greedy method is easy to implement and quite efficient in most of the cases. Hence, we can say that Greedy algorithm is an algorithmic paradigm based on heuristic that follows local optimal choice at each step with the hope of finding global optimal solution.

In many problems, it does not produce an optimal solution though it gives an approximate (near optimal) solution in a reasonable time.

Components of Greedy Algorithm

Greedy algorithms have the following five components −

  • A candidate set − A solution is created from this set.

  • A selection function − Used to choose the best candidate to be added to the solution.

  • A feasibility function − Used to determine whether a candidate can be used to contribute to the solution.

  • An objective function − Used to assign a value to a solution or a partial solution.

  • A solution function − Used to indicate whether a complete solution has been reached.

Areas of Application

Greedy approach is used to solve many problems, such as

  • Finding the shortest path between two vertices using Dijkstra's algorithm.

  • Finding the minimal spanning tree in a graph using Prim's /Kruskal's algorithm, etc.

Counting Coins Problem

The Counting Coins 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 −

  • 1 − Select one 10 coin, the remaining count is 8

  • 2 − Then select one 5 coin, the remaining count is 3

  • 3 − Then select one 2 coin, the remaining count is 1

  • 4 − 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.

Where Greedy Approach Fails

In many problems, Greedy algorithm fails to find an optimal solution, moreover it may produce a worst solution. Problems like Travelling Salesman and Knapsack cannot be solved using this approach.

Examples

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

We will discuss these examples elaborately in the further chapters of this tutorial.

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