Greedy Algorithm in data structure [ with basic concept]

Greedy Algorithm in data structure [ with basic concept]

Greedy Algorithm in Data Structure

 Basic Concept of Greedy Algorithm

A Greedy Algorithm is an approach that makes the best possible choice at each step to find the optimal solution for a problem. It never looks back or revises previous choices. Instead, it follows a step-by-step process, always choosing the option that seems best at that moment.

Key Idea:
 Always take the locally optimal choice, hoping it leads to a globally optimal solution.

 Characteristics of Greedy Algorithms

Locally Optimal Choice – Picks the best option at each step.
No Backtracking – Does not reconsider previous decisions.
Fast & Efficient – Works well for specific problems.
Not Always Optimal – Sometimes fails to find the best solution.

Steps in a Greedy Algorithm

Define the problem – Break it into steps.
Choose the best solution – Pick the most beneficial option at each step.
Repeat until complete – Continue selecting optimal choices until a solution is reached.

 Examples of Greedy Algorithms

 Coin Change Problem

Problem: Find the minimum number of coins to make a given amount.

Example: If coins available are ₹1, ₹2, ₹5, ₹10, and the target amount is ₹18, the greedy approach picks:
₹10 → ₹5 → ₹2 → ₹1 → (Total: 4 coins)

Limitation: Doesn’t work for all denominations (e.g., {₹1, ₹3, ₹4}, target = ₹6).

 Fractional Knapsack Problem

Problem: Given items with values & weights, maximize the total value within a weight limit.

Solution: Choose items with the highest value-to-weight ratio first.

Works well for fractional selection (items can be broken into parts).
Fails in the 0/1 Knapsack Problem (where items can’t be split).

 Activity Selection Problem

Problem: Select the maximum number of non-overlapping activities from a given set of activities with start and end times.

Solution:
 Sort activities by end time.
 Always choose the earliest finishing activity that doesn’t overlap.

Greedy approach gives an optimal solution.

 Huffman Coding (Data Compression)

Problem: Reduce file size by using shorter codes for frequent characters.

Solution:
 Create a binary tree where the most frequent characters have shorter codes.
 Uses a priority queue to select the smallest elements at each step.

Used in ZIP file compression & text encoding.

 When to Use Greedy Algorithms?

When the problem has the “Greedy Choice Property” → Making a local optimal choice leads to a global optimum.
When the problem has “Optimal Substructure” → The optimal solution contains optimal sub-solutions.
When efficiency is important → Greedy algorithms are usually faster than dynamic programming.

 Time Complexity of Greedy Algorithms

Usually O(n log n) or O(n), depending on sorting & selection operations.

 Conclusion

Greedy algorithms are simple, fast, and effective for problems where local choices lead to the best global result. However, they don’t always guarantee the optimal solution, so they must be used carefully.

Best used in problems like: Huffman coding, activity selection, fractional knapsack.
Fails in problems like: 0/1 knapsack, some coin change cases.

Would you like examples in code (Python/C++) for better understanding?

Here’s a clear explanation of the Greedy Algorithm in data structures with its basic concept, examples, and applications:

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What is a Greedy Algorithm?

A greedy algorithm is an approach for solving problems by making the best possible choice at each step with the hope that this leads to an overall optimal solution.

Key idea: Take the best choice available right now, without thinking about future consequences.

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Basic Properties of Greedy Algorithms:

1. Greedy Choice Property – A global optimum can be arrived at by choosing a local optimum.

2. Optimal Substructure – A problem has an optimal solution composed of optimal solutions to its subproblems.

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Steps in a Greedy Algorithm:

1. Sort or prioritize choices (if needed).

2. At each step, choose the best available option.

3. Repeat until the problem is solved.

4. No backtracking or revision.

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Example 1: Coin Change Problem

Problem: You have coins of denominations ₹1, ₹2, ₹5, ₹10, and ₹20. You want to make ₹43 using the least number of coins.

Greedy Strategy:

• Pick the largest denomination coin <= remaining amount.

• Repeat until the amount becomes zero.

Solution:

• ₹20 → 2 coins

• ₹2 → 1 coin

• ₹1 → 1 coin
  Total coins = 5

Note: This works only with certain denominations. For arbitrary coin values, greedy may not give optimal results.

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Example 2: Activity Selection Problem

Problem: Given n activities with start and end times, choose the maximum number of activities that don’t overlap.

Greedy Strategy:

• Sort activities by earliest finish time.

• Always pick the next activity that starts after the current one ends.

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Common Applications:

• Kruskal’s Algorithm (Minimum Spanning Tree)

• Prim’s Algorithm (Minimum Spanning Tree)

• Dijkstra’s Algorithm (Shortest Path)

• Huffman Coding (Data Compression)

• Fractional Knapsack Problem

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Advantages:

• Fast and simple to implement

• Efficient for many optimization problems

Disadvantages:

• Doesn’t always give the globally optimal solution

• Not suitable for problems needing backtracking or exhaustive search

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Would you like a code example, flowchart, or visual explanation for a greedy algorithm?

Greedy Algorithm in data structure [ with basic concept]

UNIT-II1 GREEDY METHOD

Greedy Algorithms