Greedy Approach for Algorithm Design

The Greedy Approach is a simple and fast algorithm design technique. At every step, it picks the best possible choice at that moment without considering past decisions or future consequences.
It works in a top-down manner, making one greedy choice after another.

Key Points

• Greedy is fast and often saves time.
• It does not guarantee the optimal (best) solution for all problems.
• Works well for many optimization problems.
• Examples: Kruskal’s, Prim’s, Dijkstra’s, Huffman Coding, Fractional Knapsack.

Optimization Problem

These are problems where you aim to maximize or minimize a certain result under given constraints.

Example

Factory Production Optimization

• Goal (Objective Function): Maximize profit from producing two products: A and B
• Constraint:
  • Total working hours ≤ 8 hrs/day
  • Labor cost ≤ ₹500/day

Here, you must decide how many units of A and B to produce so that profit is maximum but constraints are not violated.

Optimization = Making the best possible outcome (max profit or min cost) under limitations.

What is Greedy Approach?

Greedy approach always picks the best possible choice at the current moment, without considering:

• Past decisions,
• Future consequences.

Characteristics

• Works in top-down manner (one greedy choice at a time).
• Easy to implement.
• Less time-consuming.
• But does not always guarantee an optimal solution.

Applications of Greedy Approach

✔ Fractional Knapsack Problem

✔ Activity Selection Problem

✔ Job Sequencing with Deadlines

✔ Prim’s Minimum Spanning Tree

✔ Kruskal’s Minimum Spanning Tree

✔ Dijkstra’s Shortest Path

✔ Huffman Coding