6)The Complete Greedy Algorithms Roadmap: 8 Essential Patterns from Beginner to Expert (2026 Guide)

Greedy Algorithms are the “Smart Shortcuts” of Computer Science.

While Dynamic Programming meticulously calculates every possibility ($O(N^2)$), a Greedy Algorithm makes the best local choice at every step ($O(N \log N)$ or $O(N)$) and hopes it leads to the global optimum.

For top-tier interviews, you must know when to be greedy and when to stop. Using Greedy on a DP problem is an instant rejection. This guide covers the 8 Core Patterns that solve 95% of optimization problems.

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Part 1: The “Interval Scheduling” Pattern (Time Management)

The art of fitting the most tasks into a limited time.

1. Activity Selection / N-Meetings in One Room

• The Scenario: You have N meetings with Start and End times. Select the max number of non-overlapping meetings.
• The “Professor’s Rule”: Sort by End Time.
  • Why? Ending a meeting early leaves more room for the next one.
  • Algorithm: Pick the first meeting. For the rest, if Start[i] >= End[prev], pick it.

2. Minimum Platforms (Railway Problem)

• The Scenario: Trains arrive and depart. What is the minimum number of platforms needed so no train waits?
• The “Professor’s Rule”: Sort Arrivals and Departures separately.
  • Logic: Walk through time.
  • Train Arrives to Need Platform (+1).
  • Train Departs to Free Platform (-1).
  • Track the Maximum value ever reached.

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Part 2: The “Knapsack” Pattern (Value Density)

Getting the most bang for your buck.

3. Fractional Knapsack

• The Scenario: You can take parts of an item (e.g., Gold dust).
• The “Professor’s Rule”: Sort by Value Per Unit Weight (Ratio).
  • Take the “densest” items first.
  • Warning: If items cannot be broken (0/1 Knapsack), Greedy fails. You must use DP.

4. Job Sequencing with Deadlines

• The Scenario: Jobs have Profit and Deadline.
• The “Professor’s Rule”: Sort by Profit (Descending).
  • Try to do the highest paying job on the latest possible day (closest to deadline).
  • This saves early days for other jobs.

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Part 3: The “Array Traversal” Pattern (Linear Greedy)

Making decisions while walking through an array.

5. Jump Game (I & II)

• The Scenario: Can you reach the last index? (Or min jumps to reach it).
• The “Professor’s Rule”: Track Max Reach.
  • Iterate through array i.
  • Update MaxReach = max(MaxReach, i + nums[i]).
  • If i > MaxReach, you are stuck.

6. Gas Station (Circular Tour)

• The Scenario: Can you travel around a circular route of gas stations?
• The “Professor’s Rule”: The Total Surplus logic.
  • If Total Gas < Total Cost, it’s impossible.
  • Else, iterate. If current_tank < 0, reset start point to i + 1.

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Part 4: The “Structural” Pattern (Advanced)

Building efficient structures or encodings.

7. Huffman Coding (Compression)

• The Scenario: Lossless data compression (used in ZIP files).
• The “Professor’s Rule”: Build a tree from the bottom up.
  • Use a Min-Heap.
  • Extract two smallest frequency nodes, combine them, push back.
  • Repeat until one node remains.

8. Minimum Spanning Tree (Prim’s & Kruskal’s)

• The Scenario: Connect all cities with the cheapest wire cost.
• The “Professor’s Rule”:
  • Kruskal’s: Sort all edges. Add edge if it doesn’t form a cycle (Greedy!).
  • Prim’s: Start at a node. Always pick the cheapest neighbor (Greedy!).

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The “Professor’s Trap”: When Greedy FAILS

Add this section to save your students from rejection.

You cannot use Greedy for:

1. 0/1 Knapsack: (Items are indivisible).
2. Longest Path in Graph: (NP-Hard).
3. Coin Change (General Case): If coins are {1, 3, 4} and you need 6.
   • Greedy (Descending) takes 4, 1, 1 (3 coins).
   • Optimal is 3, 3 (2 coins).
   • Fix: Use DP for these.

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The Professor’s Cheat Code Sheet

Stick this table at the bottom of your post.

Problem Type	The Greedy “Trigger” (Sort By…)	Complexity
Max Activities	Sort by End Time (Asc)	O(N log N)
Fractional Knapsack	Sort by Value/Weight Ratio (Desc)	O(N log N)
Job Sequencing	Sort by Profit (Desc) + Use Sets	O(N^2) or O(N log N)
Min Platforms	Sort Arrivals & Departures Separately	O(N log N)
Boats to Save People	Sort + Two Pointers (Lightest + Heaviest)	O(N log N)
Jump Game / Gas Station	Linear Scan (Track Max Reach/Surplus)	O(N)
Huffman Coding	Min-Heap (Frequency)	O(N log N)
Candy Distribution	Two Pass (Left-to-Right, Right-to-Left)	O(N)

The Complete Greedy Algorithms Roadmap: 8 Essential Patterns from Beginner to Expert (2026 Guide)

Greedy Algorithms for Interview, Activity Selection Problem Greedy vs Dynamic Programming Huffman Coding Explained

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