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Commonly asked Greedy questions

1. Huffman Coding​

Definition:​

Huffman Coding is a method used for lossless data compression. It assigns variable-length codes to input characters, with shorter codes assigned to more frequent characters.

Characteristics:​

  • Building a Min-Heap: Create a min-heap to store characters and their frequencies.
  • Tree Structure: Combine the two least frequent nodes iteratively to build a binary tree.
  • Prefix Codes: The binary representation of characters is derived from the tree, ensuring that no code is a prefix of another.

Applications:​

  • Data compression (e.g., ZIP files)
  • Encoding for transmission

2. Prim’s Algorithm​

Definition:​

Prim’s Algorithm finds the Minimum Spanning Tree (MST) for a weighted undirected graph.

Characteristics:​

  • Start with a Single Vertex: Initialize the tree with one vertex.
  • Add the Cheapest Edge: At each step, add the cheapest edge connecting a vertex in the tree to one outside it.
  • Repeat: Continue until all vertices are included in the MST.

Applications:​

  • Network design
  • Approximation algorithms for NP-hard problems

3. Kruskal’s Algorithm​

Definition:​

Kruskal’s Algorithm is another method to find the Minimum Spanning Tree of a graph.

Characteristics:​

  • Sort Edges: Begin by sorting all edges in ascending order of their weight.
  • Add Edges: Add edges to the MST one by one, ensuring no cycles are formed using union-find data structures.
  • Complete MST: Repeat until you have V-1 edges (where V is the number of vertices).

Applications:​

  • Network routing
  • Cluster analysis

4. Fractional Knapsack Problem​

Definition:​

The Fractional Knapsack Problem allows taking fractions of an item to maximize the total value in a knapsack.

Characteristics:​

  • Value-to-Weight Ratio: Calculate the ratio for each item.
  • Sorting: Sort items by their value-to-weight ratio.
  • Greedy Selection: Add as much of the highest ratio item as possible until the knapsack is full.

Applications:​

  • Resource allocation
  • Budget management

5. Coin Change Problem​

Definition:​

The Coin Change Problem aims to find the minimum number of coins needed to make a certain amount using given denominations.

Characteristics:​

  • Greedy Approach: Use the largest denomination first.
  • Reduction: Continue until the remaining amount is zero.
  • Optimality: Works optimally for standard denominations (like US coins).

Applications:​

  • Currency exchange
  • Financial transactions

6. Minimum Number of Platforms​

Definition:​

The Minimum Number of Platforms problem determines how many platforms are required at a railway station to accommodate all trains at their arrival and departure times.

Characteristics:​

  • Sorting Events: Sort arrival and departure times.
  • Tracking Platforms: Use a greedy approach to track the number of trains at any given time and update the platform requirement.

Applications:​

  • Scheduling at transportation hubs
  • Event management

7. Staircase Problem​

Definition:​

The Staircase Problem involves finding the number of ways to reach the top of a staircase with N steps when you can take either 1 or 2 steps at a time.

Characteristics:​

  • Recurrence Relation: The number of ways to reach the nth step can be defined as ways(n) = ways(n-1) + ways(n-2).
  • Dynamic Programming: Although greedy, can also be solved using dynamic programming for optimization.

Applications:​

  • Combinatorial problems
  • Dynamic programming practice

8. Best Time to Buy and Sell Stock​

Definition:​

This problem involves determining the maximum profit you can achieve by buying and selling a stock once, given an array of stock prices.

Characteristics:​

  • Tracking Minimum Price: Keep track of the minimum price encountered so far.
  • Calculating Profit: For each price, calculate the potential profit and update the maximum profit if it exceeds the current maximum.

Applications:​

  • Stock market analysis
  • Financial modeling

9. Minimize Maximum Distance to Assign Tasks​

Definition:​

Given a set of workers and tasks, this problem aims to assign tasks in a way that minimizes the maximum distance any worker has to travel.

Characteristics:​

  • Sorting: Sort workers and tasks based on their distances.
  • Greedy Assignment: Assign tasks to the nearest available worker to minimize the maximum distance.

Applications:​

  • Task scheduling
  • Logistics optimization

10. Rearranging Coins Problem​

Definition:​

This problem involves determining if you can rearrange a set of coins to satisfy specific conditions or form valid sequences.

Characteristics:​

  • Greedy Grouping: Use a greedy approach to group or arrange coins based on given criteria.
  • Condition Checking: Ensure conditions are met after each rearrangement or assignment.

Applications:​

  • Resource management
  • Game theory

These greedy algorithms and patterns demonstrate efficient problem-solving techniques for various applications in computer science and operations research.