Practice Problems

Practice Problems on Greedy Algorithms

Greedy algorithms are a type of algorithmic strategy where decisions are made step-by-step, taking the most optimal choice at each stage, hoping that the end result is the best overall solution. While greedy algorithms may not always guarantee the most optimal solution for all problems, they often work well for a variety of optimization problems. Here’s a collection of problems to help you practice and sharpen your skills in greedy algorithms. These problems are categorized by difficulty level, allowing you to progressively build your understanding.

Basic Problems:

These problems introduce you to foundational greedy techniques and focus on simple scenarios where a locally optimal choice leads to the globally optimal solution. Ideal for beginners, these problems help you build intuition for identifying when greedy algorithms can be applied effectively.

Activity Selection Problem:
The classic interval scheduling problem where you must select the maximum number of non-overlapping intervals. This is a fundamental example of applying greedy choices to select the most optimal sequence of activities.
Coin Change:
Solve the minimum number of coins required to make a certain amount. While this problem is often solved using dynamic programming, it can also introduce you to scenarios where greedy strategies might work.
Assign Cookies:
Distribute cookies to children in the most optimal way by satisfying as many children as possible with the given resources. This problem highlights resource allocation techniques using greedy methods.
Jump Game:
Determine if you can reach the last index of an array based on jump lengths. This problem tests your ability to make greedy decisions based on the farthest point you can reach at each step.
Minimum Platforms:
Find the minimum number of platforms required at a railway station to accommodate trains without any overlap in their schedules. This problem is an application of interval management using greedy algorithms.

Intermediate Problems:

Once you've grasped the basics, these problems offer more complex scenarios where greedy strategies can be applied. They may involve multiple decisions or constraints, requiring a deeper understanding of when and how to apply the greedy method.

Interval Scheduling Maximization:
This problem is similar to activity selection but with additional constraints. You need to remove the minimum number of intervals to prevent overlaps, requiring you to make choices that maximize the number of remaining intervals.
Huffman Coding:
A popular application of greedy algorithms, Huffman coding generates the most efficient (shortest) prefix-free binary codes for characters based on their frequencies. It demonstrates how greedy algorithms can optimize compression techniques.
Maximum Profit in Job Scheduling:
Schedule jobs to maximize profit, considering job durations and deadlines. This problem requires careful planning to balance job selections and maximize earnings over time.
Gas Station:
Determine if you can complete a circular route given a certain amount of gas at each station and the distance between them. This problem requires you to optimize your decisions to ensure you never run out of fuel.
Partition Labels:
Partition a string into as many parts as possible such that each letter appears in at most one part. This problem showcases how greedy algorithms can be used to create optimal divisions with specific constraints.

Advanced Problems:

These are more challenging problems that require a solid understanding of greedy techniques. They often involve multiple layers of decision-making and constraints that demand careful consideration and application of the greedy approach.

Minimum Number of Arrows to Burst Balloons:
Given a number of balloons, determine the minimum number of arrows required to burst all of them. This problem builds upon interval management techniques and introduces complexity in the form of overlapping intervals.
Candy:
Distribute candy to children based on their ratings in a way that satisfies certain conditions. This problem tests your ability to apply greedy choices to balance multiple constraints over an entire sequence.
Merge Intervals:
Merge overlapping intervals into as few as possible. It’s another variation of the interval scheduling problem but with the added complexity of modifying intervals as they overlap.
Stickers to Spell Word:
Given a set of stickers and a target word, determine the minimum number of stickers needed to form the word. This problem challenges you to apply greedy choices in the context of resource management.
Find Minimum in Rotated Sorted Array II:
Find the minimum element in a rotated sorted array that may contain duplicates. This problem is a test of how greedy algorithms can be applied to search and optimization problems.

Challenges:

For those looking to push their limits, these problems present even more difficult scenarios where the optimal greedy strategy may not be immediately obvious. They require a deep understanding of both the problem and the algorithmic strategy to succeed.

Minimum Cost to Hire K Workers:
Hire workers with different skill levels and wages, while minimizing the cost of hiring exactly K workers. This problem involves balancing multiple factors, such as skill-to-wage ratios, using a greedy strategy.
Job Sequencing Problem:
Given a set of jobs, each with a deadline and profit, find the sequence of jobs that maximizes profit while adhering to the deadlines. This is a classic scheduling problem requiring the application of greedy choices to optimize profits.
Largest Number:
Rearrange a list of numbers to form the largest possible number. This problem tests how greedy algorithms can be applied to sorting and number manipulation in order to maximize the result.

These problems are excellent practice for interviews and competitive programming, where greedy algorithms are frequently used. Be sure to analyze the problem constraints carefully to ensure that a greedy approach will lead to the optimal solution. Happy coding!