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What are some real-world applications of greedy algorithms that you have encountered or implemented?

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Greedy algorithms are a type of algorithm that make the optimal choice at each step, without considering the future consequences. They are often used to solve problems that involve finding the minimum or maximum of something, such as the shortest path, the largest profit, or the smallest cost. However, greedy algorithms do not always guarantee the best solution, and sometimes they can lead to suboptimal or even incorrect results. In this article, we will explore some real-world applications of greedy algorithms that you have encountered or implemented, and discuss their advantages and disadvantages.

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Akshat Rastogi

Coding Team Lead @ScaleAI | LLM Data Scientist @Turing | Ex-Quant Research @Morgan Stanley | AI Consultant | Teaching…

1 Coin change problem

One of the most classic examples of a greedy algorithm is the coin change problem, which asks how to make a given amount of money using the smallest number of coins of different denominations. A greedy algorithm would start by choosing the largest coin that does not exceed the amount, and repeat this process until the amount is zero or no more coins are available. For example, to make 36 cents using coins of 25, 10, 5, and 1 cent, a greedy algorithm would choose one 25-cent coin, one 10-cent coin, and one 1-cent coin, for a total of three coins. However, this is not the optimal solution, as we can use four 9-cent coins instead, which is smaller in both number and value.

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Akshat Rastogi

Coding Team Lead @ScaleAI | LLM Data Scientist @Turing | Ex-Quant Research @Morgan Stanley | AI Consultant | Teaching Assistant | Research Scholar | Freelancer
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A real-world analogy from the finance domain to the coin change problem can be seen when we allocate assets for portfolio optimization. Consider stocks as 'coins' with varying risks (denominations). A greedy approach might be to pick the stock with the highest expected return first, without considering its risk, and then the next highest, and so on. However, this might not provide the optimal risk-adjusted return. Just like in the coin problem, a more holistic approach might result in better portfolio performance, emphasizing the limitations of relying solely on greedy methods.

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2 Huffman coding

A common application of a greedy algorithm is Huffman coding, a technique for compressing data that assigns variable-length codes to symbols based on their frequencies. To do this, a greedy algorithm begins by creating a binary tree with each symbol as a leaf node and assigns a weight to each node equal to the frequency of the symbol. Then, it merges the two nodes with the smallest weights into a new node and assigns the sum of their weights to the new node until only one node remains. The code for each symbol is determined by the path from the root to the leaf, using 0 for left branches and 1 for right branches. For instance, if four symbols A, B, C, and D have frequencies 8, 3, 3, and 2 respectively, Huffman coding would create the following tree and codes: 16/8/A 0; 8/B 10; 8/C 11; 2/D 01. This method can reduce data size by using shorter codes for more frequent symbols and longer codes for less frequent symbols.

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Akshat Rastogi

Coding Team Lead @ScaleAI | LLM Data Scientist @Turing | Ex-Quant Research @Morgan Stanley | AI Consultant | Teaching Assistant | Research Scholar | Freelancer
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Imagine you're trying to save space in your bag by using custom-sized containers for your items. The items you use most frequently (e.g., your phone) get the smallest and easiest-to-reach container, while those used less often (e.g., a flashlight) get larger or harder-to-reach spaces. Huffman coding is like this bag optimization: the more frequent a symbol, the shorter and more accessible its code, ensuring the most efficient use of space.

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3 Activity selection problem

A third example of a greedy algorithm is the activity selection problem, which asks how to schedule the maximum number of non-overlapping activities that require a shared resource, such as a meeting room, a computer, or a person. A greedy algorithm would sort the activities by their finish times, and select the first activity that does not conflict with the previously selected ones. For example, if we have six activities with the following start and finish times:

A: (1, 4)

B: (3, 5)

C: (0, 6)

D: (5, 7)

E: (3, 9)

F: (6, 10)

A greedy algorithm would choose A, D, and F, for a total of three activities. This is also the optimal solution, as no other selection can include more than three activities.

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4 Knapsack problem

A final example of a greedy algorithm is the knapsack problem, which asks how to pack the most valuable items into a limited capacity knapsack, given the weights and values of each item. A greedy algorithm would sort the items by their value per unit weight, and select the items with the highest ratio until the knapsack is full or no more items are available. For example, if we have four items with the following weights and values:

A: (10, 60)

B: (20, 100)

C: (30, 120)

D: (40, 160)

And a knapsack capacity of 50, a greedy algorithm would choose B and C, for a total value of 220. However, this is not the optimal solution, as we can choose A and D instead, for a total value of 220.

Greedy algorithms are simple and fast to implement, and can often provide good solutions for many problems. However, they can also be misleading and unreliable, and sometimes miss better solutions or even produce wrong ones. Therefore, it is important to understand the limitations and assumptions of greedy algorithms, and to verify their correctness and optimality before using them.

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5 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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What are some real-world applications of greedy algorithms that you have encountered or implemented?

1

2

3

4

5

1 Coin change problem

2 Huffman coding

3 Activity selection problem

4 Knapsack problem

5 Here’s what else to consider

Algorithms

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What are some real-world applications of greedy algorithms that you have encountered or implemented?

1

2

3

4

5

1 Coin change problem

2 Huffman coding

3 Activity selection problem

4 Knapsack problem

5 Here’s what else to consider

Algorithms

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