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Efficient Array-Backed Priority Queue Implementation

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Introduction

A priority queue is a data structure that allows for efficient access to the minimum (or maximum) element in a collection. It is commonly used in algorithms such as Dijkstra's shortest path algorithm and Huffman coding. In this challenge, we will implement a priority queue backed by an array.

Skills Graph

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Priority Queue

Problem

Implement a priority queue backed by an array. The priority queue should support the following methods:

  • insert: insert a new element into the priority queue
  • extract_min: remove and return the minimum element from the priority queue
  • decrease_key: decrease the key of a given element in the priority queue

Requirements

To implement the priority queue, we need to meet the following requirements:

  • The methods supported by the priority queue should be insert, extract_min, and decrease_key.
  • There won't be any duplicate keys in the priority queue.
  • We don't need to validate inputs.
  • The priority queue should fit into memory.

Example Usage

Here are some examples of how to use the priority queue methods:

insert

  • insert general case: insert a new node into the priority queue.

extract_min

  • extract_min from an empty list: return None.
  • extract_min general case: remove and return the minimum node from the priority queue.

decrease_key

  • decrease_key an invalid key: return None.
  • decrease_key general case: decrease the key of a given node in the priority queue.

Summary

In this challenge, we implemented a priority queue backed by an array. The priority queue supports insert, extract_min, and decrease_key methods. We ensured that there are no duplicate keys in the priority queue, and the inputs don't need to be validated. The priority queue fits into memory.

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