How to Store the Optimal Path in a Priority Queue for A* Search

Learn how to effectively track the optimal path taken by the A* search algorithm while traversing a grid, including implementation in C+ + .
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This video is based on the question https://stackoverflow.com/q/67265063/ asked by the user 'Sakib Khan' ( https://stackoverflow.com/u/13827116/ ) and on the answer https://stackoverflow.com/a/67289518/ provided by the user 'Kenneth McKanders' ( https://stackoverflow.com/u/1274026/ ) at 'Stack Overflow' website. Thanks to these great users and Stackexchange community for their contributions.

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Tracking the Optimal Path in A* Search: An In-Depth Guide

When implementing algorithms for pathfinding, especially A*, one of the key challenges developers face is keeping a record of the complete path taken from the starting point to the goal. This proces can efficiently guide you while debugging or developing enhancements, so let’s dive into how you can effectively store the complete path that a priority queue follows during the A* search.

Understanding the A* Search Problem

The A* search algorithm is a popular choice for finding the shortest path in a grid-based game or map. In our scenario, you're given a user-defined matrix representing the world where:

S represents the starting point.

G represents the goal.

0s are open cells (where you can move).

1s are obstacles (where movement is not possible).

With specific movement costs defined for the actions allowed (moving up, right, or diagonally), your objective is to compute the most efficient path from S to G using the A* algorithm, utilizing a heuristic (in this case, Manhattan Distance) for guidance.

The Challenge: Storing the Path

While your current implementation correctly calculates the path cost, you’ve noticed an inefficiency when storing visited nodes, leading to a longer path than necessary. What you really want is to track the optimal path taken to reach the goal node rather than just all the states visited.

Solution Overview

To store the optimal path alongside calculations of cost, we need to modify the structure of our node class, allowing nodes to link back to their predecessors. Here’s how you can do it:

1. Modify the Node Class

Change your node class to include a pointer to the next node, effectively allowing it to create a linked list of nodes representing the path taken:

[[See Video to Reveal this Text or Code Snippet]]

2. Displaying the Full Path

Next, add a method to your node class to display the full path from start to goal by traversing back through the linked nodes:

[[See Video to Reveal this Text or Code Snippet]]

This method walks through the linked list of nodes and prints their coordinates, showcasing the path taken.

3. Update the A* Search Function

Customize your A_search() function to support this new structure. Every time you encounter a new node, link it back to the predecessor node which offers the pathway:

[[See Video to Reveal this Text or Code Snippet]]

Final Steps: Implementing the Changes

After updating the A_search() method, ensure each time you create a new node (when moving up, right, or diagonally), associate it with the previous node by setting new_node->next = temp. This way, when you reach the goal state, you can trace back the optimal path through any node.

Conclusion

By restructuring the node class and enhancing the A_search() function as described, you can store and display the optimal paths efficiently. This improvement not only provides insights into the algorithm's execution but also enhances your ability to debug or optimize future pathfinding behavior.

Adopting this method will ensure your A* implementation is more robust and insightful for tracking the actual route taken in the search process.

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