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Implements #12875

Implements #12850

Implements #12843

Implements #12838

Implements #12758

Implements #12744

Implements #12646

Implement Dijkstra's Algorithm for Shortest Path Computation

Task

Write a function to implement the Dijkstra's algorithm for shortest paths.

Acceptance Criteria

All tests must pass.

Summary of Changes

Added a comprehensive implementation of Dijkstra's algorithm for finding the shortest path in a weighted graph. The implementation includes:

  • A robust Dijkstra's algorithm function
  • Handling of graph representations
  • Support for weighted edges
  • Efficient path reconstruction
  • Error handling for invalid graph structures

Test Cases

  • Verify Dijkstra's algorithm correctly finds the shortest path in a simple graph
  • Check path reconstruction for complex graph structures
  • Ensure algorithm handles graphs with negative edge weights
  • Test performance with large graph inputs
  • Validate error handling for invalid graph inputs

This PR was created automatically by a Koii Network AI Agent powered by Together.ai.

This PR was created automatically by a Koii Network AI Agent powered by Together.ai.

This PR was created automatically by a Koii Network AI Agent powered by Together.ai.

This PR was created automatically by a Koii Network AI Agent powered by Together.ai.

This PR was created automatically by a Koii Network AI Agent powered by Together.ai.

This PR was created automatically by a Koii Network AI Agent powered by Together.ai.

This PR was created automatically by a Koii Network AI Agent powered by Together.ai.

Implements koii-network#12875

Implements koii-network#12850

Implements koii-network#12843

Implements koii-network#12838

Implements koii-network#12758

Implements koii-network#12744

Implements koii-network#12646

# Implement Dijkstra's Algorithm for Shortest Path Computation

## Task
Write a function to implement the Dijkstra's algorithm for shortest paths.

## Acceptance Criteria
All tests must pass.

## Summary of Changes
Added a comprehensive implementation of Dijkstra's algorithm for finding the shortest path in a weighted graph. The implementation includes:
- A robust Dijkstra's algorithm function
- Handling of graph representations
- Support for weighted edges
- Efficient path reconstruction
- Error handling for invalid graph structures

## Test Cases
 - Verify Dijkstra's algorithm correctly finds the shortest path in a simple graph
 - Check path reconstruction for complex graph structures
 - Ensure algorithm handles graphs with negative edge weights
 - Test performance with large graph inputs
 - Validate error handling for invalid graph inputs

This PR was created automatically by a Koii Network AI Agent powered by Together.ai.

This PR was created automatically by a Koii Network AI Agent powered by Together.ai.

This PR was created automatically by a Koii Network AI Agent powered by Together.ai.

This PR was created automatically by a Koii Network AI Agent powered by Together.ai.

This PR was created automatically by a Koii Network AI Agent powered by Together.ai.

This PR was created automatically by a Koii Network AI Agent powered by Together.ai.
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