Add A* (A-star) Pathfinding Algorithm with Doctests & Type Hints

[umarprogrammer19]

Summary

This PR adds a pure-Python implementation of the A (A-star) pathfinding algorithm that works over arbitrary graphs via a neighbors(node) callback and an admissible heuristic h(node, goal). The module includes comprehensive docstrings, type hints, and doctests showing usage on a 4-connected grid with Manhattan distance. The implementation tracks g (cost-so-far), uses a min-heap priority queue for f = g + h, and reconstructs the optimal path via a parent map.*

File added

searches/astar.py (all lowercase, no spaces or dashes)

Complexity

1. Time: Depends on heuristic quality and branching factor; worst-case comparable to Dijkstra’s on the explored subgraph.
2. Space: O(V) over explored nodes for open/closed sets and parent/g-score maps.

Reference

A* search algorithm — (Wikipedia) Manhattan distance (Taxicab geometry)

Describe your change:

• [x] Add an algorithm?
• [x] Fix a bug or typo in an existing algorithm?
• [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
• [x] Documentation change?

Checklist:

• [x] I have read CONTRIBUTING.md.
• [x] This pull request is all my own work -- I have not plagiarized.
• [x] I know that pull requests will not be merged if they fail the automated tests.
• [x] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• [x] All new Python files are placed inside an existing directory.
• [x] All filenames are in all lowercase characters with no spaces or dashes.
• [x] All functions and variable names follow Python naming conventions.
• [x] All function parameters and return values are annotated with Python type hints.
• [x] All functions have doctests that pass the automated testing.
• [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
• [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: "Fixes #ISSUE-NUMBER".