Add A* (A-star) pathfinding algorithm with doctests and type hints

[umarprogrammer19]

A* (A-star) pathfinding algorithm with doctests and type hints

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 keeps state with g (cost-so-far), a min-heap priority queue for f = g + h, and reconstructs the 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) for open/closed sets and parent/g-score maps on the explored set.

References

A* search algorithm — Wikipedia
Manhattan distance Taxicab geometry

Checklist

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

[algorithms-keeper]

Closing this pull request as invalid

@umarprogrammer19, this pull request is being closed as none of the checkboxes have been marked. It is important that you go through the checklist and mark the ones relevant to this pull request. Please read the Contributing guidelines.

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