Add get_word_path function to word_search.py

[kadambari25]

Describe your change:

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• Add or change doctests?
• Documentation change?

Implemented a new function get_word_path in backtracking/word_search.py.

This function returns the list of coordinates (row, column) representing the path of the given word in the board instead of just returning a boolean value.

• Uses backtracking (DFS) approach
• Returns list of tuples if the word is found
• Returns None if the word does not exist

Fixes #14500

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.
• All new Python files are placed inside an existing directory.
• 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.

[cclauss]

@priya-sundaram-dev review please as a potential solution to #14500

[priya-sundaram-dev]

Reviewed against #14500. The algorithm is correct — I ran it on the classic board [["A","B","C","E"],["S","F","C","S"],["A","D","E","E"]]:

• get_word_path(board, "ABCCED") → [(0,0),(0,1),(0,2),(1,2),(2,2),(2,1)] ✅ (valid adjacent, no cell reused)
• get_word_path(board, "SEE") → [(1,3),(2,3),(2,2)] ✅
• get_word_path(board, "ABCB") → None ✅ (correctly refuses to revisit B)
• non-present word → None ✅

Two things needed before this can merge, both to match the house style already set by word_exists directly above it:

1. Doctests are missing. The issue promised "comprehensive doctests," and TA requires a doctest for every new function (CI runs them). Please mirror word_exists's doctest block — a couple of found-path cases plus a not-found None case.

2. No input validation. word_exists validates board/word and raises ValueError with clear messages; get_word_path currently raises a bare IndexError on an empty word (word[0]) or empty board (board[0]). Since the two functions sit in the same file, the cleanest fix is to factor that validation into a small helper both call, or reuse the same guards, so the doctests can assert the same ValueError behavior.

Nit: the nested backtrack helper has no type hints — worth adding for consistency (r: int, c: int, index: int, path: list[tuple[int, int]], visited: set[tuple[int, int]]).

(The DIRECTORY.md Hamiltonian line in the diff is just the auto-generated sync — physics/hamiltonian.py already exists on main — nothing to do there.)

Nice, correct core; just needs the doctests + validation to be consistent with word_exists.