matrix/count_paths.py (TheAlgorithms#7533)

* added recursive dfs backtracking for count paths with doctests

* fixed doc testing

* added type hints

* redefined r as row, c as col

* fixed naming conventions, ran mypy, only tests that didn't pass were using List[], rathan list()

* added another doctest, as well as a explanation above

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* Update matrix/count_paths.py

Co-authored-by: Chris O <[email protected]>

* Update matrix/count_paths.py

Co-authored-by: Chris O <[email protected]>

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Apply suggestions from code review

Co-authored-by: Caeden Perelli-Harris <[email protected]>

Co-authored-by: J <[email protected]>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Chris O <[email protected]>
Co-authored-by: Caeden Perelli-Harris <[email protected]>

Author: 5 people

matrix/count_paths.py

@@ -0,0 +1,75 @@
+"""
+Given a grid, where you start from the top left position [0, 0],
+you want to find how many paths you can take to get to the bottom right position.
+
+start here  ->   0  0  0  0
+                 1  1  0  0
+                 0  0  0  1
+                 0  1  0  0  <- finish here
+how many 'distinct' paths can you take to get to the finish?
+Using a recursive depth-first search algorithm below, you are able to
+find the number of distinct unique paths (count).
+
+'*' will demonstrate a path
+In the example above, there are two distinct paths:
+1.                2.
+    *  *  *  0      *  *  *  *
+    1  1  *  0      1  1  *  *
+    0  0  *  1      0  0  *  1
+    0  1  *  *      0  1  *  *
+"""
+
+
+def depth_first_search(grid: list[list[int]], row: int, col: int, visit: set) -> int:
+    """
+    Recursive Backtracking Depth First Search Algorithm
+
+    Starting from top left of a matrix, count the number of
+    paths that can reach the bottom right of a matrix.
+    1 represents a block (inaccessible)
+    0 represents a valid space (accessible)
+
+    0  0  0  0
+    1  1  0  0
+    0  0  0  1
+    0  1  0  0
+    >>> grid = [[0, 0, 0, 0], [1, 1, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0]]
+    >>> depth_first_search(grid, 0, 0, set())
+    2
+
+    0  0  0  0  0
+    0  1  1  1  0
+    0  1  1  1  0
+    0  0  0  0  0
+    >>> grid = [[0, 0, 0, 0, 0], [0, 1, 1, 1, 0], [0, 1, 1, 1, 0], [0, 0, 0, 0, 0]]
+    >>> depth_first_search(grid, 0, 0, set())
+    2
+    """
+    row_length, col_length = len(grid), len(grid[0])
+    if (
+        min(row, col) < 0
+        or row == row_length
+        or col == col_length
+        or (row, col) in visit
+        or grid[row][col] == 1
+    ):
+        return 0
+    if row == row_length - 1 and col == col_length - 1:
+        return 1
+
+    visit.add((row, col))
+
+    count = 0
+    count += depth_first_search(grid, row + 1, col, visit)
+    count += depth_first_search(grid, row - 1, col, visit)
+    count += depth_first_search(grid, row, col + 1, visit)
+    count += depth_first_search(grid, row, col - 1, visit)
+
+    visit.remove((row, col))
+    return count
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()