Transitive Closure Algorithm

DIRECTORY.md

@@ -1032,6 +1032,7 @@
   * [Spiral Print](matrix/spiral_print.py)
   * Tests
     * [Test Matrix Operation](matrix/tests/test_matrix_operation.py)
+  * [Transitive Closure](matrix/transitive_closure.py)
   * [Validate Sudoku Board](matrix/validate_sudoku_board.py)
 
 ## [Networking Flow](networking_flow)

matrix/transitive_closure.py

@@ -0,0 +1,52 @@
+"""
+https://en.wikipedia.org/wiki/Transitive_closure#In_graph_theory
+https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm
+"""
+
+
+def transitive_closure(graph: list[list[int]]) -> list[list[int]]:
+    """
+    Compute the transitive closure of a directed graph using the
+    Floyd-Warshall algorithm.
+
+    Args:
+        graph: Adjacency matrix representation of the graph.
+
+    Returns:
+        Transitive closure matrix.
+
+    >>> graph = [
+    ...     [0, 1, 1, 0],
+    ...     [0, 0, 1, 0],
+    ...     [1, 0, 0, 1],
+    ...     [0, 0, 0, 0]
+    ... ]
+    >>> transitive_closure(graph)  # doctest: +NORMALIZE_WHITESPACE
+    [[1, 1, 1, 1],
+     [1, 1, 1, 1],
+     [1, 1, 1, 1],
+     [0, 0, 0, 1]]
+    """
+    width = len(graph)
+    ans = [[graph[i][j] for j in range(width)] for i in range(width)]
+
+    # Transitive closure of (i, i) will always be 1
+    for i in range(width):
+        ans[i][i] = 1
+
+    # Apply Floyd-Warshall Algorithm
+    # For each intermediate node k
+    for k in range(width):
+        for i in range(width):
+            for j in range(width):
+                # Check if a path exists from i to k and from k to j.
+                if ans[i][k] == 1 and ans[k][j] == 1:
+                    ans[i][j] = 1
+
+    return ans
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()