Transitive Closure Algorithm

DIRECTORY.md

@@ -828,6 +828,7 @@
   * [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

matrix/transitive_closure.py

@@ -0,0 +1,49 @@
+def transitive_closure(graph: list[list[int]]) -> list[list[int]]:
+    """
+    Computes the transitive closure of a directed graph using the
+    Floyd-Warshall algorithm.
+
+    Args:
+        graph (list[list[int]]): Adjacency matrix representation of the graph.
+
+    Returns:
+        list[list[int]]: Transitive closure matrix.
+
+    >>> graph = [
+    ...     [0, 1, 1, 0],
+    ...     [0, 0, 1, 0],
+    ...     [1, 0, 0, 1],
+    ...     [0, 0, 0, 0]
+    ... ]
+    >>> result = transitive_closure(graph)
+    >>> for row in result:
+    ...     print(row)
+    [1, 1, 1, 1]
+    [1, 1, 1, 1]
+    [1, 1, 1, 1]
+    [0, 0, 0, 1]
+    """
+    n = len(graph)
+    ans = [[graph[i][j] for j in range(n)] for i in range(n)]
+
+    # Transtive closure of (i, i) will always be 1
+    for i in range(n):
+        ans[i][i] = 1
+
+    # Apply floyd Warshall Algorithm
+    # For each intermediate node k
+    for k in range(n):
+        for i in range(n):
+            for j in range(n):
+                # Check if a path exists between i to k and
+                # between 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()