Refactor transitive closure function for clarity

Updated parameter and return type annotations for clarity. Modified variable names for consistency and corrected comments.

Author: cclauss

matrix/transitive_closure.py

@@ -4,39 +4,36 @@ def transitive_closure(graph: list[list[int]]) -> list[list[int]]:
     Floyd-Warshall algorithm.
 
     Args:
-        graph (list[list[int]]): Adjacency matrix representation of the graph.
+        graph: Adjacency matrix representation of the graph.
 
     Returns:
-        list[list[int]]: Transitive closure matrix.
+        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]
+    >>> transitive_closure(graph)  # doctest: +NORMALIZE_WHITESPACE
+    [[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)]
+    width = len(graph)
+    ans = [[graph[i][j] for j in range(width)] for i in range(width)]
 
-    # Transtive closure of (i, i) will always be 1
-    for i in range(n):
+    # Transitive closure of (i, i) will always be 1
+    for i in range(width):
         ans[i][i] = 1
 
-    # Apply floyd Warshall Algorithm
+    # 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.
+    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