Update m_coloring_problem.py

Author: sgindeed

backtracking/m_coloring_problem.py

@@ -1,9 +1,4 @@
-from typing import List
-
-
-def is_safe(
-    node: int, color: int, graph: List[List[int]], n: int, col: List[int]
-) -> bool:
+def is_safe(node: int, color: int, graph: list[list[int]], num_vertices: int, col: list[int]) -> bool:
     """
     Check if it is safe to assign a color to a node.
 
@@ -12,37 +7,37 @@ def is_safe(
     >>> is_safe(0, 2, [[0,1],[1,0]], 2, [0,1])
     True
     """
-    return all(not (graph[node][k] == 1 and col[k] == color) for k in range(n))
+    return all(not (graph[node][k] == 1 and col[k] == color) for k in range(num_vertices))
 
 
-def solve(node: int, col: List[int], m: int, n: int, graph: List[List[int]]) -> bool:
+def solve(node: int, col: list[int], max_colors: int, num_vertices: int, graph: list[list[int]]) -> bool:
     """
-    Recursively try to color the graph using at most m colors.
+    Recursively try to color the graph using at most max_colors.
 
     >>> solve(0, [0]*3, 3, 3, [[0,1,0],[1,0,1],[0,1,0]])
     True
     >>> solve(0, [0]*3, 2, 3, [[0,1,0],[1,0,1],[0,1,0]])
     False
     """
-    if node == n:
+    if node == num_vertices:
         return True
-    for c in range(1, m + 1):
-        if is_safe(node, c, graph, n, col):
+    for c in range(1, max_colors + 1):
+        if is_safe(node, c, graph, num_vertices, col):
             col[node] = c
-            if solve(node + 1, col, m, n, graph):
+            if solve(node + 1, col, max_colors, num_vertices, graph):
                 return True
             col[node] = 0
     return False
 
 
-def graph_coloring(graph: List[List[int]], m: int, n: int) -> bool:
+def graph_coloring(graph: list[list[int]], max_colors: int, num_vertices: int) -> bool:
     """
-    Determine if the graph can be colored with at most m colors.
+    Determine if the graph can be colored with at most max_colors.
 
     >>> graph_coloring([[0,1,1],[1,0,1],[1,1,0]], 3, 3)
     True
     >>> graph_coloring([[0,1,1],[1,0,1],[1,1,0]], 2, 3)
     False
     """
-    col = [0] * n
-    return solve(0, col, m, n, graph)
+    col = [0] * num_vertices
+    return solve(0, col, max_colors, num_vertices, graph)