fix(backtracking): Correct doctest in m_coloring_problem

backtracking/m_coloring_problem.py

@@ -0,0 +1,86 @@
+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.
+
+ >>> is_safe(0, 1, [[0,1],[1,0]], 2, [0,1])
+ False
+ >>> 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(num_vertices)
+ )
+
+
+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 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]])
+ True
+ """
+ if node == num_vertices:
+ return True
+ 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, max_colors, num_vertices, graph):
+ return True
+ col[node] = 0
+ return False
+
+
+def graph_coloring(graph: list[list[int]], max_colors: int, num_vertices: int) -> bool:
+ """
+ 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] * num_vertices
+ return solve(0, col, max_colors, num_vertices, graph)
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()
+
+ num_vertices = int(input("Enter vertices: "))
+ num_edges = int(input("Enter edges: "))
+ graph = [[0] * num_vertices for _ in range(num_vertices)]
+
+ print("Enter edges (u v):")
+ for _ in range(num_edges):
+ try:
+ u, v = map(int, input().split())
+ if 0 <= u < num_vertices and 0 <= v < num_vertices:
+ graph[u][v] = 1
+ graph[v][u] = 1
+ else:
+ print("Invalid edge.")
+ except ValueError:
+ print("Invalid input.")
+
+ max_colors = int(input("Enter max colors: "))
+
+ if graph_coloring(graph, max_colors, num_vertices):
+ print("Coloring possible.")
+ else:
+ print("Coloring not possible.")