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python:实现图形着色算法(附完整源码)

天蓝Sea 2022-07-27 阅读 256


python:实现图形着色算法

def valid_coloring(
neighbours: list[int], colored_vertices: list[int], color: int
) -> bool:

# Does any neighbour not satisfy the constraints
return not any(
neighbour == 1 and colored_vertices[i] == color
for i, neighbour in enumerate(neighbours)
)


def util_color(
graph: list[list[int]], max_colors: int, colored_vertices: list[int], index: int
) -> bool:
"""
Pseudo-Code

Base Case:
1. Check if coloring is complete
1.1 If complete return True (meaning that we successfully colored the graph)

Recursive Step:
2. Iterates over each color:
Check if the current coloring is valid:
2.1. Color given vertex
2.2. Do recursive call, check if this coloring leads to a solution
2.4. if current coloring leads to a solution return
2.5. Uncolor given vertex

>>> graph = [[0, 1, 0, 0, 0],
... [1, 0, 1, 0, 1],
... [0, 1, 0, 1, 0],
... [0, 1, 1, 0, 0],
... [0, 1, 0, 0, 0]]
>>> max_colors = 3
>>> colored_vertices = [0, 1, 0, 0, 0]
>>> index = 3

>>> util_color(graph, max_colors, colored_vertices, index)
True

>>> max_colors = 2
>>> util_color(graph, max_colors, colored_vertices, index)
False
"""

# Base Case
if index == len(graph):
return True

# Recursive Step
for i in range(max_colors):
if valid_coloring(graph[index], colored_vertices, i):
# Color current vertex
colored_vertices[index] = i
# Validate coloring
if util_color(graph, max_colors, colored_vertices, index + 1):
return True
# Backtrack
colored_vertices[index] = -1
return False


def color(graph: list[list[int]], max_colors: int) -> list[int]:
"""
Wrapper function to call subroutine called util_color
which will either return True or False.
If True is returned colored_vertices list is filled with correct colorings

>>> graph = [[0, 1, 0, 0, 0],
... [1, 0, 1, 0, 1],
... [0, 1, 0, 1, 0],
... [0, 1, 1, 0, 0],
... [0, 1, 0, 0, 0]]

>>> max_colors = 3
>>> color(graph, max_colors)
[0, 1, 0, 2, 0]

>>> max_colors = 2
>>> color(graph, max_colors)
[]
"""
colored_vertices = [-1] * len(graph)

if util_color(graph, max_colors, colored_vertices, 0):
return colored_vertices

return []


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