65 lines
1.7 KiB
Python
65 lines
1.7 KiB
Python
import sys
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input = sys.stdin.readline
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class TriangleTrees:
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def __init__(self, n, m, e):
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"""
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input graph should be triangle-trees
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"""
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self.n, self.m = n, m
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self.e: list[int] = e
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self.e_find: list[list[int]] = [[] for _ in range(self.n)]
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for u, v in self.e:
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self.e_find[u - 1].append(v - 1)
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self.e_find[v - 1].append(u - 1)
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def check_cycle(self) -> bool:
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D = [(-1, i) for i in range(self.n)]
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vis = [0] * self.n
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cycle_flag = False
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while D:
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before, now = D.pop()
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if vis[now]:
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continue
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vis[now] = 1
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for nxt in self.e_find[now]:
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if nxt == before:
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continue
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elif vis[nxt]:
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cycle_flag = True
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break
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else:
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D.append((now, nxt))
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if cycle_flag:
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break
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return cycle_flag
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def solve(self) -> list[int]:
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K_MAX = 3 if self.check_cycle() else 2
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vis = [0] * self.n
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colour = [-1] * self.n
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D = [(i, i) for i in range(self.n)]
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while D:
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(before, now) = D.pop()
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if vis[now]:
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continue
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else:
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vis[now] = 1
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now_color = (colour[before] + 1) % K_MAX
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colour[now] = now_color
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for nxt in self.e_find[now]:
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if not vis[nxt]:
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D.append((now, nxt))
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return colour
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if __name__ == "__main__":
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n, m = map(int, input().split())
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e = [tuple(map(int, input().split())) for _ in range(m)]
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print(*map(lambda x: x + 1, TriangleTrees(n, m, e).solve()), sep=" ")
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