提出 #42249860

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ソースコード 拡げる

from sklearn import mixture
import numpy as np
import typing
from math import sqrt, ceil
import networkx as nx


class DSU:
    def __init__(self, n: int = 0) -> None:
        self._n = n
        self.parent_or_size = [-1] * n
    def merge(self, a: int, b: int) -> int:
        assert 0 <= a < self._n
        assert 0 <= b < self._n
        x = self.leader(a)
        y = self.leader(b)
        if x == y:
            return x
        if -self.parent_or_size[x] < -self.parent_or_size[y]:
            x, y = y, x
        self.parent_or_size[x] += self.parent_or_size[y]
        self.parent_or_size[y] = x
        return x
    def same(self, a: int, b: int) -> bool:
        assert 0 <= a < self._n
        assert 0 <= b < self._n
        return self.leader(a) == self.leader(b)
    def leader(self, a: int) -> int:
        assert 0 <= a < self._n
        parent = self.parent_or_size[a]
        while parent >= 0:
            if self.parent_or_size[parent] < 0:
                return parent
            self.parent_or_size[a], a, parent = (
                self.parent_or_size[parent],
                self.parent_or_size[parent],
                self.parent_or_size[self.parent_or_size[parent]]
            )
        return a
    def size(self, a: int) -> int:
        assert 0 <= a < self._n
        return -self.parent_or_size[self.leader(a)]
    def groups(self) -> typing.List[typing.List[int]]:
        leader_buf = [self.leader(i) for i in range(self._n)]
        result: typing.List[typing.List[int]] = [[] for _ in range(self._n)]
        for i in range(self._n):
            result[leader_buf[i]].append(i)
        return list(filter(lambda r: r, result))


def distance(a, b):
    return ((a[0] - b[0]) ** 2 + (a[1] - b[1]) ** 2)


def main():
    # Input
    n, m, k = map(int, input().split())
    verticles = np.array([list(map(int, input().split())) for _ in range(n)], dtype=int)
    edges = {}
    Graph = nx.Graph()
    for i in range(m):
        u, v, c = map(int, input().split())
        edges[(u - 1, v - 1)] = i
        edges[(v - 1, u - 1)] = i
        Graph.add_edge(u - 1, v - 1, weight=c)
    people = np.array([list(map(int, input().split())) for _ in range(k)], dtype=int)
    power = np.zeros(n)

    # Clustering
    model = mixture.GaussianMixture(n_components=50).fit(people)
    result = model.predict(people)
    nearest = np.array([-1] * k, dtype=int)
    for i in range(50):
        # クラスタの中心を求める
        center = model.means_[i]
        # クラスタの中心から最も近い点を求める
        minim = (0, 10 ** 9)
        for j in range(n):
            dst = distance(center, verticles[j])
            if minim[1] > dst:
                minim = (j, dst)
        # 最も遠い人
        farthest = 0
        for j in range(k):
            if result[j] == i and nearest[j] == -1:
                dst = distance(people[j], verticles[minim[0]])
                if farthest < dst:
                    farthest = dst
        power[minim[0]] = max(power[minim[0]], farthest)

    powers = [(i, power[i]) for i in range(n)]
    powers = filter(lambda x: x[1] > 0, powers)
    powers = sorted(powers, key=lambda x: x[1], reverse=True)
    nearest = np.array([-1] * k, dtype=int)
    for (i, p) in powers:
        farthest = 0
        for j in range(k):
            if distance(people[j], verticles[i]) <= p and nearest[j] == -1:
                nearest[j] = i
                farthest = max(farthest, distance(people[j], verticles[i]))
        power[i] = farthest

    # 使う予定の頂点について MST
    tmp_edges = []
    for i in range(0, n):
        if power[i] == 0:
            continue
        tmp_edges.append((nx.shortest_path_length(Graph, 0, i, weight="weight"), 0, i))
        for j in range(i + 1, n):
            if power[j] == 0:
                continue
            tmp_edges.append((nx.shortest_path_length(Graph, i, j, weight="weight"), i, j))
    tmp_edges = sorted(tmp_edges, key=lambda x: x[0])
    dsu = DSU(n)
    used_edges = np.zeros(m)
    for (c, u, v) in tmp_edges:
        if not dsu.same(u, v):
            dsu.merge(u, v)
            path = nx.shortest_path(Graph, u, v, weight="weight")
            for i in range(len(path) - 1):
                used_edges[edges[(path[i], path[i + 1])]] = 1

    # Output
    for i in range(n):
        print(min(int(ceil(sqrt(power[i]))), 5000), end=" ")
    print()
    for i in range(m):
        if used_edges[i] == 1:
            print(1, end=" ")
        else:
            print(0, end=" ")
    print()


if __name__ == "__main__":
    main()

提出情報

ジャッジ結果