結果

問題 No.114 遠い未来
ユーザー toyuzukotoyuzuko
提出日時 2021-01-31 16:47:13
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 4,345 bytes
コンパイル時間 440 ms
コンパイル使用メモリ 82,280 KB
実行使用メモリ 96,864 KB
最終ジャッジ日時 2024-06-29 01:34:53
合計ジャッジ時間 7,567 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 309 ms
78,876 KB
testcase_01 TLE -
testcase_02 -- -
testcase_03 -- -
testcase_04 -- -
testcase_05 -- -
testcase_06 -- -
testcase_07 -- -
testcase_08 -- -
testcase_09 -- -
testcase_10 -- -
testcase_11 -- -
testcase_12 -- -
testcase_13 -- -
testcase_14 -- -
testcase_15 -- -
testcase_16 -- -
testcase_17 -- -
testcase_18 -- -
testcase_19 -- -
testcase_20 -- -
testcase_21 -- -
testcase_22 -- -
testcase_23 -- -
testcase_24 -- -
testcase_25 -- -
testcase_26 -- -
testcase_27 -- -
権限があれば一括ダウンロードができます

ソースコード

diff # 

from heapq import heappop, heappush

class Heap():
    def __init__(self):
        self.heap = []

    def pop(self):
        res = heappop(self.heap)
        return res

    def push(self, x):
        heappush(self.heap, x)

    def top(self):
        return self.heap[0]

    def size(self):
        return len(self.heap)

    def is_empty(self):
        return self.size() == 0

class DisjointSetUnion():
    def __init__(self, n):
        self.n = n
        self.par_size = [-1] * n

    def merge(self, a, b):
        x = self.leader(a)
        y = self.leader(b)
        if x == y: return x
        if -self.par_size[x] < -self.par_size[y]: x, y = y, x
        self.par_size[x] += self.par_size[y]
        self.par_size[y] = x
        return x

    def same(self, a, b):
        return self.leader(a) == self.leader(b)

    def leader(self, a):
        x = a
        while self.par_size[x] >= 0:
            x = self.par_size[x]
        while self.par_size[a] >= 0:
            self.par_size[a] = x
            a = self.par_size[a]
        return x

    def size(self, a):
        return -self.par_size[self.leader(a)]

INF = 10**18

class Graph():
    def __init__(self, n):
        self.n = n
        self.graph = [[] for _ in range(n)]
        self.edge = dict()

    def add_edge(self, u, v, c):
        if v < u: u, v = v, u
        self.graph[u].append(v)
        self.graph[v].append(u)
        self.edge[u * self.n + v] = c

    def minimum_steiner_tree(self, terminal):
        t = len(terminal)
        if t <= 1: return 0
        dp = [[INF] * self.n for _ in range(1 << t)]
        for i, v in enumerate(terminal):
            dp[1 << i][v] = 0
        for bit in range(1, 1 << t):
            for v in range(self.n):
                subset = bit
                while subset:
                    dp[bit][v] = min(dp[bit][v], dp[subset][v] + dp[bit ^ subset][v])
                    subset = (subset - 1) & bit
            if bit == (1 << t) - 1: break
            heap = Heap()
            for v in range(self.n):
                heap.push((dp[bit][v], v))
            while not heap.is_empty():
                d, v = heap.pop()
                if dp[bit][v] < d: continue
                for adj in self.graph[v]:
                    if v < adj:
                        c = self.edge[v * self.n + adj]
                    else:
                        c = self.edge[adj * self.n + v]
                    if dp[bit][adj] > dp[bit][v] + c:
                        dp[bit][adj] = dp[bit][v] + c
                        heap.push((dp[bit][adj], adj))
        return dp[-1][terminal[0]]

    def kruskal(self):
        res = 0
        dsu = DisjointSetUnion(self.n)
        edges = []
        for v, g in enumerate(self.graph):
            for u in g:
                if u < v:
                    edges.append(u * self.n + v)
        edges.sort(key=lambda x: self.edge[x])
        for e in edges:
            u, v = divmod(e, self.n)
            if dsu.same(u, v): continue
            res += self.edge[e]
            dsu.merge(u, v)
        return res

import sys
input = sys.stdin.buffer.readline

N, M, T = map(int, input().split())

if T < 16:
    g = Graph(N)

    for _ in range(M):
        a, b, c = map(int, input().split())
        g.add_edge(a - 1, b - 1, c)

    V = [int(input()) - 1 for _ in range(T)]

    print(g.minimum_steiner_tree(V))

else:
    edge = [tuple(map(int, input().split())) for _ in range(M)]
    V = dict()

    for i in range(T):
        v = int(input())
        V[v - 1] = i

    W = []

    for i in range(N):
        if not i in V:
            W.append(i)

    res = 10**18

    for bit in range(1 << (N - T)):
        p = 0
        w = dict()
        for i in range(N):
            if (bit >> i) & 1:
                w[W[i]] = p
                p += 1
        g = Graph(T + p)
        for a, b, c in edge:
            if a - 1 in V:
                if b - 1 in V:
                    g.add_edge(V[a - 1], V[b - 1], c)
                elif b - 1 in w:
                    g.add_edge(V[a - 1], w[b - 1] + T, c)
            elif a - 1 in w:
                if b - 1 in V:
                    g.add_edge(w[a - 1] + T, V[b - 1], c)
                elif b - 1 in w:
                    g.add_edge(w[a - 1] + T, w[b - 1] + T, c)
        mst = g.kruskal()
        res = min(res, mst)

    print(res)
0