結果

問題 No.1950 片道きゃっちぼーる
コンテスト
ユーザー tktk_snsn
提出日時 2022-05-20 22:31:43
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,146 ms / 3,000 ms
コード長 4,655 bytes
コンパイル時間 211 ms
コンパイル使用メモリ 82,376 KB
実行使用メモリ 460,520 KB
最終ジャッジ日時 2024-09-20 08:45:51
合計ジャッジ時間 12,970 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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ファイルパターン 結果
other AC * 23
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 # 

import sys
input = sys.stdin.buffer.readline
sys.setrecursionlimit(10 ** 7)


class SCC_graph(object):
    def __init__(self, n):
        """n:ノード数"""
        self.n = n
        self.edges = []

    def add_edge(self, frm, to):
        """frm -> toへ有効辺を張る"""
        self.edges.append((frm, to))

    def __csr(self):
        self.start = [0] * (self.n + 1)
        self.elist = [0] * len(self.edges)
        for frm, to in self.edges:
            self.start[frm + 1] += 1
        for i in range(1, self.n + 1):
            self.start[i] += self.start[i - 1]
        cnt = self.start[:]
        for frm, to in self.edges:
            self.elist[cnt[frm]] = to
            cnt[frm] += 1

    def __dfs(self, v):
        self.low[v] = self.now_ord
        self.order[v] = self.now_ord
        self.now_ord += 1
        self.visited.append(v)
        for i in range(self.start[v], self.start[v + 1]):
            to = self.elist[i]
            if self.order[to] == -1:
                self.__dfs(to)
                self.low[v] = min(self.low[v], self.low[to])
            else:
                self.low[v] = min(self.low[v], self.order[to])
        if self.low[v] == self.order[v]:
            while self.visited:
                u = self.visited.pop()
                self.order[u] = self.n
                self.ids[u] = self.group_num
                if u == v:
                    break
            self.group_num += 1

    def _make_scc_ids(self):
        self.__csr()
        self.now_ord = 0
        self.group_num = 0
        self.visited = []
        self.low = [0] * self.n
        self.ids = [0] * self.n
        self.order = [-1] * self.n
        for i in range(self.n):
            if self.order[i] == -1:
                self.__dfs(i)
        for i in range(self.n):
            self.ids[i] = self.group_num - 1 - self.ids[i]

    def scc(self):
        """
        強連結成分分解O(N+M), groupsを返す
        self.ids[i] -> 頂点iがトポロジカル順で何番目の成分に属するか
        groups[j] -> トポロジカル順でj番目の強連結成分に属する頂点集合
        """
        self._make_scc_ids()
        groups = [[] for _ in range(self.group_num)]
        for i in range(self.n):
            groups[self.ids[i]].append(i)
        return groups

    def make_condensation_graph(self):
        """強連結成分間の隣接リスト、入次数/出次数のリストを返す"""
        n = self.n
        G = [[] for _ in range(self.group_num)]
        indeg = [0] * self.group_num
        outdeg = [0] * self.group_num
        used = set()
        for s, t in self.edges:
            s = self.ids[s]
            t = self.ids[t]
            if s == t:
                continue
            if s * n + t in used:
                continue
            # G[s].append(t)
            G[t].append(s)
            indeg[t] += 1
            outdeg[s] += 1
            used.add(s * n + t)
        return G, indeg, outdeg


class TwoSAT(SCC_graph):
    def __init__(self, n):
        """ n: ノード数"""
        self._n = n
        super().__init__(2 * n)

    def add_clause(self, i, f, j, g):
        """ (xi == f) or (xj == g)というクローズを追加 """
        x = 2 * i + (0 if f else 1)
        y = 2 * j + (1 if g else 0)
        self.add_edge(x, y)
        x = 2 * j + (0 if g else 1)
        y = 2 * i + (1 if f else 0)
        self.add_edge(x, y)

    def satisfiable(self):
        """ 条件を満たす割り当てが存在するか判定する """
        self._make_scc_ids()
        self._answer = [False] * self._n
        for i in range(self._n):
            if self.ids[2 * i] == self.ids[2 * i + 1]:
                return False
            self._answer[i] = (self.ids[2 * i] < self.ids[2 * i + 1])
        return True

    def answer(self):
        """ 最後に読んだsatisfiableのクローズを満たす割り当てを返す """
        return self._answer


N = int(input())
X = list(map(int, input().split()))
A = list(map(int, input().split()))
E = [x + a for x, a in zip(X, A)]

xtoi = {x: i for i, x in enumerate(X)}
XS = set(X)

G = SCC_graph(N)
for i in range(N):
    if X[i] + A[i] in XS:
        G.add_edge(i, xtoi[X[i] + A[i]])
    if X[i] - A[i] in XS:
        G.add_edge(i, xtoi[X[i] - A[i]])


groups = G.scc()
M = len(groups)
d = [0] * M
for i in range(M):
    for j in groups[i]:
        d[i] = max(d[i], E[j])

rG, _, _ = G.make_condensation_graph()
for i in reversed(range(M)):
    for j in rG[i]:
        d[j] = max(d[j], d[i])

ans = [0] * N
for i in range(M):
    for j in groups[i]:
        ans[j] = d[i] - X[j]

print(*ans, sep="\n")
0