結果

問題 No.470 Inverse S+T Problem
ユーザー 前田悠真
提出日時 2025-06-11 23:06:51
言語 PyPy3
(7.3.15)
結果
MLE  
実行時間 -
コード長 4,466 bytes
コンパイル時間 329 ms
コンパイル使用メモリ 82,596 KB
実行使用メモリ 849,732 KB
最終ジャッジ日時 2025-06-11 23:07:12
合計ジャッジ時間 4,819 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 2 MLE * 1 -- * 24
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 typing
import sys

class CSR:
    def __init__(
            self, n: int, edges: typing.List[typing.Tuple[int, int]]) -> None:
        self.start = [0] * (n + 1)
        self.elist = [0] * len(edges)

        for e in edges:
            self.start[e[0] + 1] += 1

        for i in range(1, n + 1):
            self.start[i] += self.start[i - 1]

        counter = self.start.copy()
        for e in edges:
            self.elist[counter[e[0]]] = e[1]
            counter[e[0]] += 1

class SCCGraph:
    '''
    Reference:
    R. Tarjan,
    Depth-First Search and Linear Graph Algorithms
    '''

    def __init__(self, n: int) -> None:
        self._n = n
        self._edges: typing.List[typing.Tuple[int, int]] = []

    def num_vertices(self) -> int:
        return self._n

    def add_edge(self, from_vertex: int, to_vertex: int) -> None:
        self._edges.append((from_vertex, to_vertex))
    
    def scc_ids(self) -> typing.Tuple[int, typing.List[int]]:
        # print(self._n, self._edges)
        g = CSR(self._n, self._edges)
        now_ord = 0
        group_num = 0
        visited = []
        low = [0] * self._n
        order = [-1] * self._n
        ids = [0] * self._n

        sys.setrecursionlimit(max(self._n + 1000, sys.getrecursionlimit()))

        def dfs(v: int) -> None:
            nonlocal now_ord
            nonlocal group_num
            nonlocal visited
            nonlocal low
            nonlocal order
            nonlocal ids

            low[v] = now_ord
            order[v] = now_ord
            now_ord += 1
            visited.append(v)
            for i in range(g.start[v], g.start[v + 1]):
                to = g.elist[i]
                if order[to] == -1:
                    dfs(to)
                    low[v] = min(low[v], low[to])
                else:
                    low[v] = min(low[v], order[to])

            if low[v] == order[v]:
                while True:
                    u = visited[-1]
                    visited.pop()
                    order[u] = self._n
                    ids[u] = group_num
                    if u == v:
                        break
                group_num += 1

        for i in range(self._n):
            if order[i] == -1:
                dfs(i)

        for i in range(self._n):
            ids[i] = group_num - 1 - ids[i]

        return group_num, ids

    def scc(self) -> typing.List[typing.List[int]]:
        ids = self.scc_ids()
        group_num = ids[0]
        counts = [0] * group_num
        for x in ids[1]:
            counts[x] += 1
        groups: typing.List[typing.List[int]] = [[] for _ in range(group_num)]
        for i in range(self._n):
            groups[ids[1][i]].append(i)

        return groups

n = int(input())

ts = SCCGraph(10*n)

def add(n1, f, n2, g):
   ts.add_edge(2*n1+1*(not f), 2*n2+1*g)
   ts.add_edge(2*n2+1*(not g), 2*n1+1*f)

A = [input() for _ in range(n)]
B = []
I = {}
p = 0
for i, a in enumerate(A):
    for t, s in (a[:1], 0), (a[1:], 0), (a[:2], 1), (a[2:], 1):
      if t not in I:
          I[t] = p
          B.append([])
          p += 1
      idx = I[t]
      B[idx].append((i, s))

cnt = n
I_ = {b:a for a, b in I.items()}
# print(B)
for i in range(p):
    size = len(B[i])
    for j in range(cnt, cnt+size-1):
        add(j, 1, j+1, 0)
        add(B[i][j-cnt][0], B[i][j-cnt][1], j, 0)
        add(B[i][j-cnt+1][0], B[i][j-cnt+1][1], j, 1)
    add(B[i][size-1][0], B[i][size-1][1], cnt+size-1, 0)
    cnt += size

# print(cnt)
m, C = ts.scc_ids()
for i in range(n):
    if C[2*i]==C[2*i+1]:
        print('Impossible')
        exit()

G = [set() for _ in range(m)]
G_ = [set() for _ in range(m)]
edges = ts._edges
for u, v in edges:
    u, v = C[u], C[v]
    if u!=v:
      G[u].add(v)
      G_[v].add(u)

que = []
for i in range(m):
    if len(G[i])==0:
        que.append(i)

order = []
while que:
    v = que.pop()
    order.append(v)
    for v_ in G_[v]:
        G[v_].remove(v)
        if not G[v_]:
            que.append(v_)

groups = ts.scc()

done = set()
answer = [0]*n
for i in order[::-1]:
    for v in groups[i]:
        if v//2 in done:
            break
    else:
        for v in groups[i]:
            done.add(v//2)
            if v<2*n:
                answer[v//2] = v&1

for i in range(n):
    if answer[i]:
        print(A[i][:2], A[i][2:])
    else:
        print(A[i][:1], A[i][1:])
0