結果

問題 No.470 Inverse S+T Problem
コンテスト
ユーザー rin204
提出日時 2025-02-16 21:58:06
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 103 ms / 2,000 ms
コード長 3,928 bytes
コンパイル時間 408 ms
コンパイル使用メモリ 82,028 KB
実行使用メモリ 79,144 KB
最終ジャッジ日時 2025-02-16 21:58:10
合計ジャッジ時間 4,175 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
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 * 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 # 

class SCC:
    def __init__(self, n, edges=None):
        self.n = n
        if edges is None:
            self.edges = []
        else:
            self.edges = edges

    def add_edge(self, u, v):
        self.edges.append((u, v))

    def read_edges(self, m, indexed=1):
        for _ in range(m):
            u, v = map(int, input().split())
            u -= indexed
            v -= indexed
            self.add_edge(u, v)

    def build(self):
        start = [0] * (self.n + 1)
        elist = [0] * len(self.edges)
        for u, _ in self.edges:
            start[u + 1] += 1
        for i in range(1, self.n + 1):
            start[i] += start[i - 1]

        counter = start[:]
        for u, v in self.edges:
            elist[counter[u]] = v
            counter[u] += 1

        now_ord = 0
        group_num = 0
        visited = []
        low = [0] * self.n
        ord = [-1] * self.n
        ids = [0] * self.n
        bpos = [-1] * self.n

        def dfs(v):
            nonlocal now_ord, group_num

            visited.append(v)
            stack = [~v, v]
            while stack:
                pos = stack.pop()
                if pos >= 0:
                    if ord[pos] == -1:
                        low[pos] = ord[pos] = now_ord
                        now_ord += 1
                        visited.append(pos)
                        for i in range(start[pos], start[pos + 1]):
                            to = elist[i]
                            if ord[to] == -1:
                                stack.append(~to)
                                stack.append(to)
                                bpos[to] = pos
                            else:
                                low[pos] = min(low[pos], ord[to])
                else:
                    pos = ~pos
                    if low[pos] == ord[pos]:
                        while 1:
                            u = visited.pop()
                            ord[u] = self.n
                            ids[u] = group_num
                            if u == pos:
                                break
                        group_num += 1
                    if bpos[pos] != -1:
                        low[bpos[pos]] = min(low[bpos[pos]], low[pos])

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

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

        return group_num, ids


class TwoSAT:
    def __init__(self, n):
        self.n = n
        self.scc = SCC(2 * n)
        self._build = False

    def add_clause(self, i, pos_i, j, pos_j):
        """
        a V b
        pos_i = True -> a = i,
        pos_i = False -> a = ¬i
        """
        i0 = i
        i1 = i + self.n
        if not pos_i:
            i0, i1 = i1, i0

        j0 = j
        j1 = j + self.n
        if not pos_j:
            j0, j1 = j1, j0

        self.scc.add_edge(i1, j0)
        self.scc.add_edge(j1, i0)

    def check(self):
        _, self.ids = self.scc.build()

        for i in range(self.n):
            if self.ids[i] == self.ids[i + self.n]:
                return False
        return True

    def assign(self):
        ret = [False] * self.n
        for i in range(self.n):
            if self.ids[i] > self.ids[i + self.n]:
                ret[i] = True

        return ret


n = int(input())
U = [input() for _ in range(n)]

if n > 52:
    print("Impossible")
    exit()

G = TwoSAT(n)
for i in range(n):
    for j in range(i + 1, n):
        for t1 in range(2):
            li = U[i][: 1 + t1]
            ri = U[i][1 + t1 :]
            for t2 in range(2):
                lj = U[j][: 1 + t2]
                rj = U[j][1 + t2 :]
                if len(set([li, ri, lj, rj])) != 4:
                    G.add_clause(i, t1 ^ 1, j, t2 ^ 1)

if not G.check():
    print("Impossible")
    exit()


res = G.assign()
for S, t in zip(U, res):
    print(S[: 1 + t], S[1 + t :])
0