結果

問題 No.470 Inverse S+T Problem
コンテスト
ユーザー vwxyz
提出日時 2023-05-17 01:04:59
言語 Python3
(3.13.1 + numpy 2.2.1 + scipy 1.14.1)
結果
AC  
実行時間 61 ms / 2,000 ms
コード長 5,407 bytes
コンパイル時間 143 ms
コンパイル使用メモリ 13,312 KB
実行使用メモリ 16,768 KB
最終ジャッジ日時 2024-12-14 22:24:49
合計ジャッジ時間 3,128 ms
ジャッジサーバーID
（参考情報） 		judge4 / 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 * 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 # 

import sys
readline=sys.stdin.readline
from collections import defaultdict

class Prime:
    def __init__(self,N):
        assert N<=10**8
        self.smallest_prime_factor=[None]*(N+1)
        for i in range(2,N+1,2):
            self.smallest_prime_factor[i]=2
        n=int(N**.5)+1
        for p in range(3,n,2):
            if self.smallest_prime_factor[p]==None:
                self.smallest_prime_factor[p]=p
                for i in range(p**2,N+1,2*p):
                    if self.smallest_prime_factor[i]==None:
                        self.smallest_prime_factor[i]=p
        for p in range(n,N+1):
            if self.smallest_prime_factor[p]==None:
                self.smallest_prime_factor[p]=p
        self.primes=[p for p in range(N+1) if p==self.smallest_prime_factor[p]]

    def Factorize(self,N):
        assert N>=1
        factors=defaultdict(int)
        if N<=len(self.smallest_prime_factor)-1:
            while N!=1:
                factors[self.smallest_prime_factor[N]]+=1
                N//=self.smallest_prime_factor[N]
        else:
            for p in self.primes:
                while N%p==0:
                    N//=p
                    factors[p]+=1
                if N<p*p:
                    if N!=1:
                        factors[N]+=1
                    break
                if N<=len(self.smallest_prime_factor)-1:
                    while N!=1:
                        factors[self.smallest_prime_factor[N]]+=1
                        N//=self.smallest_prime_factor[N]
                    break
            else:
                if N!=1:
                    factors[N]+=1
        return factors

    def Divisors(self,N):
        assert N>0
        divisors=[1]
        for p,e in self.Factorize(N).items():
            pow_p=[1]
            for _ in range(e):
                pow_p.append(pow_p[-1]*p)
            divisors=[i*j for i in divisors for j in pow_p]
        return divisors

    def Is_Prime(self,N):
        return N==self.smallest_prime_factor[N]

    def Totient(self,N):
        for p in self.Factorize(N).keys():
            N*=p-1
            N//=p
        return N

    def Mebius(self,N):
        fact=self.Factorize(N)
        for e in fact.values():
            if e>=2:
                return 0
        else:
            if len(fact)%2==0:
                return 1
            else:
                return -1

def SCC(N,edges):
    start = [0] * (N + 1)
    elist = [0] * len(edges)
    for e in edges:
        start[e[0] + 1] += 1
    for i in range(1, N + 1):
        start[i] += start[i - 1]
    counter = start[:]
    for e in edges:
        elist[counter[e[0]]] = e[1]
        counter[e[0]] += 1
    N = N
    now_ord = group_num = 0
    visited = []
    low = [0] * N
    order = [-1] * N
    ids = [0] * N
    parent = [-1] * N
    stack = []
    for i in range(N):
        if order[i] == -1:
            stack.append(i)
            stack.append(i)
            while stack:
                v = stack.pop()
                if order[v] == -1:
                    low[v] = order[v] = now_ord
                    now_ord += 1
                    visited.append(v)
                    for i in range(start[v], start[v + 1]):
                        to = elist[i]
                        if order[to] == -1:
                            stack.append(to)
                            stack.append(to)
                            parent[to] = v
                        else:
                            low[v] = min(low[v], order[to])
                else:
                    if low[v] == order[v]:
                        while True:
                            u = visited.pop()
                            order[u] = N
                            ids[u] = group_num
                            if u == v:
                                break
                        group_num += 1
                    if parent[v] != -1:
                        low[parent[v]] = min(low[parent[v]], low[v])
    for i, x in enumerate(ids):
        ids[i] = group_num - 1 - x
    groups = [[] for _ in range(group_num)]
    for i, x in enumerate(ids):
        groups[x].append(i)
    return groups

class TwoSAT:
    def __init__(self,N):
        self.N=N
        self.edges=[]

    def Add_Clause(self,i,f,j,g):
        assert 0<=i<self.N
        assert 0<=j<self.N
        self.edges.append((2*i+(0 if f else 1),2*j+(1 if g else 0)))
        self.edges.append((2*j+(0 if g else 1),2*i+(1 if f else 0)))

    def Satisfiable(self):
        scc=SCC(2*self.N,self.edges)
        idx=[None]*2*self.N
        for i,lst in enumerate(scc):
            for x in lst:
                idx[x]=i
        retu=[None]*self.N
        for i in range(self.N):
            if idx[2*i]==idx[2*i+1]:
                return None
            retu[i]=idx[2*i]<idx[2*i+1]
        return retu

N=int(readline())
U=[readline().rstrip() for n in range(N)]
if 26*26+2<2*N:
    print("Impossible")
    exit()
dct=defaultdict(list)
for n in range(N):
    for b in (0,1):
        dct[U[n][:b+1]].append((n,b))
        dct[U[n][b+1:]].append((n,b))
TSAT=TwoSAT(N)
for lst in dct.values():
    le=len(lst)
    for i in range(le):
        for j in range(i+1,le):
            n,b=lst[i]
            nn,bb=lst[j]
            TSAT.Add_Clause(n,b^1,nn,bb^1)
lst=TSAT.Satisfiable()
if lst==None:
    print("Impossible")
else:
    for u,b in zip(U,lst):
        print(u[:b+1],u[b+1:])
0