結果

問題 No.1955 Not Prime
コンテスト
ユーザー rin204
提出日時 2022-05-20 23:55:03
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 365 ms / 2,000 ms
コード長 4,753 bytes
コンパイル時間 183 ms
コンパイル使用メモリ 82,048 KB
実行使用メモリ 101,808 KB
最終ジャッジ日時 2024-09-20 10:20:49
合計ジャッジ時間 4,979 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
other AC * 26
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 # 

def scc(N, G):
    order = []
    used = [False]*N
    group = [None]*N
    RG = [[] for _ in range(N)]
    for i in range(N):
        for j in G[i]:
            RG[j].append(i)
    
    def dfs(pos):
        stack = [(1, pos), (0, pos)]
        while stack:
            t, pos = stack.pop()
            if t == 0:
                if used[pos]:
                    stack.pop()
                    continue
                used[pos] = True
                for npos in G[pos]:
                    if not used[npos]:
                        stack.append((1, npos))
                        stack.append((0, npos))
            else:
                order.append(pos)

    def rdfs(pos, col):
        stack = [pos]
        group[pos] = col
        used[pos] = True
        while stack:
            pos = stack.pop()
            for npos in RG[pos]:
                if not used[npos]:
                    used[npos] = True
                    group[npos] = col
                    stack.append(npos)
                    
    for i in range(N):
        if not used[i]:
            dfs(i)
    used = [False]*N
    label = 0
    for s in reversed(order):
        if not used[s]:
            rdfs(s, label)
            label += 1
    return label, group

class Two_SAT:
    def __init__(self, n):
        self.n = n
        self.G = [[] for _ in range(2 * n)]
    
    # a V B
    # neg_i = False -> a = i
    # neg_i = True -> a = ¬i
    def add_edge(self, i, j, neg_i, neg_j):
        i0 = i
        i1 = i + self.n
        if neg_i:
            i0, i1 = i1, i0
        j0 = j
        j1 = j + self.n
        if neg_j:
            j0, j1 = j1, j0
        self.G[i1].append(j0)
        self.G[j1].append(i0)
            
    def const(self):
        _, self.group = scc(2 * self.n, self.G)
    
    def check(self):
        for i in range(self.n):
            if self.group[i] == self.group[i + self.n]:
                return False
        return True
        
    def assign(self):
        ret = [False] * self.n
        for i in range(self.n):
            if self.group[i] > self.group[i + self.n]:
                ret[i] = True
        return ret

N = 1000100
isprime = [True] * N
isprime[0] = isprime[1] = False
for i in range(2, int(N ** 0.5 + 1)):
    if not isprime[i]:
        continue
    for j in range(i * i, N, i):
        isprime[j] = False

n = int(input())
ab = [input().split() for _ in range(n)]

sat = Two_SAT(n)
for i in range(n):
    ai, bi = ab[i]
    c1 = int(ai + bi)
    c2 = int(bi + ai)
    
    if not isprime[c1] and not isprime[c2]:
        pass
    elif not isprime[c1]:
        sat.add_edge(i, i, False, False)
    elif not isprime[c2]:
        sat.add_edge(i, i, True, True)
    else:
        print("No")
        exit()
    for j in range(i + 1, n):
        aj, bj = ab[j]
        
        f1 = (not isprime[int(ai + bj)]) and (not isprime[int(aj + bi)])
        f2 = (not isprime[int(bi + bj)]) and (not isprime[int(aj + ai)])
        f3 = (not isprime[int(ai + aj)]) and (not isprime[int(bj + bi)])
        f4 = (not isprime[int(bi + aj)]) and (not isprime[int(bj + ai)])
        cnt = f1 + f2 + f3 + f4
        if cnt == 0:
            print("No")
            exit()
        elif cnt == 4:
            continue
        elif cnt == 3:
            if f1 and f3:
                t1 = False
            else:
                t1 = True
            if f1 and f2:
                t2 = False
            else:
                t2 = True
            sat.add_edge(i, j, t1, t2)
        elif cnt == 2:
            if f1 and f3:
                sat.add_edge(i, j, False, True)
                sat.add_edge(i, j, False, False)
            elif f2 and f4:
                sat.add_edge(i, j, True, True)
                sat.add_edge(i, j, True, False)
            elif f1 and f2:
                sat.add_edge(i, j, False, False)
                sat.add_edge(i, j, True, False)
            elif f3 and f4:
                sat.add_edge(i, j, False, True)
                sat.add_edge(i, j, True, True)
            elif f1 and f4:
                sat.add_edge(i, j, False, True)
                sat.add_edge(i, j, True, False)
            else:
                sat.add_edge(i, j, False, False)
                sat.add_edge(i, j, True, True)

        else:
            if f1:
                t1 = False
                t2 = False
            elif f2:
                t1 = True
                t2 = False
            elif f3:
                t1 = False
                t2 = True
            else:
                t1 = True
                t2 = True
            sat.add_edge(i, j, t1, t2)
            sat.add_edge(i, j, t1 ^ True, t2)
            sat.add_edge(i, j, t1, t2 ^ True)
sat.const()

if sat.check():
    print("Yes")
else:
    print("No")
0