結果

問題 No.1955 Not Prime
コンテスト
ユーザー mkawa2
提出日時 2024-05-27 23:21:52
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 569 ms / 2,000 ms
コード長 5,597 bytes
コンパイル時間 370 ms
コンパイル使用メモリ 82,688 KB
実行使用メモリ 201,900 KB
最終ジャッジ日時 2024-12-20 20:36:41
合計ジャッジ時間 13,228 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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ファイルパターン 結果
other AC * 26
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ソースコード

diff # 

import sys

# sys.setrecursionlimit(1000005)
# sys.set_int_max_str_digits(200005)
int1 = lambda x: int(x)-1
pDB = lambda *x: print(*x, end="\n", file=sys.stderr)
p2D = lambda x: print(*x, sep="\n", end="\n\n", file=sys.stderr)
def II(): return int(sys.stdin.readline())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]
def SI(): return sys.stdin.readline().rstrip()

dij = [(0, 1), (-1, 0), (0, -1), (1, 0)]
# dij = [(0, 1), (-1, 0), (0, -1), (1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)]
# inf = -1-(-1 << 31)
inf = -1-(-1 << 62)

# md = 10**9+7
md = 998244353

class StronglyConnectedComponents:
    def __init__(self, n):
        self.n = n
        self.graph = [[] for _ in range(n)]
        self.ord = [-1]*n
        self.low = [-1]*n
        self.labels = [-1]*n
        self.lb_cnt = 0

    def add_edge(self, v, nxt_v):
        self.graph[v].append(nxt_v)

    def build(self):
        k = 0
        idxs = [0]*self.n
        for v in range(self.n):
            if self.ord[v] == -1:
                k = self.dfs(v, k, idxs)
        self.labels = [self.lb_cnt-lb-1 for lb in self.labels]

    def dfs(self, root, k, idxs):
        dfs_stack = [root]
        scc_stack = []
        while dfs_stack:
            v = dfs_stack[-1]
            if v < 0:
                v = ~v
                prv_v = dfs_stack[-2]
                self.low[prv_v] = min(self.low[prv_v], self.low[v])
                dfs_stack.pop()
                continue
            idx = idxs[v]
            if self.ord[v] == -1:
                self.ord[v] = self.low[v] = k
                k += 1
                scc_stack.append(v)
            if idx < len(self.graph[v]):
                nxt_v = self.graph[v][idx]
                idxs[v] += 1
                if self.ord[nxt_v] == -1:
                    dfs_stack.append(~nxt_v)
                    dfs_stack.append(nxt_v)
                elif self.labels[nxt_v] == -1:
                    self.low[v] = min(self.low[v], self.ord[nxt_v])
            else:
                if self.ord[v] == self.low[v]:
                    while True:
                        prv_v = scc_stack.pop()
                        self.labels[prv_v] = self.lb_cnt
                        if prv_v == v:
                            break
                    self.lb_cnt += 1
                dfs_stack.pop()
        return k

    def construct_dag(self):
        self.dag = [[] for i in range(self.lb_cnt)]
        self.groups = [[] for i in range(self.lb_cnt)]
        for v, lb in enumerate(self.labels):
            for nxt_v in self.graph[v]:
                nxt_lb = self.labels[nxt_v]
                if lb == nxt_lb:
                    continue
                self.dag[lb].append(nxt_lb)
            self.groups[lb].append(v)
        return self.dag, self.groups

class TwoSAT:
    # nは2倍化する前の頂点数
    def __init__(self, n):
        self.n = n
        self.scc = StronglyConnectedComponents(2*n)
        self.ans = [False]*self.n

    # (uがf)または(vがg) u,v頂点、f,g真偽
    def add_clause(self, u, f, v, g):
        self.scc.add_edge(2*u+int(not f), 2*v+int(g))
        self.scc.add_edge(2*v+int(not g), 2*u+int(f))

    def satisfy(self):
        self.scc.build()
        for i in range(self.n):
            if self.scc.labels[2*i] == self.scc.labels[2*i+1]:
                return False
            self.ans[i] = self.scc.labels[2*i] < self.scc.labels[2*i+1]
        return True

    def answer(self):
        return self.ans

class Sieve:
    def __init__(self, n):
        self.plist = [2]
        min_prime_factor = [2, 0]*(n//2+1)
        for x in range(3, n+1, 2):
            if min_prime_factor[x] == 0:
                min_prime_factor[x] = x
                self.plist.append(x)
                if x**2 > n: continue
                for y in range(x**2, n+1, 2*x):
                    if min_prime_factor[y] == 0:
                        min_prime_factor[y] = x
        self.min_prime_factor = min_prime_factor

    def isprime(self, x):
        return self.min_prime_factor[x] == x

    def pf(self, x):
        pp, ee = [], []
        while x > 1:
            mpf = self.min_prime_factor[x]
            if pp and mpf == pp[-1]:
                ee[-1] += 1
            else:
                pp.append(mpf)
                ee.append(1)
            x //= mpf
        return pp, ee

    # unsorted
    def factor(self, a):
        ff = [1]
        pp, ee = self.pf(a)
        for p, e in zip(pp, ee):
            ff, gg = [], ff
            w = p
            for _ in range(e):
                for f in gg: ff.append(f*w)
                w *= p
            ff += gg
        return ff

sv = Sieve(10001000)
n = II()
ab = [SI().split() for _ in range(n)]
ts = TwoSAT(n)
for u, (a, b) in enumerate(ab):
    cnt = 0
    for f in range(2):
        x = int(a+b)
        if sv.isprime(x):
            cnt += 1
            ts.add_clause(u, f ^ 1, u, f ^ 1)
        a, b = b, a
    if cnt == 2:
        # print(u,a,b)
        print("No")
        exit()

for u in range(n):
    a, b = ab[u]
    for v in range(u):
        s, t = ab[v]
        for f in range(2):
            for g in range(2):
                x = int(a+t)
                y = int(s+b)
                if sv.isprime(x) or sv.isprime(y):
                    ts.add_clause(u, f ^ 1, v, g ^ 1)
                s, t = t, s
            a, b = b, a

print("Yes" if ts.satisfy() else "No")
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