結果
| 問題 | No.803 Very Limited Xor Subset |
| ユーザー |
 chineristAC
|
| 提出日時 | 2022-09-23 12:22:37 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 86 ms / 2,000 ms |
| コード長 | 9,177 bytes |
| コンパイル時間 | 271 ms |
| コンパイル使用メモリ | 82,048 KB |
| 実行使用メモリ | 71,168 KB |
| 最終ジャッジ日時 | 2024-12-22 05:13:59 |
| 合計ジャッジ時間 | 5,917 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge5 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 43 |
ソースコード
class UnionFindVerSize():def __init__(self, N):self._parent = [n for n in range(0, N)]self._size = [1] * Nself.group = Ndef find_root(self, x):if self._parent[x] == x: return xself._parent[x] = self.find_root(self._parent[x])return self._parent[x]def unite(self, x, y):gx = self.find_root(x)gy = self.find_root(y)if gx == gy: returnself.group -= 1if self._size[gx] < self._size[gy]:self._parent[gx] = gyself._size[gy] += self._size[gx]else:self._parent[gy] = gxself._size[gx] += self._size[gy]def get_size(self, x):return self._size[self.find_root(x)]def is_same_group(self, x, y):return self.find_root(x) == self.find_root(y)"""引用元: https://atcoder.jp/contests/practice2/submissions/24974537"""mod = 998244353omega = pow(3,119,mod)rev_omega = pow(omega,mod-2,mod)N = 2*10**5g1 = [1]*(N+1) # 元テーブルg2 = [1]*(N+1) #逆元テーブルinv = [1]*(N+1) #逆元テーブル計算用テーブルfor i in range( 2, N + 1 ):g1[i]=( ( g1[i-1] * i ) % mod )inv[i]=( ( -inv[mod % i] * (mod//i) ) % mod )g2[i]=( (g2[i-1] * inv[i]) % mod )inv[0]=0_fft_mod = 998244353_fft_imag = 911660635_fft_iimag = 86583718_fft_rate2 = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601,842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899)_fft_irate2 = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960,354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235)_fft_rate3 = (372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099,183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204)_fft_irate3 = (509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500,771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681)def _butterfly(a):n = len(a)h = (n - 1).bit_length()len_ = 0while len_ < h:if h - len_ == 1:p = 1 << (h - len_ - 1)rot = 1for s in range(1 << len_):offset = s << (h - len_)for i in range(p):l = a[i + offset]r = a[i + offset + p] * rot % _fft_moda[i + offset] = (l + r) % _fft_moda[i + offset + p] = (l - r) % _fft_modif s + 1 != (1 << len_):rot *= _fft_rate2[(~s & -~s).bit_length() - 1]rot %= _fft_modlen_ += 1else:p = 1 << (h - len_ - 2)rot = 1for s in range(1 << len_):rot2 = rot * rot % _fft_modrot3 = rot2 * rot % _fft_modoffset = s << (h - len_)for i in range(p):a0 = a[i + offset]a1 = a[i + offset + p] * rota2 = a[i + offset + p * 2] * rot2a3 = a[i + offset + p * 3] * rot3a1na3imag = (a1 - a3) % _fft_mod * _fft_imaga[i + offset] = (a0 + a2 + a1 + a3) % _fft_moda[i + offset + p] = (a0 + a2 - a1 - a3) % _fft_moda[i + offset + p * 2] = (a0 - a2 + a1na3imag) % _fft_moda[i + offset + p * 3] = (a0 - a2 - a1na3imag) % _fft_modif s + 1 != (1 << len_):rot *= _fft_rate3[(~s & -~s).bit_length() - 1]rot %= _fft_modlen_ += 2def _butterfly_inv(a):n = len(a)h = (n - 1).bit_length()len_ = hwhile len_:if len_ == 1:p = 1 << (h - len_)irot = 1for s in range(1 << (len_ - 1)):offset = s << (h - len_ + 1)for i in range(p):l = a[i + offset]r = a[i + offset + p]a[i + offset] = (l + r) % _fft_moda[i + offset + p] = (l - r) * irot % _fft_modif s + 1 != (1 << (len_ - 1)):irot *= _fft_irate2[(~s & -~s).bit_length() - 1]irot %= _fft_modlen_ -= 1else:p = 1 << (h - len_)irot = 1for s in range(1 << (len_ - 2)):irot2 = irot * irot % _fft_modirot3 = irot2 * irot % _fft_modoffset = s << (h - len_ + 2)for i in range(p):a0 = a[i + offset]a1 = a[i + offset + p]a2 = a[i + offset + p * 2]a3 = a[i + offset + p * 3]a2na3iimag = (a2 - a3) * _fft_iimag % _fft_moda[i + offset] = (a0 + a1 + a2 + a3) % _fft_moda[i + offset + p] = (a0 - a1 +a2na3iimag) * irot % _fft_moda[i + offset + p * 2] = (a0 + a1 -a2 - a3) * irot2 % _fft_moda[i + offset + p * 3] = (a0 - a1 -a2na3iimag) * irot3 % _fft_modif s + 1 != (1 << (len_ - 1)):irot *= _fft_irate3[(~s & -~s).bit_length() - 1]irot %= _fft_modlen_ -= 2def _convolution_naive(a, b):n = len(a)m = len(b)ans = [0] * (n + m - 1)if n < m:for j in range(m):for i in range(n):ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_modelse:for i in range(n):for j in range(m):ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_modreturn ansdef _convolution_fft(a, b):a = a.copy()b = b.copy()n = len(a)m = len(b)z = 1 << (n + m - 2).bit_length()a += [0] * (z - n)_butterfly(a)b += [0] * (z - m)_butterfly(b)for i in range(z):a[i] = a[i] * b[i] % _fft_mod_butterfly_inv(a)a = a[:n + m - 1]iz = pow(z, _fft_mod - 2, _fft_mod)for i in range(n + m - 1):a[i] = a[i] * iz % _fft_modreturn adef _convolution_square(a):a = a.copy()n = len(a)z = 1 << (2 * n - 2).bit_length()a += [0] * (z - n)_butterfly(a)for i in range(z):a[i] = a[i] * a[i] % _fft_mod_butterfly_inv(a)a = a[:2 * n - 1]iz = pow(z, _fft_mod - 2, _fft_mod)for i in range(2 * n - 1):a[i] = a[i] * iz % _fft_modreturn adef convolution(a, b):"""It calculates (+, x) convolution in mod 998244353.Given two arrays a[0], a[1], ..., a[n - 1] and b[0], b[1], ..., b[m - 1],it calculates the array c of length n + m - 1, defined by> c[i] = sum(a[j] * b[i - j] for j in range(i + 1)) % 998244353.It returns an empty list if at least one of a and b are empty.Constraints-----------> len(a) + len(b) <= 8388609Complexity----------> O(n log n), where n = len(a) + len(b)."""n = len(a)m = len(b)if n == 0 or m == 0:return []if min(n, m) <= 0:return _convolution_naive(a, b)if a is b:return _convolution_square(a)return _convolution_fft(a, b)import sys,random,bisectfrom collections import deque,defaultdict,Counterfrom heapq import heapify,heappop,heappushfrom itertools import cycle, permutationsfrom math import log,gcdinput = lambda :sys.stdin.readline().rstrip()mi = lambda :map(int,input().split())li = lambda :list(mi())N,M,X = mi()A = li()edge = [[] for i in range(N+1)]for _ in range(M):t,l,r = mi()edge[r].append((l-1,t))edge[l-1].append((r,t))B = [0] * (N+1)for i in range(N):B[i+1] ^= A[i]B[i] ^= A[i]cond = [-1] * (N+1)C = []for r in range(N+1):if cond[r]!=-1:continuex,y = 0,0x ^= B[r]cond[r] = 0stack = [r]while stack:v = stack.pop()for nv,t in edge[v]:if cond[nv]!=-1:if cond[nv]!=t^cond[v]:exit(print(0))else:cond[nv] = t^cond[v]stack.append(nv)if cond[nv] == 0:x ^= B[nv]else:y ^= B[nv]if r == 0:X ^= xelse:X ^= xC.append(y^x)base = []for c in C:for b in base:c = min(c,b^c)if c!=0:base.append(c)for b in base:X = min(X,X^b)if X == 0:print(pow(2,len(C)-len(base),10**9+7))else:print(0)