結果
問題 | No.931 Multiplicative Convolution |
ユーザー | Navier_Boltzmann |
提出日時 | 2023-11-25 18:52:22 |
言語 | PyPy3 (7.3.15) |
結果 |
WA
|
実行時間 | - |
コード長 | 5,417 bytes |
コンパイル時間 | 423 ms |
コンパイル使用メモリ | 81,920 KB |
実行使用メモリ | 120,724 KB |
最終ジャッジ日時 | 2024-09-26 11:09:06 |
合計ジャッジ時間 | 8,974 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge3 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 43 ms
56,320 KB |
testcase_01 | AC | 43 ms
56,704 KB |
testcase_02 | AC | 44 ms
56,320 KB |
testcase_03 | AC | 45 ms
56,576 KB |
testcase_04 | WA | - |
testcase_05 | WA | - |
testcase_06 | WA | - |
testcase_07 | WA | - |
testcase_08 | WA | - |
testcase_09 | AC | 636 ms
109,864 KB |
testcase_10 | AC | 648 ms
119,644 KB |
testcase_11 | AC | 637 ms
109,220 KB |
testcase_12 | WA | - |
testcase_13 | WA | - |
testcase_14 | WA | - |
testcase_15 | WA | - |
testcase_16 | WA | - |
ソースコード
from collections import * from itertools import * from functools import * import math,sys input = sys.stdin.readline def convolution(f,g,mod): def _convolution(f,g,_mod): n = len(bin(len(f)+len(g)-1)) - 2 fft_length = 1<<n f = f + [0]*(fft_length - len(f)) g = g + [0]*(fft_length - len(g)) if _mod==998244353: w = [1, 998244352, 911660635, 372528824, 929031873, 452798380, 922799308, 781712469, 476477967, 166035806, 258648936, 584193783, 63912897, 350007156, 666702199, 968855178, 629671588, 24514907, 996173970, 363395222, 565042129, 733596141, 267099868, 15311432] iw = [1, 998244352, 86583718, 509520358, 337190230, 87557064, 609441965, 135236158, 304459705, 685443576, 381598368, 335559352, 129292727, 358024708, 814576206, 708402881, 283043518, 3707709, 121392023, 704923114, 950391366, 428961804, 382752275, 469870224] if _mod==897581057: w = [1, 897581056, 200527991, 850960045, 227655573, 685177417, 661961559, 717889083, 688546301, 64431346, 762907769, 781659575, 604882016, 471181658, 242773703, 313099125, 288794207, 732004569, 437566725, 430897771, 279727937, 91704119, 523358721, 872686320] iw =[1, 897581056, 697053066, 442470459, 502631723, 192192108, 366473218, 285218810, 627498913, 632928577, 715124372, 829482092, 895669752, 835819291, 210274124, 7242324, 530138839, 365592405, 712687518, 812501856, 244025573, 353112847, 793229247, 354917575] if _mod==880803841: w = [1, 880803840, 121444121, 547680885, 836988352, 170630252, 547743738, 390590270, 755881750, 119481987, 622213777, 634844223, 496183605, 872875137, 41469254, 551868471, 219288049, 198000217, 579409128, 733691905, 566136041, 374515633, 402082372, 273508579] iw = [1, 880803840, 759359720, 339414624, 282082127, 83908436, 623501316, 879302015, 26105166, 708522529, 769895303, 843755407, 710708181, 623500536, 528308065, 542164623, 817679620, 571049407, 409417309, 504998132, 352282463, 252040680, 400443141, 109748732] def fft(a): for i in range(fft_length): j = 0 for k in range(n): j |= ((i>>k)&1) << (n - 1 - k) if i<j: a[i],a[j] = a[j],a[i] for nn in range(n): b = 1<<nn wj = 1 _wj = iw[nn+1] for j in range(b): for k in range(0,fft_length,2*b): s = a[j+k] t = a[j+k+b]*wj%_mod a[j+k] = (s+t)%_mod a[j+k+b] = (s-t)%_mod wj = wj*_wj%_mod return a def ifft(a): for i in range(fft_length): j = 0 for k in range(n): j |= ((i>>k)&1) << (n - 1 - k) if i<j: a[i],a[j] = a[j],a[i] for nn in range(n): b = 1<<nn wj = 1 _wj = w[nn+1] for j in range(b): for k in range(0,fft_length,2*b): s = a[j+k] t = a[j+k+b]*wj%_mod a[j+k] = (s+t)%_mod a[j+k+b] = (s-t)%_mod wj = wj*_wj%_mod inv = pow(fft_length,_mod-2,_mod) return [i*inv%_mod for i in a] F = fft(f) G = fft(g) H = [i*j%_mod for i,j in zip(F,G)] return [i for i in ifft(H)] f = [i%mod for i in f] g = [i%mod for i in g] x = _convolution(f,g,998244353) if mod==998244353: return x y = _convolution(f,g,897581057) z = _convolution(f,g,880803841) m1 = 998244353 m2 = 897581057 m3 = 880803841 m1_inv_m2 = pow(m1,m2-2,m2) m12_inv_m3 = pow(m1*m2,m3-2,m3) m12_mod = m1*m2%mod res = [0]*len(x) for i in range(len(x)): v1 = (y[i]-x[i])*m1_inv_m2%m2 v2 = (z[i]-(x[i]+m1*v1)%m3)*m12_inv_m3%m3 c3 = (x[i]+ m1*v1 + m12_mod*v2)%mod res[i] = c3 return res def mul_convolution(f,g,p,mod): #C_k = (sum(A_i*B_j)(k=i*j%p))%modを求める if p==2: return [0,f[0]*g[0]%mod] #p-1の約数列挙 _p = p-1 pp = [] for j in range(2,int(_p**(1/2)) + 3): if j**2>p: break if _p%j==0: if j**2!=_p: pp.append(j) pp.append(_p//j) #2から順に原始根になるか計算 for i in range(2,p): if all(pow(i,s,p)!=1 for s in pp): p_root = i break #R[i] = (p_root)**i R = [1]*(p) for i in range(1,p): R[i] = p_root*R[i-1]%p R_inv = {r:i for i,r in enumerate(R)} F = [0]*p G = [0]*p for i in range(p-1): gg = g[i] ff = f[i] G[R_inv[i+1]] = gg F[R_inv[i+1]] = ff h = convolution(F,G,mod) H = [0]*p # print(h) for i in range(len(h)): hh = h[i] idx = ((i-1)%(p-1))+1 H[R[idx]] += hh return H p = int(input()) A = list(map(int,input().split())) B = list(map(int,input().split())) mod = 998244353 H = mul_convolution(A,B,p,mod) print(*H[1:])