結果
問題 | No.950 行列累乗 |
ユーザー | convexineq |
提出日時 | 2020-01-31 01:20:39 |
言語 | PyPy3 (7.3.13) |
結果 |
AC
|
実行時間 | 748 ms / 2,000 ms |
コード長 | 3,380 bytes |
コンパイル時間 | 359 ms |
コンパイル使用メモリ | 87,160 KB |
実行使用メモリ | 122,860 KB |
最終ジャッジ日時 | 2023-10-14 09:44:36 |
合計ジャッジ時間 | 22,781 ms |
ジャッジサーバーID (参考情報) |
judge14 / judge11 |
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 | 192 ms
86,412 KB |
testcase_01 | AC | 209 ms
86,504 KB |
testcase_02 | AC | 72 ms
71,624 KB |
testcase_03 | AC | 71 ms
71,628 KB |
testcase_04 | AC | 70 ms
71,820 KB |
testcase_05 | AC | 289 ms
92,120 KB |
testcase_06 | AC | 87 ms
76,916 KB |
testcase_07 | AC | 86 ms
76,736 KB |
testcase_08 | AC | 82 ms
76,752 KB |
testcase_09 | AC | 78 ms
75,888 KB |
testcase_10 | AC | 75 ms
75,784 KB |
testcase_11 | AC | 83 ms
76,708 KB |
testcase_12 | AC | 78 ms
75,880 KB |
testcase_13 | AC | 89 ms
76,528 KB |
testcase_14 | AC | 86 ms
76,748 KB |
testcase_15 | AC | 73 ms
71,816 KB |
testcase_16 | AC | 79 ms
76,624 KB |
testcase_17 | AC | 71 ms
71,764 KB |
testcase_18 | AC | 74 ms
75,608 KB |
testcase_19 | AC | 71 ms
71,688 KB |
testcase_20 | AC | 71 ms
71,748 KB |
testcase_21 | AC | 680 ms
110,432 KB |
testcase_22 | AC | 616 ms
111,776 KB |
testcase_23 | AC | 558 ms
106,532 KB |
testcase_24 | AC | 536 ms
105,580 KB |
testcase_25 | AC | 457 ms
100,092 KB |
testcase_26 | AC | 590 ms
108,788 KB |
testcase_27 | AC | 555 ms
103,960 KB |
testcase_28 | AC | 547 ms
110,488 KB |
testcase_29 | AC | 578 ms
106,016 KB |
testcase_30 | AC | 568 ms
106,732 KB |
testcase_31 | AC | 535 ms
105,904 KB |
testcase_32 | AC | 734 ms
118,608 KB |
testcase_33 | AC | 585 ms
105,476 KB |
testcase_34 | AC | 406 ms
99,808 KB |
testcase_35 | AC | 583 ms
108,684 KB |
testcase_36 | AC | 195 ms
86,216 KB |
testcase_37 | AC | 196 ms
88,388 KB |
testcase_38 | AC | 201 ms
88,688 KB |
testcase_39 | AC | 200 ms
86,108 KB |
testcase_40 | AC | 610 ms
117,284 KB |
testcase_41 | AC | 628 ms
117,052 KB |
testcase_42 | AC | 748 ms
116,328 KB |
testcase_43 | AC | 647 ms
121,508 KB |
testcase_44 | AC | 376 ms
103,900 KB |
testcase_45 | AC | 742 ms
116,076 KB |
testcase_46 | AC | 748 ms
122,040 KB |
testcase_47 | AC | 71 ms
71,668 KB |
testcase_48 | AC | 404 ms
103,352 KB |
testcase_49 | AC | 728 ms
122,400 KB |
testcase_50 | AC | 730 ms
120,940 KB |
testcase_51 | AC | 723 ms
122,860 KB |
testcase_52 | AC | 242 ms
93,068 KB |
testcase_53 | AC | 238 ms
93,484 KB |
testcase_54 | AC | 69 ms
71,968 KB |
testcase_55 | AC | 70 ms
71,896 KB |
testcase_56 | AC | 211 ms
91,652 KB |
testcase_57 | AC | 343 ms
95,844 KB |
testcase_58 | AC | 71 ms
71,820 KB |
testcase_59 | AC | 231 ms
93,520 KB |
testcase_60 | AC | 215 ms
93,328 KB |
ソースコード
def log_mod(a,b,MOD,permit0): a %= MOD; b %= MOD q = int(MOD**0.5)+2 # baby-step h = 1 if MOD != 1 else 0 memo = {} for i in range(q): if h==b and (permit0 or i): return i memo[h*b%MOD] = i h = h*a%MOD # giant-step #ここに来た時 h = a^q g = h for i in range(q): if g in memo: res = (i+1)*q-memo[g] if pow(a,res,MOD) == b: return res else: return -1 g = g*h%MOD return -1 #見つからない場合 def extgcd(x,y): if y==0: return 1,0 #g=x r0,r1,s0,s1 = x,y,1,0 while r1 != 0: r0,r1, s0,s1 = r1,r0%r1, s1,s0-r0//r1*s1 #g = r0 return s0,(r0-s0*x)//y def modinv(a,MOD): x,y = extgcd(a,MOD) return x%MOD def matmul(A,B,mod): # A,B: 行列 res = [[0]*len(B[0]) for _ in [None]*len(A)] for i, resi in enumerate(res): for k, aik in enumerate(A[i]): for j,bkj in enumerate(B[k]): resi[j] += aik*bkj resi[j] %= mod return res def matpow(A,p,M): #A^p mod M if p%2: return matmul(A, matpow(A,p-1,M), M) elif p > 0: b = matpow(A,p//2,M) return matmul(b,b,M) else: return [[1 if i == j else 0 for j in range(len(A))] for i in range(len(A))] # coding: utf-8 # Your code here! import sys sys.setrecursionlimit(10**6) readline = sys.stdin.readline read = sys.stdin.read def hash_projective(A): c = A[0]+A[1] for i in range(4): if c[i] != 0: cinv = modinv(c[i],MOD) return tuple([i*cinv%MOD for i in c]) else: return((0,0,0,0)) def hash_equal(A): return tuple(A[0]+A[1]) def discrete_logarithm(a,b,MOD,hashing,permit0): q = int(MOD**0.5)+2 # baby-step h = [[1,0],[0,1]] memo = {} for i in range(q): if hashing(h)==hashing(b) and (permit0 or i): return i memo[hashing(matmul(h,b,MOD))] = i h = matmul(h,a,MOD) # giant-step #ここに来た時 h = a^q g = [i[:] for i in h] for i in range(q): if hashing(g) in memo: res = (i+1)*q-memo[hashing(g)] if hashing(matpow(a,res,MOD)) == hashing(b): return res else: return -1 g = matmul(g,h,MOD) return -1 #見つからない場合 def det(A): return (A[0][0]*A[1][1]-A[1][0]*A[0][1])%MOD MOD = int(input()) A = [[int(i) for i in readline().split()] for _ in range(2)] B = [[int(i) for i in readline().split()] for _ in range(2)] E = [[1,0],[0,1]] if det(A) == 0: print(discrete_logarithm(A,B,MOD,hash_equal,0)) else: # A^ai == r E , A^bi == s B # A^(xai+bi) == B なら r^x E= (B (A^bi)^{-1}) ai = discrete_logarithm(A,E,MOD,hash_projective,0) Ar = matpow(A,ai,MOD) r = Ar[0][0] bi = discrete_logarithm(A,B,MOD,hash_projective,1) C = matpow(A,bi,MOD) dd = modinv(det(C),MOD) #print(C,B) Cinv = [[C[1][1]*dd%MOD,-C[0][1]*dd%MOD], [-C[1][0]*dd%MOD,C[0][0]*dd%MOD]] B = matmul(B,Cinv,MOD) s = B[0][0] #print(Ar,B) if bi == -1: print(-1) exit() # r^x = s mod P を解く x = log_mod(r,s,MOD,1) #print(r,s,x,ai,bi) if x == -1: print(-1) else: ans = x*ai+bi if ans == 0: ans = log_mod(r,s,MOD,0)*ai print(ans) #print(matpow(A,ans,MOD))