結果
問題 | No.950 行列累乗 |
ユーザー | convexineq |
提出日時 | 2020-01-31 01:12:54 |
言語 | PyPy3 (7.3.15) |
結果 |
WA
|
実行時間 | - |
コード長 | 3,363 bytes |
コンパイル時間 | 402 ms |
コンパイル使用メモリ | 87,292 KB |
実行使用メモリ | 122,340 KB |
最終ジャッジ日時 | 2023-10-14 09:36:26 |
合計ジャッジ時間 | 20,040 ms |
ジャッジサーバーID (参考情報) |
judge13 / judge14 |
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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 | 175 ms
87,004 KB |
testcase_01 | AC | 189 ms
87,332 KB |
testcase_02 | AC | 61 ms
71,680 KB |
testcase_03 | AC | 59 ms
71,836 KB |
testcase_04 | AC | 62 ms
71,776 KB |
testcase_05 | AC | 247 ms
91,984 KB |
testcase_06 | AC | 81 ms
77,040 KB |
testcase_07 | AC | 80 ms
76,836 KB |
testcase_08 | AC | 76 ms
76,852 KB |
testcase_09 | AC | 70 ms
76,604 KB |
testcase_10 | AC | 64 ms
75,640 KB |
testcase_11 | AC | 69 ms
76,832 KB |
testcase_12 | AC | 68 ms
76,760 KB |
testcase_13 | AC | 76 ms
76,800 KB |
testcase_14 | AC | 75 ms
76,980 KB |
testcase_15 | AC | 64 ms
71,680 KB |
testcase_16 | AC | 70 ms
76,616 KB |
testcase_17 | AC | 63 ms
71,816 KB |
testcase_18 | AC | 69 ms
76,448 KB |
testcase_19 | AC | 59 ms
71,584 KB |
testcase_20 | AC | 61 ms
71,808 KB |
testcase_21 | AC | 586 ms
110,344 KB |
testcase_22 | AC | 540 ms
111,688 KB |
testcase_23 | AC | 472 ms
106,584 KB |
testcase_24 | AC | 453 ms
105,600 KB |
testcase_25 | AC | 372 ms
100,432 KB |
testcase_26 | AC | 515 ms
108,736 KB |
testcase_27 | AC | 476 ms
103,840 KB |
testcase_28 | AC | 475 ms
110,628 KB |
testcase_29 | AC | 486 ms
105,260 KB |
testcase_30 | AC | 506 ms
106,760 KB |
testcase_31 | AC | 453 ms
106,164 KB |
testcase_32 | AC | 630 ms
118,440 KB |
testcase_33 | AC | 499 ms
105,316 KB |
testcase_34 | WA | - |
testcase_35 | AC | 501 ms
108,656 KB |
testcase_36 | AC | 166 ms
85,940 KB |
testcase_37 | AC | 157 ms
88,304 KB |
testcase_38 | AC | 177 ms
88,884 KB |
testcase_39 | AC | 165 ms
86,012 KB |
testcase_40 | AC | 514 ms
117,060 KB |
testcase_41 | AC | 517 ms
116,936 KB |
testcase_42 | AC | 617 ms
115,160 KB |
testcase_43 | AC | 532 ms
121,492 KB |
testcase_44 | WA | - |
testcase_45 | AC | 620 ms
115,316 KB |
testcase_46 | AC | 634 ms
121,248 KB |
testcase_47 | AC | 61 ms
71,612 KB |
testcase_48 | WA | - |
testcase_49 | AC | 626 ms
121,160 KB |
testcase_50 | AC | 629 ms
120,984 KB |
testcase_51 | AC | 672 ms
122,340 KB |
testcase_52 | AC | 212 ms
93,340 KB |
testcase_53 | AC | 222 ms
93,316 KB |
testcase_54 | AC | 63 ms
71,660 KB |
testcase_55 | AC | 63 ms
72,076 KB |
testcase_56 | AC | 188 ms
91,900 KB |
testcase_57 | AC | 314 ms
96,020 KB |
testcase_58 | WA | - |
testcase_59 | AC | 198 ms
93,272 KB |
testcase_60 | AC | 199 ms
93,456 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)+10 # 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() assert ai != -1 # 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: print(ans) else: print(log_mod(r,s,MOD,0))