結果

問題 No.950 行列累乗
ユーザー convexineqconvexineq
提出日時 2020-01-31 00:34:23
言語 PyPy3
(7.3.15)
結果
WA  
実行時間 -
コード長 3,375 bytes
コンパイル時間 243 ms
コンパイル使用メモリ 82,048 KB
実行使用メモリ 120,704 KB
最終ジャッジ日時 2024-09-16 04:12:20
合計ジャッジ時間 20,000 ms
ジャッジサーバーID
(参考情報)
judge3 / judge1
このコードへのチャレンジ
(要ログイン)

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 162 ms
84,864 KB
testcase_01 AC 173 ms
84,352 KB
testcase_02 AC 39 ms
52,736 KB
testcase_03 AC 40 ms
53,376 KB
testcase_04 AC 38 ms
52,992 KB
testcase_05 WA -
testcase_06 AC 62 ms
66,304 KB
testcase_07 WA -
testcase_08 AC 53 ms
63,872 KB
testcase_09 WA -
testcase_10 AC 43 ms
59,264 KB
testcase_11 AC 51 ms
63,616 KB
testcase_12 AC 45 ms
60,288 KB
testcase_13 AC 58 ms
66,048 KB
testcase_14 AC 61 ms
66,432 KB
testcase_15 AC 41 ms
53,632 KB
testcase_16 AC 51 ms
61,696 KB
testcase_17 AC 40 ms
53,248 KB
testcase_18 AC 43 ms
58,880 KB
testcase_19 AC 40 ms
53,248 KB
testcase_20 AC 43 ms
53,376 KB
testcase_21 WA -
testcase_22 AC 575 ms
111,872 KB
testcase_23 WA -
testcase_24 AC 495 ms
102,912 KB
testcase_25 AC 395 ms
97,280 KB
testcase_26 WA -
testcase_27 AC 522 ms
102,400 KB
testcase_28 AC 506 ms
106,368 KB
testcase_29 AC 519 ms
104,448 KB
testcase_30 WA -
testcase_31 AC 479 ms
105,216 KB
testcase_32 AC 699 ms
117,888 KB
testcase_33 WA -
testcase_34 AC 370 ms
98,816 KB
testcase_35 AC 515 ms
105,728 KB
testcase_36 AC 169 ms
83,968 KB
testcase_37 AC 162 ms
86,400 KB
testcase_38 AC 167 ms
86,656 KB
testcase_39 AC 165 ms
83,840 KB
testcase_40 AC 558 ms
109,696 KB
testcase_41 WA -
testcase_42 WA -
testcase_43 AC 572 ms
117,504 KB
testcase_44 AC 318 ms
98,944 KB
testcase_45 WA -
testcase_46 AC 681 ms
119,936 KB
testcase_47 AC 38 ms
52,992 KB
testcase_48 AC 365 ms
101,376 KB
testcase_49 AC 671 ms
118,784 KB
testcase_50 AC 661 ms
120,320 KB
testcase_51 AC 688 ms
115,968 KB
testcase_52 AC 220 ms
90,880 KB
testcase_53 AC 211 ms
91,136 KB
testcase_54 AC 39 ms
52,864 KB
testcase_55 AC 37 ms
52,608 KB
testcase_56 AC 186 ms
89,728 KB
testcase_57 WA -
testcase_58 AC 39 ms
52,864 KB
testcase_59 AC 202 ms
91,136 KB
testcase_60 AC 197 ms
91,264 KB
権限があれば一括ダウンロードができます

ソースコード

diff #

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: break
    else: return((0,0,0,0))
    
    cinv = modinv(c[i],MOD)
    return tuple([i*cinv%MOD for i in c])    

def hash_equal(A):
    return tuple(A[0]+A[1])

def discrete_logarithm(a,b,MOD,hashing,permit0):
    q = int(MOD**0.5)+3
    # baby-step
    h = [[1 if i == j else 0 for j in range(2)] for i in range(2)]
    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)]

if det(A) == 0:
    print(discrete_logarithm(A,B,MOD,hash_equal,0))

else:
    E = [[1 if i == j else 0 for j in range(2)] for i in range(2)]
    # 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)
        
    # r^x = s mod P を解く
    x = log_mod(r,s,MOD,0)
    #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,1))

    



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