#518890 (Python3) No.950 行列累乗

提出ソース

結果

問題	No.950 行列累乗
ユーザー	toyuzuko
提出日時	2020-07-26 18:19:32
言語	Python3 (3.12.2 + numpy 1.26.4 + scipy 1.12.0)
結果	WA
実行時間	-
コード長	6,852 bytes
コンパイル時間	97 ms
コンパイル使用メモリ	11,768 KB
実行使用メモリ	23,592 KB
最終ジャッジ日時	2023-09-11 04:50:36
合計ジャッジ時間	30,459 ms
ジャッジサーバーID （参考情報）	judge12 / judge15

このコードへのチャレンジ
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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	445 ms 15,304 KB
testcase_01	AC	535 ms 15,296 KB
testcase_02	AC	20 ms 9,236 KB
testcase_03	AC	35 ms 9,452 KB
testcase_04	AC	172 ms 9,256 KB
testcase_05	AC	24 ms 9,312 KB
testcase_06	AC	37 ms 9,492 KB
testcase_07	AC	26 ms 9,248 KB
testcase_08	AC	33 ms 9,368 KB
testcase_09	AC	37 ms 9,496 KB
testcase_10	AC	31 ms 9,500 KB
testcase_11	AC	28 ms 9,404 KB
testcase_12	AC	36 ms 9,312 KB
testcase_13	WA	-
testcase_14	WA	-
testcase_15	AC	36 ms 9,280 KB
testcase_16	AC	32 ms 9,504 KB
testcase_17	AC	22 ms 9,304 KB
testcase_18	AC	37 ms 9,512 KB
testcase_19	AC	22 ms 9,164 KB
testcase_20	AC	22 ms 9,160 KB
testcase_21	AC	921 ms 23,344 KB
testcase_22	WA	-
testcase_23	AC	574 ms 18,860 KB
testcase_24	AC	568 ms 18,096 KB
testcase_25	AC	395 ms 16,804 KB
testcase_26	AC	577 ms 19,528 KB
testcase_27	AC	597 ms 18,420 KB
testcase_28	WA	-
testcase_29	WA	-
testcase_30	AC	584 ms 18,392 KB
testcase_31	WA	-
testcase_32	WA	-
testcase_33	AC	679 ms 18,784 KB
testcase_34	WA	-
testcase_35	WA	-
testcase_36	AC	492 ms 17,048 KB
testcase_37	AC	498 ms 18,872 KB
testcase_38	AC	542 ms 19,256 KB
testcase_39	AC	515 ms 17,288 KB
testcase_40	AC	685 ms 23,496 KB
testcase_41	AC	676 ms 23,432 KB
testcase_42	AC	929 ms 23,360 KB
testcase_43	WA	-
testcase_44	WA	-
testcase_45	AC	932 ms 23,344 KB
testcase_46	WA	-
testcase_47	AC	20 ms 9,288 KB
testcase_48	WA	-
testcase_49	WA	-
testcase_50	WA	-
testcase_51	WA	-
testcase_52	AC	924 ms 23,548 KB
testcase_53	AC	930 ms 23,428 KB
testcase_54	AC	20 ms 9,292 KB
testcase_55	AC	20 ms 9,152 KB
testcase_56	AC	561 ms 19,200 KB
testcase_57	AC	20 ms 9,160 KB
testcase_58	AC	20 ms 9,212 KB
testcase_59	AC	887 ms 23,360 KB
testcase_60	AC	928 ms 23,364 KB

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ソースコード

raw source code

class SquareMatrix():
    def __init__(self, n, mod=1000000007):
        self.n = n
        self.mat = [[0 for j in range(n)] for i in range(n)]
        self.mod = mod

    @staticmethod
    def id(n, mod=1000000007):
        res = SquareMatrix(n, mod)
        for i in range(n):
            res.mat[i][i] = 1
        return res

    @staticmethod
    def modinv(n, mod):
        assert n % mod != 0
        c0, c1 = n, mod
        a0, a1 = 1, 0
        b0, b1 = 0, 1
        while c1:
            a0, a1 = a1, a0 - c0 // c1 * a1
            b0, b1 = b1, b0 - c0 // c1 * b1
            c0, c1 = c1, c0 % c1
        return a0 % mod

    def set(self, arr):
        for i in range(self.n):
            for j in range(self.n):
                self.mat[i][j] = arr[i][j] % self.mod

    def operate(self, vec):
        assert len(vec) == self.n
        res = [0 for _ in range(self.n)]
        for i in range(self.n):
            for j in range(self.n):
                res[i] += self.mat[i][j] * vec[j]
                res[i] %= self.mod
        return res

    def add(self, other):
        assert other.n == self.n
        res = SquareMatrix(self.n, self.mod)
        for i in range(self.n):
            for j in range(self.n):
                res.mat[i][j] = self.mat[i][j] + other.mat[i][j]
                res.mat[i][j] %= self.mod
        return res

    def subtract(self, other):
        assert other.n == self.n
        res = SquareMatrix(self.n, self.mod)
        for i in range(self.n):
            for j in range(self.n):
                res.mat[i][j] = self.mat[i][j] - other.mat[i][j]
                res.mat[i][j] %= self.mod
        return res

    def times(self, k):
        res = SquareMatrix(self.n, self.mod)
        for i in range(self.n):
            for j in range(self.n):
                res.mat[i][j] = self.mat[i][j] * k
                res.mat[i][j] %= self.mod
        return res

    def multiply(self, other):
        assert self.n == other.n
        res = SquareMatrix(self.n, self.mod)
        for i in range(self.n):
            for j in range(self.n):
                for k in range(self.n):
                    res.mat[i][j] += self.mat[i][k] * other.mat[k][j]
                    res.mat[i][j] %= self.mod
        return res

    def power(self, k):
        tmp = SquareMatrix(self.n, self.mod)
        for i in range(self.n):
            for j in range(self.n):
                tmp.mat[i][j] = self.mat[i][j]
        res = SquareMatrix.id(self.n, self.mod)
        while k:
            if k & 1:
                res = res.multiply(tmp)
            tmp = tmp.multiply(tmp)
            k >>= 1
        return res

    def trace(self):
        res = 0
        for i in range(self.n):
            res += self.mat[i][i]
            res %= self.mod
        return res

    def determinant(self):
        res = 1
        tmp = SquareMatrix(self.n, self.mod)
        for i in range(self.n):
            for j in range(self.n):
                tmp.mat[i][j] = self.mat[i][j]
        for j in range(self.n):
            if tmp.mat[j][j] == 0:
                for i in range(j + 1, self.n):
                    if tmp.mat[i][j] != 0:
                        idx = i
                        break
                else:
                    return 0
                for k in range(self.n):
                    tmp.mat[j][k], tmp.mat[idx][k] = tmp.mat[idx][k], tmp.mat[j][k]
                res *= -1
            inv = SquareMatrix.modinv(tmp.mat[j][j], self.mod)
            for i in range(j + 1, self.n):
                c = -inv * tmp.mat[i][j] % self.mod
                for k in range(self.n):
                    tmp.mat[i][k] += c * tmp.mat[j][k]
                    tmp.mat[i][k] %= self.mod
        for i in range(self.n):
            res *= tmp.mat[i][i]
            res %= self.mod
        return res

    def transpose(self):
        res = SquareMatrix(self.n, self.mod)
        for i in range(self.n):
            for j in range(self.n):
                res.mat[i][j] = self.mat[j][i]
        return res

    def inverse(self): #self.determinant() != 0
        res = SquareMatrix.id(self.n, self.mod)
        tmp = SquareMatrix(self.n, self.mod)
        sgn = 1
        for i in range(self.n):
            for j in range(self.n):
                tmp.mat[i][j] = self.mat[i][j]
        for j in range(self.n):
            if tmp.mat[j][j] == 0:
                for i in range(j + 1, self.n):
                    if tmp.mat[i][j] != 0:
                        idx = i
                        break
                else:
                    return 0
                for k in range(self.n):
                    tmp.mat[j][k], tmp.mat[idx][k] = tmp.mat[idx][k], tmp.mat[j][k]
                    res.mat[j][k], res.mat[idx][k] = res.mat[idx][k], res.mat[j][k]
            inv = SquareMatrix.modinv(tmp.mat[j][j], self.mod)
            for k in range(self.n):
                tmp.mat[j][k] *= inv
                tmp.mat[j][k] %= self.mod
                res.mat[j][k] *= inv
                res.mat[j][k] %= self.mod
            for i in range(self.n):
                c = tmp.mat[i][j]
                for k in range(self.n):
                    if i == j:
                        continue
                    tmp.mat[i][k] -= tmp.mat[j][k] * c
                    tmp.mat[i][k] %= self.mod
                    res.mat[i][k] -= res.mat[j][k] * c
                    res.mat[i][k] %= self.mod
        return res

    def linear_equations(self, vec):
        return self.inverse().operate(vec)

    def print(self):
        print(*self.mat, sep='\n')

def is_same(A, B):
    if A.n != B.n:
        return False
    n = A.n
    for i in range(n):
        for j in range(n):
            if A.mat[i][j] != B.mat[i][j]:
                return False
    return True

from itertools import chain

def discrete_logarithm(x, y, mod): #x**k % mod == y
    if is_same(x, SquareMatrix(2, mod)) and is_same(y, SquareMatrix(2, mod)): return 1
    sqrt_mod = int(mod**0.5 + 1000)
    power_x = {}
    p = SquareMatrix.id(2, mod)
    for i in range(sqrt_mod):
        if is_same(p, y) and i > 0:
            return i #x**i % mod == y
        tmp = p.multiply(y)
        tmp = tuple(chain.from_iterable(tmp.mat))
        power_x[tmp] = i
        p = p.multiply(x)
    z = x.power(sqrt_mod)
    g = SquareMatrix.id(2, mod)
    for i in range(1, sqrt_mod + 3):
        g = g.multiply(z)
        tmp = tuple(chain.from_iterable(g.mat))
        if tmp in power_x:
            res = i * sqrt_mod - power_x[tmp]
            if res > 0 and is_same(x.power(res), y):
                return res
    return -1

MOD = int(input())
a = [tuple(map(int, input().split())) for _ in range(2)]
b = [tuple(map(int, input().split())) for _ in range(2)]

A = SquareMatrix(2, MOD)
B = SquareMatrix(2, MOD)
A.set(a)
B.set(b)

print(discrete_logarithm(A, B, MOD))

yukicoder

結果

テストケース

ソースコード