結果

問題 No.1516 simple 門松列 problem Re:MASTER
コンテスト
ユーザー hir355
提出日時 2021-05-21 23:31:51
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 183 ms / 6,000 ms
コード長 3,853 bytes
コンパイル時間 180 ms
コンパイル使用メモリ 82,276 KB
実行使用メモリ 76,904 KB
最終ジャッジ日時 2024-10-10 10:14:53
合計ジャッジ時間 2,735 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 19
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 # 

MOD = 998244353
 
class Matrix():
    def __init__(self, n, m, mat=None):
        self.n = n
        self.m = m
        self.mat = [[0] * self.m for _ in range(self.n)]
        if mat:
            assert len(mat) == n and len(mat[0]) == m
            for i in range(self.n):
                self.mat[i] = mat[i].copy()
 
    def is_square(self):
        return self.n == self.m
 
    def __getitem__(self, key):
        if isinstance(key, slice):
            return self.mat[key]
        else:
            assert key >= 0
            return self.mat[key]
 
    def id(n):
        res = Matrix(n, n)
        for i in range(n):
            res[i][i] = 1
        return res
 
    def __len__(self):
        return len(self.mat)
 
    def __str__(self):
        return '\n'.join(' '.join(map(str, self[i])) for i in range(self.n))
 
    def times(self, k):
        res = [[0] * self.m for _ in range(self.n)]
        for i in range(self.n):
            res_i, self_i = res[i], self[i]
            for j in range(self.m):
                res_i[j] = k * self_i[j] % MOD
        return Matrix(self.n, self.m, res)
 
    def __pos__(self):
        return self
 
    def __neg__(self):
        return self.times(-1)
 
    def __add__(self, other):
        assert self.n == other.n and self.m == other.m
        res = [[0] * self.m for _ in range(self.n)]
        for i in range(self.n):
            res_i, self_i, other_i = res[i], self[i], other[i]
            for j in range(self.m):
                res_i[j] = (self_i[j] + other_i[j]) % MOD
        return Matrix(self.n, self.m, res)
 
    def __sub__(self, other):
        assert self.n == other.n and self.m == other.m
        res = [[0] * self.m for _ in range(self.n)]
        for i in range(self.n):
            res_i, self_i, other_i = res[i], self[i], other[i]
            for j in range(self.m):
                res_i[j] = (self_i[j] - other_i[j]) % MOD
        return Matrix(self.n, self.m, res)
 
    def __mul__(self, other):
        if other.__class__ == Matrix:
            assert self.m == other.n
            res = [[0] * other.m for _ in range(self.n)]
            for i in range(self.n):
                res_i, self_i = res[i], self[i]
                for k in range(self.m):
                    self_ik, other_k = self_i[k], other[k]
                    for j in range(other.m):
                        res_i[j] += self_ik * other_k[j]
                        res_i[j] %= MOD
            return Matrix(self.n, other.m, res)
        elif other.__class__ == list:
            assert self.m == len(other)
            res = [0] * self.n
            for i in range(self.n):
                self_i = self[i]
                for j in range(self.m):
                    res[i] += self_i[j] * other[j]
                    res[i] %= MOD
            return res
        else:
            return self.times(other)
 
    def __rmul__(self, other):
        return self.times(other)
 
    def __pow__(self, k):
        assert self.is_square()
        tmp = Matrix(self.n, self.n, self.mat)
        res = Matrix.id(self.n)
        while k:
            if k & 1:
                res *= tmp
            tmp *= tmp
            k >>= 1
        return res

n, k = map(int, input().split())
mat = [[0] * (k * k) for _ in range(k * k)]
for i in range(k):
    for j in range(i + 1, k):
        for p in range(j):
            if i == p:
                continue
            mat[j + p * k][i + j * k] = 1
for i in range(k):
    for j in range(i):
        for p in range(j + 1, k):
            if i == p:
                continue
            mat[j + p * k][i + j * k] = 1
f1 = Matrix(k * k, k * k, mat)
a = [0] * (k * k)
for i in range(k):
    for j in range(k):
        if i != j:
            a[i * k + j] = 1
ans1 = sum(f1 ** (n - 2) * a) % MOD
ans2 = ans1 * n * (k - 1) * pow(2, MOD - 2, MOD) % MOD
print(ans1, ans2)
0