結果

問題 No.2883 K-powered Sum of Fibonacci
ユーザー Rac
提出日時 2024-08-02 20:14:45
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 812 ms / 3,000 ms
コード長 1,286 bytes
コンパイル時間 286 ms
コンパイル使用メモリ 82,256 KB
実行使用メモリ 77,320 KB
最終ジャッジ日時 2024-08-02 20:14:59
合計ジャッジ時間 13,665 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
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ファイルパターン 結果
sample AC * 3
other AC * 40
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 #
プレゼンテーションモードにする

#
N, K = map(int, input().split())
# O(K^2)
comb = [[0] * (K + 1) for i in range(K + 1)]
for i in range(K + 1):
comb[i][0] = 1
for j in range(1, i + 1):
comb[i][j] = (comb[i - 1][j - 1] + comb[i - 1][j]) % 998244353
#  
# [ (F[1]^K)*(F[0]^0), (F[1]^(K-1))*(F[0]^1), ... , (F[1]^0)*(F[0]^K), 0 ]
r = [1] * (K + 2)
r[K + 1] = 0
# 0()
# S[i-1]S[i]
p = [[0] * (K + 2) for i in range(K + 2)]
for i in range(K + 1):
for j in range(K + 1 - i):
p[i][j] = comb[K - i][K - i - j]
p[K + 1][K] = 1
p[K + 1][K + 1] = 1
# O(K^3 log N)
while N != 0:
if N % 2 == 1:
# r *= p O(K^2)
tmp = [0] * (K + 2)
for i in range(K + 2):
for j in range(K + 2):
tmp[i] = (tmp[i] + r[j] * p[i][j]) % 998244353
r = tmp
N //= 2
# p *= p O(K^3)
tmp = [[0] * (K + 2) for i in range(K + 2)]
for i in range(K + 2):
for j in range(K + 2):
for k in range(K + 2):
tmp[i][j] = (tmp[i][j] + p[i][k] * p[k][j]) % 998244353
p = tmp
# S[N]
print(r[K + 1])
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