結果

問題 No.2004 Incremental Coins
ユーザー to-omerto-omer
提出日時 2021-11-27 16:35:10
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,091 ms / 2,000 ms
コード長 3,542 bytes
コンパイル時間 209 ms
コンパイル使用メモリ 82,572 KB
実行使用メモリ 197,384 KB
最終ジャッジ日時 2024-07-03 01:52:52
合計ジャッジ時間 20,373 ms
ジャッジサーバーID
(参考情報)
judge4 / 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 * 2
other AC * 20
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

MOD = 998244353
def init_ntt_cache():
n = 1 << 18
C = [1]
rC = [1]
m = 1
while m < n:
p = pow(3, (MOD - 1) // (m * 4), MOD)
ip = pow(p, MOD - 2, MOD)
for i in range(m):
C.append(C[i] * p % MOD)
rC.append(rC[i] * ip % MOD)
m *= 2
return C, rC
C, rC = init_ntt_cache()
def ntt(f, n):
u, v = 1, n // 2
for i in range(len(bin(n)) - 3, 0, -1):
for jh in range(u):
wj = C[jh]
for j in range(jh << i, (jh << i) + v):
k = j + v
fjv = wj * f[k] % MOD
f[k] = f[j] - fjv
if f[k] < 0:
f[k] += MOD
f[j] += fjv
if f[j] >= MOD:
f[j] -= MOD
u <<= 1
v >>= 1
return f
def intt(f, n):
u, v = n // 2, 1
for i in range(1, len(bin(n)) - 2):
for jh in range(u):
wj = rC[jh]
for j in range(jh << i, (jh << i) + v):
k = j + v
fjv = f[j] - f[k]
if fjv < 0:
fjv += MOD
f[j] += f[k]
if f[j] >= MOD:
f[j] -= MOD
f[k] = wj * fjv % MOD
u >>= 1
v <<= 1
return f
def convolve(f, g, index):
n = 2
m = len(f) + len(g) - 1
while 2 * n < m:
n *= 2
n *= 2
while len(f) < n:
f.append(0)
while len(g) < n:
g.append(0)
Ff = ntt(f, n)
Fg = ntt(g, n)
Fh = [x * y % MOD for x, y in zip(Ff, Fg)]
h = intt(Fh, n)[:index]
ninv = pow(n, MOD - 2, MOD)
return [x * ninv % MOD for x in h]
def main():
N, K = map(int, input().split())
N += 1
A = list(map(int, input().split()))
B = list(map(int, input().split()))
g = [[] for _ in range(N)]
for i, b in enumerate(B):
g[b].append(i + 1)
d = [0] * N
for u in range(N):
for v in g[u]:
d[v] = d[u] + 1
for u in range(N - 1, -1, -1):
for v in g[u]:
d[u] = max(d[u], d[v])
for u in range(N):
for i in range(1, len(g[u])):
if d[g[u][0]] < d[g[u][i]]:
g[u][0], g[u][i] = g[u][i], g[u][0]
dp = [[] for _ in range(N)]
for u in range(N - 1, -1, -1):
if g[u]:
dpl = dp[g[u][0]]
for v in g[u][1:]:
for i in range(-len(dp[v]), 0):
dpl[i] += dp[v][i]
if dpl[i] >= MOD:
dpl[i] -= MOD
dp[u], dp[g[u][0]] = dp[g[u][0]], dp[u]
dp[u].append(A[u])
fact = [1] * N
ifact = [1] * N
for i in range(2, N):
fact[i] = fact[i - 1] * i % MOD
ifact[-1] = pow(fact[-1], MOD - 2, MOD)
for i in range(N - 1, 1, -1):
ifact[i - 1] = ifact[i] * i % MOD
c = [0] * N
acc = 1
for i in range(N):
c[i] = acc * ifact[i] % MOD
acc = acc * (K - i) % MOD
for i, d in enumerate(dp):
if not d:
continue
dp[i] = convolve(d, c[: len(d)], len(d))
ans = [0] * N
for u in range(N):
ans[u] = dp[u].pop()
if g[u]:
dp[u], dp[g[u][0]] = dp[g[u][0]], dp[u]
dpl = dp[g[u][0]]
for v in g[u][1:]:
for i in range(-len(dp[v]), 0):
dpl[i] -= dp[v][i]
if dpl[i] < 0:
dpl[i] += MOD
print(*ans, sep="\n")
if __name__ == "__main__":
main()
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