結果
| 問題 | No.2876 Infection |
| ユーザー |
 kainade
|
| 提出日時 | 2024-09-12 08:58:23 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 1,198 ms / 2,000 ms |
| コード長 | 29,713 bytes |
| コンパイル時間 | 334 ms |
| コンパイル使用メモリ | 82,528 KB |
| 実行使用メモリ | 97,776 KB |
| 最終ジャッジ日時 | 2024-09-12 08:58:37 |
| 合計ジャッジ時間 | 13,827 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
（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 | 83 ms
77,180 KB |
| testcase_01 | AC | 81 ms
77,640 KB |
| testcase_02 | AC | 83 ms
77,616 KB |
| testcase_03 | AC | 81 ms
77,236 KB |
| testcase_04 | AC | 82 ms
77,128 KB |
| testcase_05 | AC | 82 ms
77,548 KB |
| testcase_06 | AC | 110 ms
77,180 KB |
| testcase_07 | AC | 1,198 ms
97,592 KB |
| testcase_08 | AC | 1,194 ms
97,732 KB |
| testcase_09 | AC | 1,176 ms
97,776 KB |
| testcase_10 | AC | 323 ms
82,100 KB |
| testcase_11 | AC | 304 ms
81,872 KB |
| testcase_12 | AC | 280 ms
81,884 KB |
| testcase_13 | AC | 407 ms
83,980 KB |
| testcase_14 | AC | 1,071 ms
94,908 KB |
| testcase_15 | AC | 80 ms
77,608 KB |
| testcase_16 | AC | 164 ms
79,488 KB |
| testcase_17 | AC | 86 ms
78,168 KB |
| testcase_18 | AC | 81 ms
77,088 KB |
| testcase_19 | AC | 128 ms
79,504 KB |
| testcase_20 | AC | 767 ms
85,696 KB |
| testcase_21 | AC | 128 ms
79,172 KB |
| testcase_22 | AC | 801 ms
87,276 KB |
| testcase_23 | AC | 413 ms
83,764 KB |
| testcase_24 | AC | 327 ms
82,180 KB |
| testcase_25 | AC | 806 ms
86,592 KB |
| testcase_26 | AC | 124 ms
79,244 KB |
| testcase_27 | AC | 346 ms
83,028 KB |
| testcase_28 | AC | 133 ms
79,748 KB |
| testcase_29 | AC | 1,035 ms
92,732 KB |
ソースコード
def main():
N,x=MI()
if x==0:return print(1)
if x==100:return print(N)
nume=pow(100,-1,MOD)
p,q=x*nume%MOD,(100-x)*nume%MOD
C=Comb(N+100,MOD)
comb,fac,finv=C.comb,C.fac,C.finv
fft=FFT(MOD)
powp=[1]
for _ in range(N+99):
powp.append(powp[-1]*p%MOD)
dp=[[0]*(N+1)for _ in range(N+1)]
dp[1][N-1]=1
subdp=[[0]*(N+1)for _ in range(N+1)]
subdp[1][N-1]=powp[N-1]*fac[N-1]%MOD
blue=[pow(q*pow(p,-1,MOD)%MOD,k,MOD)*finv[k]%MOD for k in range(N+10)]
kf=finv[:N+1][::-1]
for i in range(1,N):
#dp[i+1]を埋める.
res=fft.convolution(subdp[i],kf)
for k in range(N-i):
dp[i+1][k]=blue[k]*res[N+k]%MOD
for k in range(N-i):
subdp[i+1][k]=dp[i+1][k]*powp[k]%MOD*fac[k]%MOD
print(sum_table(dp)%MOD)
# https://github.com/shakayami/ACL-for-python/blob/master/convolution.py
class FFT():
def primitive_root_constexpr(self,m):
if m==2:return 1
if m==167772161:return 3
if m==469762049:return 3
if m==754974721:return 11
if m==998244353:return 3
divs=[0]*20
divs[0]=2
cnt=1
x=(m-1)//2
while(x%2==0):x//=2
i=3
while(i*i<=x):
if (x%i==0):
divs[cnt]=i
cnt+=1
while(x%i==0):
x//=i
i+=2
if x>1:
divs[cnt]=x
cnt+=1
g=2
while(1):
ok=True
for i in range(cnt):
if pow(g,(m-1)//divs[i],m)==1:
ok=False
break
if ok:
return g
g+=1
def bsf(self,x):
res=0
while(x%2==0):
res+=1
x//=2
return res
rank2=0
root=[]
iroot=[]
rate2=[]
irate2=[]
rate3=[]
irate3=[]
def __init__(self,MOD):
self.mod=MOD
self.g=self.primitive_root_constexpr(self.mod)
self.rank2=self.bsf(self.mod-1)
self.root=[0 for i in range(self.rank2+1)]
self.iroot=[0 for i in range(self.rank2+1)]
self.rate2=[0 for i in range(self.rank2)]
self.irate2=[0 for i in range(self.rank2)]
self.rate3=[0 for i in range(self.rank2-1)]
self.irate3=[0 for i in range(self.rank2-1)]
self.root[self.rank2]=pow(self.g,(self.mod-1)>>self.rank2,self.mod)
self.iroot[self.rank2]=pow(self.root[self.rank2],self.mod-2,self.mod)
for i in range(self.rank2-1,-1,-1):
self.root[i]=(self.root[i+1]**2)%self.mod
self.iroot[i]=(self.iroot[i+1]**2)%self.mod
prod=1;iprod=1
for i in range(self.rank2-1):
self.rate2[i]=(self.root[i+2]*prod)%self.mod
self.irate2[i]=(self.iroot[i+2]*iprod)%self.mod
prod=(prod*self.iroot[i+2])%self.mod
iprod=(iprod*self.root[i+2])%self.mod
prod=1;iprod=1
for i in range(self.rank2-2):
self.rate3[i]=(self.root[i+3]*prod)%self.mod
self.irate3[i]=(self.iroot[i+3]*iprod)%self.mod
prod=(prod*self.iroot[i+3])%self.mod
iprod=(iprod*self.root[i+3])%self.mod
def butterfly(self,a):
n=len(a)
h=(n-1).bit_length()
LEN=0
while(LEN<h):
if (h-LEN==1):
p=1<<(h-LEN-1)
rot=1
for s in range(1<<LEN):
offset=s<<(h-LEN)
for i in range(p):
l=a[i+offset]
r=a[i+offset+p]*rot
a[i+offset]=(l+r)%self.mod
a[i+offset+p]=(l-r)%self.mod
rot*=self.rate2[(~s & -~s).bit_length()-1]
rot%=self.mod
LEN+=1
else:
p=1<<(h-LEN-2)
rot=1
imag=self.root[2]
for s in range(1<<LEN):
rot2=(rot*rot)%self.mod
rot3=(rot2*rot)%self.mod
offset=s<<(h-LEN)
for i in range(p):
a0=a[i+offset]
a1=a[i+offset+p]*rot
a2=a[i+offset+2*p]*rot2
a3=a[i+offset+3*p]*rot3
a1na3imag=(a1-a3)%self.mod*imag
a[i+offset]=(a0+a2+a1+a3)%self.mod
a[i+offset+p]=(a0+a2-a1-a3)%self.mod
a[i+offset+2*p]=(a0-a2+a1na3imag)%self.mod
a[i+offset+3*p]=(a0-a2-a1na3imag)%self.mod
rot*=self.rate3[(~s & -~s).bit_length()-1]
rot%=self.mod
LEN+=2
def butterfly_inv(self,a):
n=len(a)
h=(n-1).bit_length()
LEN=h
while(LEN):
if (LEN==1):
p=1<<(h-LEN)
irot=1
for s in range(1<<(LEN-1)):
offset=s<<(h-LEN+1)
for i in range(p):
l=a[i+offset]
r=a[i+offset+p]
a[i+offset]=(l+r)%self.mod
a[i+offset+p]=(l-r)*irot%self.mod
irot*=self.irate2[(~s & -~s).bit_length()-1]
irot%=self.mod
LEN-=1
else:
p=1<<(h-LEN)
irot=1
iimag=self.iroot[2]
for s in range(1<<(LEN-2)):
irot2=(irot*irot)%self.mod
irot3=(irot*irot2)%self.mod
offset=s<<(h-LEN+2)
for i in range(p):
a0=a[i+offset]
a1=a[i+offset+p]
a2=a[i+offset+2*p]
a3=a[i+offset+3*p]
a2na3iimag=(a2-a3)*iimag%self.mod
a[i+offset]=(a0+a1+a2+a3)%self.mod
a[i+offset+p]=(a0-a1+a2na3iimag)*irot%self.mod
a[i+offset+2*p]=(a0+a1-a2-a3)*irot2%self.mod
a[i+offset+3*p]=(a0-a1-a2na3iimag)*irot3%self.mod
irot*=self.irate3[(~s & -~s).bit_length()-1]
irot%=self.mod
LEN-=2
def convolution(self,a,b):
n=len(a);m=len(b)
if not(a) or not(b):
return []
if min(n,m)<=40:
res=[0]*(n+m-1)
for i in range(n):
for j in range(m):
res[i+j]+=a[i]*b[j]
res[i+j]%=self.mod
return res
z=1<<((n+m-2).bit_length())
a=a+[0]*(z-n)
b=b+[0]*(z-m)
self.butterfly(a)
self.butterfly(b)
c=[(a[i]*b[i])%self.mod for i in range(z)]
self.butterfly_inv(c)
iz=pow(z,self.mod-2,self.mod)
for i in range(n+m-1):
c[i]=(c[i]*iz)%self.mod
return c[:n+m-1]
# user config
############
DEBUG_MODE=1
############
# import
import sys
import itertools
import bisect
import math
from collections import *
from functools import cache
from heapq import *
# alias
DD = defaultdict
BSL = bisect.bisect_left
BSR = bisect.bisect_right
# config
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
# input
def II(): return int(input())
def IS(): return input()[:-1]
def MI(): return map(int,input().split())
def LM(): return list(MI())
def LL(n): return [LM() for _ in range(n)]
def MI_1(): return map(lambda x:int(x)-1,input().split())
def LM_1(): return list(MI_1())
def LL_1(n): return [LM_1() for _ in range(n)]
def ALPHABET_TO_NUM(string, upper=False): return list(map(lambda elm:ord(elm)-ord("A") if upper else ord(elm)-ord("a"), string))
# functions
def DB(*args,**kwargs):
global DEBUG_MODE
if not DEBUG_MODE:
return
if args:
print(*args)
return
for name, value in kwargs.items():
print(f"{name} : {value}")
def bit_count(num):
length = num.bit_length()
res = 0
for i in range(length):
if num >> i & 1:
res += 1
return res
def popcount64(n):
# 63桁まで高速に動く.64桁まで正常に動く.
c=(n&0x5555555555555555)+((n>>1)&0x5555555555555555)
c=(c&0x3333333333333333)+((c>>2)&0x3333333333333333)
c=(c&0x0f0f0f0f0f0f0f0f)+((c>>4)&0x0f0f0f0f0f0f0f0f)
c=(c&0x00ff00ff00ff00ff)+((c>>8)&0x00ff00ff00ff00ff)
c=(c&0x0000ffff0000ffff)+((c>>16)&0x0000ffff0000ffff)
c=(c&0x00000000ffffffff)+((c>>32)&0x00000000ffffffff)
return c
def argmax(*args):
if len(args) == 1 and hasattr(args[0], '__iter__'):
lst = args[0]
else:
lst = args
return lst.index(max(lst))
def argmin(*args):
if len(args) == 1 and hasattr(args[0], '__iter__'):
lst = args[0]
else:
lst = args
return lst.index(min(lst))
def prefix_op(lst, op=lambda x,y:x+y, e=0):
N = len(lst)
res = [e]*(N+1)
for i in range(N):
res[i+1] = op(res[i], lst[i])
return res
def suffix_op(lst, op=lambda x,y:x+y, e=0):
N = len(lst)
res = [e]*(N+1)
for i in range(N):
res[N-1-i] = op(lst[N-1-i], res[N-i])
return res
def sigma_LinearFunc(coeff1, coeff0, left, right, MOD=None):
"""
coeff1*x + coeff0
の x = [left, right] の和を求める.
MODで計算したい場合、区間の引数をMOD取った上で代入しても良い.
そのとき、left > right となってもよい.
"""
if MOD:
# MODが素数でない場合にも対応するように、和公式を適応後に剰余を計算.
return ((coeff0%MOD*((right-left+1)%MOD)%MOD) + (coeff1%MOD*((left+right)*(right-left+1)//2%MOD)%MOD))%MOD
return coeff0*(right-left+1) + coeff1*(left+right)*(right-left+1)//2
def find_divisors(n):
divs_small, divs_big = [], []
i = 1
while i * i <= n:
if n % i == 0:
divs_small.append(i)
divs_big.append(n // i)
i += 1
if divs_big[-1] == divs_small[-1]:
divs_big.pop()
for e in reversed(divs_big):
divs_small.append(e)
return divs_small
def prime_factorization(n):
n_intact = n
ret = []
i = 2
while i * i <= n_intact:
if n % i == 0:
cnt = 0
while n % i == 0:
n //= i
cnt += 1
ret.append((i,cnt))
i += 1
if n != 1: ret.append((n,1))
return ret
""" 矩形の二次元配列を扱う諸関数 """
def copy_table(table):
H,W = len(table), len(table[0])
res = []
for i in range(H):
res.append([])
for j in range(W):
res[-1].append(table[i][j])
return res
def sum_table(table, MOD=None):
H,W = len(table), len(table[0])
res = 0
for i in range(H):
for j in range(W):
res += table[i][j]
if MOD:
res %= MOD
return res
def transpose_table(table):
H,W = len(table), len(table[0])
res = [[None]*H for _ in range(W)]
for i in range(H):
for j in range(W):
res[j][i] = table[i][j]
return res
def convert_table_to_bit(table, letter1="#", rev=False):
H,W = len(table), len(table[0])
res = []
for h in range(H):
rowBit = 0
for w in range(W):
if rev:
if table[h][w] == letter1:
rowBit += 2**w
else:
if table[h][W-w-1] == letter1:
rowBit += 2**w
res.append(rowBit)
return res
def rotate_table_cc(S): return list(zip(*S))[::-1]
def rotate_table_c(S): return list(zip(*S[::-1]))
def mul_matrix(A, B, mod=None):
N = len(A)
K = len(A[0])
if not hasattr(B[0], "__iter__"):
B = [[e] for e in B]
M = len(B[0])
res = [[0 for _ in range(M)] for _ in range(N)]
if mod is None:
for i in range(N):
for j in range(M):
for k in range(K):
res[i][j] += A[i][k] * B[k][j]
else:
for i in range(N):
for j in range(M):
for k in range(K):
res[i][j] += A[i][k] * B[k][j]
res[i][j] %= mod
return res
def pow_matrix(mat, exp, mod):
N = len(mat)
res = [[1 if i == j else 0 for i in range(N)] for j in range(N)]
while exp > 0 :
if exp%2 == 1 :
res = mul_matrix(res, mat, mod)
mat = mul_matrix(mat, mat, mod)
exp //= 2
return res
def compress(lst):
D = {e:i for i,e in enumerate(sorted(set(lst)))}
return [D[e] for e in lst]
def highDimCompress(lst):
#(x,y)の配列や,(x,y,z)の配列が与えられたとき,軸ごとに座圧する.
return list(zip(*list(map(compress,list(zip(*lst))))))
#classes
# https://github.com/tatyam-prime/SortedSet/blob/main/SortedSet.py
from bisect import bisect_left, bisect_right
from typing import Generic, Iterable, Iterator, List, Tuple, TypeVar, Optional
T = TypeVar('T')
class SortedSet(Generic[T]):
BUCKET_RATIO = 16
SPLIT_RATIO = 24
def __init__(self, a: Iterable[T] = []) -> None:
"Make a new SortedSet from iterable. / O(N) if sorted and unique / O(N log N)"
a = list(a)
n = self.size = len(a)
if any(a[i] > a[i + 1] for i in range(n - 1)):
a.sort()
if any(a[i] >= a[i + 1] for i in range(n - 1)):
a, b = [], a
for x in b:
if not a or a[-1] != x:
a.append(x)
bucket_size = int(math.ceil(math.sqrt(n / self.BUCKET_RATIO)))
self.a = [a[n * i // bucket_size : n * (i + 1) // bucket_size] for i in range(bucket_size)]
def __iter__(self) -> Iterator[T]:
for i in self.a:
for j in i: yield j
def __reversed__(self) -> Iterator[T]:
for i in reversed(self.a):
for j in reversed(i): yield j
def __eq__(self, other) -> bool:
return list(self) == list(other)
def __len__(self) -> int:
return self.size
def __repr__(self) -> str:
return "SortedSet" + str(self.a)
def __str__(self) -> str:
s = str(list(self))
return "{" + s[1 : len(s) - 1] + "}"
def _position(self, x: T) -> Tuple[List[T], int, int]:
"return the bucket, index of the bucket and position in which x should be. self must not be empty."
for i, a in enumerate(self.a):
if x <= a[-1]: break
return (a, i, bisect_left(a, x))
def __contains__(self, x: T) -> bool:
if self.size == 0: return False
a, _, i = self._position(x)
return i != len(a) and a[i] == x
def add(self, x: T) -> bool:
"Add an element and return True if added. / O(√N)"
if self.size == 0:
self.a = [[x]]
self.size = 1
return True
a, b, i = self._position(x)
if i != len(a) and a[i] == x: return False
a.insert(i, x)
self.size += 1
if len(a) > len(self.a) * self.SPLIT_RATIO:
mid = len(a) >> 1
self.a[b:b+1] = [a[:mid], a[mid:]]
return True
def _pop(self, a: List[T], b: int, i: int) -> T:
ans = a.pop(i)
self.size -= 1
if not a: del self.a[b]
return ans
def discard(self, x: T) -> bool:
"Remove an element and return True if removed. / O(√N)"
if self.size == 0: return False
a, b, i = self._position(x)
if i == len(a) or a[i] != x: return False
self._pop(a, b, i)
return True
def lt(self, x: T) -> Optional[T]:
"Find the largest element < x, or None if it doesn't exist."
for a in reversed(self.a):
if a[0] < x:
return a[bisect_left(a, x) - 1]
def le(self, x: T) -> Optional[T]:
"Find the largest element <= x, or None if it doesn't exist."
for a in reversed(self.a):
if a[0] <= x:
return a[bisect_right(a, x) - 1]
def gt(self, x: T) -> Optional[T]:
"Find the smallest element > x, or None if it doesn't exist."
for a in self.a:
if a[-1] > x:
return a[bisect_right(a, x)]
def ge(self, x: T) -> Optional[T]:
"Find the smallest element >= x, or None if it doesn't exist."
for a in self.a:
if a[-1] >= x:
return a[bisect_left(a, x)]
def __getitem__(self, i: int) -> T:
"Return the i-th element."
if i < 0:
for a in reversed(self.a):
i += len(a)
if i >= 0: return a[i]
else:
for a in self.a:
if i < len(a): return a[i]
i -= len(a)
raise IndexError
def pop(self, i: int = -1) -> T:
"Pop and return the i-th element."
if i < 0:
for b, a in enumerate(reversed(self.a)):
i += len(a)
if i >= 0: return self._pop(a, ~b, i)
else:
for b, a in enumerate(self.a):
if i < len(a): return self._pop(a, b, i)
i -= len(a)
raise IndexError
def index(self, x: T) -> int:
"Count the number of elements < x."
ans = 0
for a in self.a:
if a[-1] >= x:
return ans + bisect_left(a, x)
ans += len(a)
return ans
def index_right(self, x: T) -> int:
"Count the number of elements <= x."
ans = 0
for a in self.a:
if a[-1] > x:
return ans + bisect_right(a, x)
ans += len(a)
return ans
"""
(num, cnt)を要素としたSSを管理してMultiset化したいとき用.
"""
def exist(self, x):
ret = self.gt((x,0))
if ret is None:
return False
elif ret[0] == x:
return True
else:
return False
def increment(self, x):
if not self.exist(x):
self.add((x,1))
else:
num, cnt = self.gt((x,0))
self.discard((x,cnt))
self.add((x,cnt+1))
def decrement(self, x):
if not self.exist(x):
return
num, cnt = self.gt((x,0))
if cnt == 1:
self.discard((x,cnt))
else:
self.discard((x,cnt))
self.add((x,cnt-1))
def multi_add(self, x, y):
if not self.exist(x):
self.add((x,y))
else:
num, cnt = self.gt((x,0))
self.discard((x,cnt))
self.add((x,cnt+y))
def multi_sub(self, x, y):
if not self.exist(x):
return
num, cnt = self.gt((x,0))
if cnt <= y:
self.discard((x,cnt))
else:
self.discard((x,cnt))
self.add((x,cnt-y))
# https://github.com/tatyam-prime/SortedSet/blob/main/SortedMultiset.py
T = TypeVar('T')
class SortedMultiset(Generic[T]):
BUCKET_RATIO = 16
SPLIT_RATIO = 24
def __init__(self, a: Iterable[T] = []) -> None:
"Make a new SortedMultiset from iterable. / O(N) if sorted / O(N log N)"
a = list(a)
n = self.size = len(a)
if any(a[i] > a[i + 1] for i in range(n - 1)):
a.sort()
num_bucket = int(math.ceil(math.sqrt(n / self.BUCKET_RATIO)))
self.a = [a[n * i // num_bucket : n * (i + 1) // num_bucket] for i in range(num_bucket)]
def __iter__(self) -> Iterator[T]:
for i in self.a:
for j in i: yield j
def __reversed__(self) -> Iterator[T]:
for i in reversed(self.a):
for j in reversed(i): yield j
def __eq__(self, other) -> bool:
return list(self) == list(other)
def __len__(self) -> int:
return self.size
def __repr__(self) -> str:
return "SortedMultiset" + str(self.a)
def __str__(self) -> str:
s = str(list(self))
return "{" + s[1 : len(s) - 1] + "}"
def _position(self, x: T) -> Tuple[List[T], int, int]:
"return the bucket, index of the bucket and position in which x should be. self must not be empty."
for i, a in enumerate(self.a):
if x <= a[-1]: break
return (a, i, bisect_left(a, x))
def __contains__(self, x: T) -> bool:
if self.size == 0: return False
a, _, i = self._position(x)
return i != len(a) and a[i] == x
def count(self, x: T) -> int:
"Count the number of x."
return self.index_right(x) - self.index(x)
def add(self, x: T) -> None:
"Add an element. / O(√N)"
if self.size == 0:
self.a = [[x]]
self.size = 1
return
a, b, i = self._position(x)
a.insert(i, x)
self.size += 1
if len(a) > len(self.a) * self.SPLIT_RATIO:
mid = len(a) >> 1
self.a[b:b+1] = [a[:mid], a[mid:]]
def _pop(self, a: List[T], b: int, i: int) -> T:
ans = a.pop(i)
self.size -= 1
if not a: del self.a[b]
return ans
def discard(self, x: T) -> bool:
"Remove an element and return True if removed. / O(√N)"
if self.size == 0: return False
a, b, i = self._position(x)
if i == len(a) or a[i] != x: return False
self._pop(a, b, i)
return True
def lt(self, x: T) -> Optional[T]:
"Find the largest element < x, or None if it doesn't exist."
for a in reversed(self.a):
if a[0] < x:
return a[bisect_left(a, x) - 1]
def le(self, x: T) -> Optional[T]:
"Find the largest element <= x, or None if it doesn't exist."
for a in reversed(self.a):
if a[0] <= x:
return a[bisect_right(a, x) - 1]
def gt(self, x: T) -> Optional[T]:
"Find the smallest element > x, or None if it doesn't exist."
for a in self.a:
if a[-1] > x:
return a[bisect_right(a, x)]
def ge(self, x: T) -> Optional[T]:
"Find the smallest element >= x, or None if it doesn't exist."
for a in self.a:
if a[-1] >= x:
return a[bisect_left(a, x)]
def __getitem__(self, i: int) -> T:
"Return the i-th element."
if i < 0:
for a in reversed(self.a):
i += len(a)
if i >= 0: return a[i]
else:
for a in self.a:
if i < len(a): return a[i]
i -= len(a)
raise IndexError
def pop(self, i: int = -1) -> T:
"Pop and return the i-th element."
if i < 0:
for b, a in enumerate(reversed(self.a)):
i += len(a)
if i >= 0: return self._pop(a, ~b, i)
else:
for b, a in enumerate(self.a):
if i < len(a): return self._pop(a, b, i)
i -= len(a)
raise IndexError
def index(self, x: T) -> int:
"Count the number of elements < x."
ans = 0
for a in self.a:
if a[-1] >= x:
return ans + bisect_left(a, x)
ans += len(a)
return ans
def index_right(self, x: T) -> int:
"Count the number of elements <= x."
ans = 0
for a in self.a:
if a[-1] > x:
return ans + bisect_right(a, x)
ans += len(a)
return ans
class Comb:
def __init__(self,table_len,mod):
"""
modが素数の場合しか使用できない.
table_len に指定した数まで法modでのコンビネーションの計算が可能になる.
"""
self.fac = [1,1]
self.inv = [1,1]
self.finv = [1,1]
self.mod = mod
for i in range(2,table_len+1):
self.fac.append(self.fac[i-1]*i%mod)
self.inv.append(-self.inv[mod%i]*(mod//i)%mod)
self.finv.append(self.finv[i-1]*self.inv[i]%mod)
def comb(self,a,b):
return self.fac[a]*self.finv[b]*self.finv[a-b]%self.mod
class GridBFS:
def __init__(self, table):
#二次元配列や文字列の配列を受け取る.
self.table = table
self.H = len(table)
self.W = len(table[0])
self.wall = "#"
def find(self, c):
#table から引数の文字を探しインデックスを返す. 無い時、None.
for h in range(self.H):
for w in range(self.W):
if self.table[h][w] == c:
return (h,w)
return None
def set_wall_string(self, string):
#壁として扱う文字を "#!^" の様に文字列リテラルで格納. 初期値は、"#"
self.wall = string
def island(self, transition = [[-1,0],[0,1],[1,0],[0,-1]]):
H, W = self.H, self.W
self.island_id = [[-1]*W for _ in range(H)]
self.island_size = [[-1]*W for _ in range(W)]
crr_id = 0
id2size = dict()
for sh in range(H):
for sw in range(W):
if self.table[sh][sw] in self.wall:
continue
if self.island_id[sh][sw] != -1:
continue
deq = deque()
deq.append((sh,sw))
crr_size = 1
self.island_id[sh][sw] = crr_id
while deq:
h,w = deq.popleft()
for dh, dw in transition:
nh, nw = h+dh, w+dw
if (not 0<=nh<H) or (not 0<=nw<W):
continue
if self.table[nh][nw] in self.wall:
continue
if self.island_id[nh][nw] == -1:
self.island_id[nh][nw] = crr_id
deq.append((nh, nw))
crr_size += 1
id2size[crr_id] = crr_size
crr_id += 1
for h in range(H):
for w in range(W):
if self.table[h][w] in self.wall:
continue
self.island_size[h][w] = id2size[self.island_id[h][w]]
return self.island_id, self.island_size
def distance(self, start, goal=None, transition = [[-1,0],[0,1],[1,0],[0,-1]]):
#goal指定したら、goalまでの最短距離を、指定しなければdist配列を返す. 到達不可能は -1.
#二次元配列上での遷移方法を transition で指定できる. 初期値は上下左右.
H, W, tab, wall = self.H, self.W, self.table, self.wall
INF = 1<<60
deq = deque()
deq.append(start)
dist = [[INF]*W for _ in range(H)]
dist[start[0]][start[1]] = 0
if start == goal:
return 0
while deq:
h,w = deq.popleft()
for dh, dw in transition:
nh = h+dh
nw = w+dw
# gridの範囲外.
if (not 0<=nh<H) or (not 0<=nw<W):
continue
# wallに設定されている文字なら.
if tab[nh][nw] in wall:
continue
new_dist = dist[h][w] + 1
#goalが引数で与えられていてgoalに達したら終了.
if goal and (nh,nw)==goal:
return new_dist
if dist[nh][nw] > new_dist:
dist[nh][nw] = new_dist
deq.append((nh,nw))
# goalが設定されていていまだreturnされていないなら,
# goalに到達できなかったということ.
if goal:
return -1
return dist
class nth_root:
def __init__(self):
self.ngs = [-1, -1, 4294967296, 2642246, 65536, 7132, 1626, 566, 256, 139, 85, 57, 41, 31, 24, 20, 16, 14, 12, 11, 10, 9, 8, 7, 7, 6, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]
""" pre-calculated by this code """
# self.ngs = [-1,-1]
# for n in range(2,64):
# ok,ng=2**33,0
# while abs(ok-ng)>1:
# mid=ok+ng>>1
# if mid**n>=2**64:
# ok=mid
# else:
# ng=mid
# self.ngs.append(ok)
""" xが64bitに収まる時高速. そうでないときも動作するが速度の保証無し. """
def calc(self, x, n, is_x_within_64bit=True):
if x<=1 or n==1: return x
if is_x_within_64bit:
if n>=64: return 1
ng = self.ngs[n]
else:
ng = x
ok = 0
while abs(ok-ng)>1:
mid = ok+ng>>1
if mid**n <= x:
ok = mid
else:
ng = mid
return ok
# well-used const
global DIRECTION_4, DIRECTION_8, DIRECTION_DIAGONAL, DIRECTION_URDL_TABLE, DIRECTION_URDL_COORD_PLANE, MOD, INF, LOWER_ALP, UPPER_ALP, ALL_ALP
# clockwise from top.
DIRECTION_4 = [[-1,0],[0,1],[1,0],[0,-1]]
DIRECTION_8 = [[-1,0],[-1,1],[0,1],[1,1],[1,0],[1,-1],[0,-1],[-1,-1]]
DIRECTION_DIAGONAL = [[-1,1],[1,1],[1,-1],[-1,-1]]
DIRECTION_URDL_TABLE = {'U':(-1,0), 'R':(0,1), 'D':(1,0), 'L':(0,-1)}
DIRECTION_URDL_COORD_PLANE = {'U':(0,1), 'R':(1,0), 'D':(0,-1), 'L':(-1,0)}
MOD = 998244353
INF = 1<<60
LOWER_ALP = "abcdefghijklmnopqrstuvwxyz"
UPPER_ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
ALL_ALP = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"
main()