結果
| 問題 | No.2912 ０次パーシステントホモロジー |
| ユーザー |
 lif4635
|
| 提出日時 | 2024-10-04 21:39:36 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 699 ms / 2,000 ms |
| コード長 | 59,290 bytes |
| コンパイル時間 | 225 ms |
| コンパイル使用メモリ | 91,052 KB |
| 実行使用メモリ | 106,368 KB |
| 最終ジャッジ日時 | 2024-10-04 21:39:43 |
| 合計ジャッジ時間 | 6,314 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
（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 | 85 ms
77,552 KB |
| testcase_01 | AC | 86 ms
77,316 KB |
| testcase_02 | AC | 82 ms
77,440 KB |
| testcase_03 | AC | 81 ms
77,568 KB |
| testcase_04 | AC | 81 ms
77,312 KB |
| testcase_05 | AC | 81 ms
77,448 KB |
| testcase_06 | AC | 80 ms
77,312 KB |
| testcase_07 | AC | 82 ms
77,312 KB |
| testcase_08 | AC | 81 ms
77,300 KB |
| testcase_09 | AC | 92 ms
77,312 KB |
| testcase_10 | AC | 80 ms
77,328 KB |
| testcase_11 | AC | 80 ms
77,184 KB |
| testcase_12 | AC | 82 ms
77,312 KB |
| testcase_13 | AC | 83 ms
77,184 KB |
| testcase_14 | AC | 79 ms
77,312 KB |
| testcase_15 | AC | 113 ms
79,872 KB |
| testcase_16 | AC | 346 ms
97,796 KB |
| testcase_17 | AC | 368 ms
90,240 KB |
| testcase_18 | AC | 452 ms
92,272 KB |
| testcase_19 | AC | 699 ms
104,320 KB |
| testcase_20 | AC | 691 ms
104,424 KB |
| testcase_21 | AC | 510 ms
106,368 KB |
| testcase_22 | AC | 531 ms
105,856 KB |
ソースコード
def main():
n,m = MI()
edge = LLI(m)
edge.sort(key = lambda x: x[2])
t = II()
r = LI()
r = [(r[i],i) for i in range(t)]
r.sort()
uf = dsu(n)
idx = 0
cnt = n
ans = [0]*t
for w,k in r:
while idx < m and edge[idx][2] <= w:
a,b,_ = edge[idx]
if not uf.same(a,b):
uf.merge(a,b)
cnt -= 1
idx += 1
ans[k] = cnt
for i in ans:
print(i)
"""==================fold line=================="""
class dsu():
n=1
parent_or_size=[-1 for i in range(n)]
def __init__(self,N):
self.n=N
self.parent_or_size=[-1 for i in range(N)]
def merge(self,a,b):
assert 0<=a<self.n, "0<=a<n,a={0},n={1}".format(a,self.n)
assert 0<=b<self.n, "0<=b<n,b={0},n={1}".format(b,self.n)
x=self.leader(a)
y=self.leader(b)
if x==y:
return x
if (-self.parent_or_size[x]<-self.parent_or_size[y]):
x,y=y,x
self.parent_or_size[x]+=self.parent_or_size[y]
self.parent_or_size[y]=x
return x
def same(self,a,b):
assert 0<=a<self.n, "0<=a<n,a={0},n={1}".format(a,self.n)
assert 0<=b<self.n, "0<=b<n,b={0},n={1}".format(b,self.n)
return self.leader(a)==self.leader(b)
def leader(self,a):
assert 0<=a<self.n, "0<=a<n,a={0},n={1}".format(a,self.n)
if (self.parent_or_size[a]<0):
return a
self.parent_or_size[a]=self.leader(self.parent_or_size[a])
return self.parent_or_size[a]
def size(self,a):
assert 0<=a<self.n, "0<=a<n,a={0},n={1}".format(a,self.n)
return -self.parent_or_size[self.leader(a)]
def groups(self):
leader_buf=[0 for i in range(self.n)]
group_size=[0 for i in range(self.n)]
for i in range(self.n):
leader_buf[i]=self.leader(i)
group_size[leader_buf[i]]+=1
result=[[] for i in range(self.n)]
for i in range(self.n):
result[leader_buf[i]].append(i)
result2=[]
for i in range(self.n):
if len(result[i])>0:
result2.append(result[i])
return result2
"""import"""
# array
from bisect import bisect_left,bisect_right
from heapq import heapify,heappop,heappush
from collections import deque,defaultdict,Counter
# math
import math,random,cmath
from math import comb,ceil,floor,factorial,gcd,lcm,atan2,sqrt,isqrt,pi,e
from itertools import product,permutations,combinations,accumulate
from functools import cmp_to_key, cache
# system
from typing import Generic, Iterable, Iterator, List, Tuple, TypeVar, Optional
T = TypeVar('T')
import sys
sys.setrecursionlimit(10**9)
"""input"""
#int-input
def II() -> int : return int(input())
def MI() -> int : return map(int, input().split())
def TI() -> tuple[int] : return tuple(MI())
def LI() -> list[int] : return list(MI())
#str-input
def SI() -> str : return input()
def MSI() -> str : return input().split()
def SI_L() -> list[str] : return list(SI())
def SI_LI() -> list[int] : return list(map(int, SI()))
#multiple-input
def LLI(n) -> list[list[int]]: return [LI() for _ in range(n)]
def LSI(n) -> list[str]: return [SI() for _ in range(n)]
#1-indexを0-indexでinput
def MI_1() -> int : return map(lambda x:int(x)-1, input().split())
def TI_1() -> tuple[int] : return tuple(MI_1())
def LI_1() -> list[int] : return list(MI_1())
def ordalp(s:str) -> int|list[int]:
if len(s) == 1:
return ord(s)-ord("A") if s.isupper() else ord(s)-ord("a")
return list(map(lambda i: ord(i)-ord("A") if i.isupper() else ord(i)-ord("a"), s))
def ordallalp(s:str) -> int|list[int]:
if len(s) == 1:
return ord(s)-ord("A")+26 if s.isupper() else ord(s)-ord("a")
return list(map(lambda i: ord(i)-ord("A")+26 if i.isupper() else ord(i)-ord("a"), s))
def graph(n:str, m:str, dir:bool=False , index=-1) -> list[set[int]]:
"""
(頂点,辺,有向か,indexの調整)
defaultは無向辺、(index)-1
"""
edge = [set() for i in range(n+1+index)]
for _ in range(m):
a,b = map(int, input().split())
a,b = a+index,b+index
edge[a].add(b)
if not dir:
edge[b].add(a)
return edge
def graph_w(n:str, m:str, dir:bool=False , index=-1) -> list[set[tuple]]:
"""
(頂点,辺,有向か,indexの調整)
defaultは無向辺、index-1
"""
edge = [set() for i in range(n+1+index)]
for _ in range(m):
a,b,c = map(int, input().split())
a,b = a+index,b+index
edge[a].add((b,c))
if not dir:
edge[b].add((a,c))
return edge
"""const"""
mod, inf = 998244353, 1<<60
isnum = {int,float,complex}
true, false, none = True, False, None
def yes() -> None: print("Yes")
def no() -> None: print("No")
def yn(flag:bool) -> None: print("Yes" if flag else "No")
def ta(flag:bool) -> None: print("Takahashi" if flag else "Aoki")
alplow = "abcdefghijklmnopqrstuvwxyz"
alpup = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
alpall = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"
URDL = {'U':(-1,0), 'R':(0,1), 'D':(1,0), 'L':(0,-1)}
DIR_4 = [[-1,0],[0,1],[1,0],[0,-1]]
DIR_8 = [[-1,0],[-1,1],[0,1],[1,1],[1,0],[1,-1],[0,-1],[-1,-1]]
DIR_BISHOP = [[-1,1],[1,1],[1,-1],[-1,-1]]
prime60 = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59]
# alias
DD = defaultdict
BSL = bisect_left
BSR = bisect_right
"""math fanctions"""
"""point"""
cross_pro = lambda p1,p2 : p2[0]*p1[1] - p2[1]*p1[0] #外積
dist = lambda p1,p2 : sqrt(pow(p1[0]-p2[0],2) + pow(p1[1]-p2[1],2))
def max_min_cross(p1, p2, p3, p4, touch = False):
min_ab, max_ab = min(p1, p2), max(p1, p2)
min_cd, max_cd = min(p3, p4), max(p3, p4)
if touch:
if min_ab > max_cd or max_ab < min_cd:
return False
return True
else:
if min_ab >= max_cd or max_ab <= min_cd:
return False
return True
def cross_judge(a, b, c, d, touch = False):
"""線分abとcdの交差判定 接するも含むかどうか"""
# x座標による判定
if not max_min_cross(a[0], b[0], c[0], d[0], touch):
return False
# y座標による判定
if not max_min_cross(a[1], b[1], c[1], d[1], touch):
return False
tc1 = (a[0] - b[0]) * (c[1] - a[1]) + (a[1] - b[1]) * (a[0] - c[0])
tc2 = (a[0] - b[0]) * (d[1] - a[1]) + (a[1] - b[1]) * (a[0] - d[0])
td1 = (c[0] - d[0]) * (a[1] - c[1]) + (c[1] - d[1]) * (c[0] - a[0])
td2 = (c[0] - d[0]) * (b[1] - c[1]) + (c[1] - d[1]) * (c[0] - b[0])
if touch:
return tc1 * tc2 <= 0 and td1 * td2 <= 0
else:
return tc1 * tc2 < 0 and td1 * td2 < 0
"""primary function"""
def prod(lst:list[int|str], mod = None) -> int|str:
"""product 文字列の場合連結"""
ans = 1
if type(lst[0]) in isnum:
for i in lst:
ans *= i
if mod: ans %= mod
return ans
else:
return "".join(lst)
def sigma(first:int, diff:int, term:int) -> int: #等差数列の和
return term*(first*2+(term-1)*diff)//2
def xgcd(a:int, b:int) -> tuple[int,int,int]: #Euclid互除法
"""ans = a*x0 + b*y0"""
x0, y0, x1, y1 = 1, 0, 0, 1
while b != 0:
q, a, b = a // b, b, a % b
x0, x1 = x1, x0 - q * x1
y0, y1 = y1, y0 - q * y1
return a, x0, y0
def modinv(a:int, mod = mod) -> int: #逆元
"""逆元"""
g, x, y = xgcd(a, mod)
#g != 1は逆元が存在しない
return -1 if g != 1 else x % m
def nth_root(x:int, n:int, is_x_within_64bit = True) -> int: #n乗根
"""floor(n√x)"""
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]
if x <= 1 or n == 1:
return x
if is_x_within_64bit:
if n >= 64:
return 1
ng = ngs[n]
else:
ng = x
ok = 0
while abs(ok - ng) > 1:
mid = (ok + ng)//2
if mid**n <= x:
ok = mid
else:
ng = mid
return ok
def pi_base(p:list) -> Iterator:
l = len(p)
num = [0]*l
while True:
yield num
num[~0] += 1
for i in range(l):
if num[~i] == p[~i]:
if i == l-1:
return
num[~i] = 0
num[~(i+1)] += 1
else:
break
"""prime"""
def primefact(n:int) -> dict[int,int]: #素因数分解
"""素因数分解"""
i = 2
pdict = dict()
while i*i <= n:
if n%i == 0:
cnt = 0
while n%i == 0:
n //= i
cnt += 1
pdict[i] = cnt
i += 1
if n != 1:
pdict[n] = 1
return pdict
def primenumber(lim:int, get = None) -> list[int]: #素数列挙
"""
素数列挙 sieve(n)もあります
get == None : リスト
get >= 1 : flag
get < 1 : 累積和
"""
lim += 1
#素数にはflagを立てる
p = [1]*lim
#それ以下の素数の数を保管
cntp = [0]*lim
#素数列を格納
plist = []
p[0],p[1] = 0,0
for i in range(2,lim):
if p[i]:
plist.append(i)
for j in range(2*i,lim,i):
p[j] = 0
for i in range(1,lim):
cntp[i] = cntp[i-1] + p[i]
if get is None:
return plist
elif get >= 1:
return p
else:
return cntp
def divisors(n:int) -> list[int] : #約数列挙
"""約数列挙"""
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
"""binary number"""
lenbit = lambda bit: (bit).bit_length()
def popcnt(n:int) -> int: #popcnt
"""int.bit_count() があります 64bitまで"""
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 binchange(n:int,fill0 = None) -> str:
"""10進数(int)→2進数(str) fill0:0埋め桁数"""
return format(n, "0"+str(fill0)+"b") if fill0 else format(n,"b")
"""list"""
def prefix_op(lst:list, op = lambda x,y:x+y, e = 0) -> list: #累積和
"""defaultは累積和"""
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:list, op = lambda x,y:x+y, e = 0) -> list: #累積和
"""defaultは累積和"""
n = len(lst)
res = [e]*(n+1)
for i in reversed(range(n)):
res[i] = op(res[i+1], lst[i])
return res
def mex(lst:list) -> int:
"""補集合の最小非負整数"""
l = set(lst)
ans = 0
while ans in l:
ans += 1
return ans
def inversion_cnt(lst:list, flag = None) -> int: #転倒数
"""転倒数 not順列→flag立てる"""
n = len(lst)
if not flag is None:
comp = Compress(lst)
lst = comp.comp
else:
lst = list(map(lambda x : x-1, lst))
ft = FenwickTree(n)
ans = [0]*n #i要素目の転倒への寄与
for i in range(n):
ans[i] = ft.sum(lst[i]+1,n)
ft.add(lst[i], 1)
return ans
def doubling(nex:list, k:int = None ,a:list = None) -> list:
"""nex:操作列 k:回数 a:初期列"""
n = len(nex)
if k is None:
log = 60
else:
log = (k+1).bit_length()
res = [[-1]*n for _ in range(log)] #ダブリング配列
res[0] = nex[:]
for cnt in range(1,log):
for i in range(n):
tmp = res[cnt-1][i]
res[cnt][i] = res[cnt-1][tmp]
if k is None:
return res
ans = (nex[:] if a is None else a[:])
for cnt in range(log):
if k & (1<<cnt) != 0:
ans = [ans[res[cnt][i]] for i in range(n)]
return ans
def swapcnt(a:list, b:list) -> int:
"""
順列（同じ要素がない）が前提
最小操作回数を返す
"""
if sorted(a) != sorted(b):
return -1
t = dict()
cnt = 0
for i in range(n):
x,y = a[i],b[i]
if x == y:
continue
if x in t:
while x in t:
x_ = t[x]
del t[x]
x = x_
cnt += 1
if x == y:
break
else:
t[y] = x
else:
t[y] = x
return cnt
"""matrix"""
def mul_matrix(A, B, mod = mod): #行列の積 A*B
N = len(A)
K = len(A[0])
M = len(B[0])
res = [[0 for _ in range(M)] for _ in range(N)]
for i in range(N) :
for j in range(K) :
for k in range(M) :
res[i][k] += A[i][j] * B[j][k]
res[i][k] %= mod
return res
def pow_matrix(mat, exp, mod = mod): #二分累乗
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
"""enumerate"""
def fact_enu(lim): #階乗列挙
#階乗
fac = [1]
#階乗の逆数
divfac = [1]
factorial = 1
for i in range(1,lim+1):
factorial *= i
factorial %= mod
fac.append(factorial)
divfac.append(pow(factorial,-1,mod))
return fac,divfac
class Comb_enu: #combination列挙
def __init__(self,lim,mod = mod):
"""
mod : prime指定
lim以下のmodでcomdination計算
"""
self.fac = [1,1]
self.inv = [1,1]
self.finv = [1,1]
self.mod = mod
for i in range(2,lim+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):
if a < b:
return 0
if a < 0:
return 0
return self.fac[a]*self.finv[b]*self.finv[a-b]%self.mod
"""str"""
def int_0(str,l,r = None, over_ok = False): #str→int
"""
strの[l,r)桁をintで返す(0-index)
取れない場合はNone
over_okを立てればrが桁を超えても返す
"""
lstr = len(str)
if l > len(str):
return None
l = lstr - l
if r == None:
if "" == str[r:l]:
return 0
return int(str[:l])
if r > len(str):
if over_ok:
return int(str[:l])
else:
return None
r = lstr - r
if "" == str[r:l]:
return 0
return int(str[r:l])
def lis(l): #後でちゃんと書き直してね
# STEP1: LIS長パート with 使用位置
n = len(l)
lisDP = [inf] * n # いまi文字目に使っている文字
indexList = [None] * n # lの[i]文字目が使われた場所を記録する
for i in range(n):
# 通常のLISを求め、indexListに使った場所を記録する
ind = bisect_left(lisDP, l[i])
lisDP[ind] = l[i]
indexList[i] = ind
# STEP2: LIS復元パート by 元配列の使用した位置
# 後ろから見ていくので、まずは、LIS長目(targetIndex)のindexListを探したいとする
targetIndex = max(indexList)
ans = [0] * (targetIndex + 1) # 復元結果(indexListは0-indexedなのでlen=4ならmax=3で格納されているので+1する)
# 後ろから見ていく
for i in range(n - 1, -1, -1):
# もし、一番最後に出てきているtargetIndexなら
if indexList[i] == targetIndex:
ans[targetIndex] = l[i] # ansのtargetIndexを確定
targetIndex -= 1
return ans
"""table operation"""
def acc_sum(lst:list, dim = 2) -> list:
if dim == 2:
h,w = len(lst),len(lst[0])
res = [[0]*(w+1)]
for i in range(h):
res.append([0])
for j in range(w):
res[-1].append(res[i+1][j] + lst[i][j])
for j in range(w):
for i in range(h):
res[i+1][j+1] += res[i][j+1]
return res
elif dim == 3:
d1,d2,d3 = len(lst),len(lst[0]),len(lst[0][0])
res = [[[0]*(d3+1) for i in range(d2+1)]]
for i in range(d1):
res.append([[0]*(d3+1)])
for j in range(d2):
res[-1].append([0])
for k in range(d3):
res[-1][-1].append(res[i+1][j+1][k] + lst[i][j][k])
for j in range(d2):
for k in range(d3):
for i in range(d1):
res[i+1][j+1][k+1] += res[i][j+1][k+1]
for k in range(d3):
for i in range(d1):
for j in range(d2):
res[i+1][j+1][k+1] += res[i+1][j][k+1]
return res
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 rotate_table(table): #反時計回りに回転
return list(map(list, zip(*table)))[::-1]
def transpose_table(l): #行と列を入れ替え
return [list(x) for x in zip(*l)]
def bitconvert_table(table, letter1="#", rev=False): #各行bitに変換
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 += 1<<w
else:
if table[h][W-w-1] == letter1:
rowBit += 1<<w
res.append(rowBit)
return res
"""sort"""
def argment_sort(points): #偏角ソート
yposi,ynega = [],[]
for x,y in points:
if y > 0 or (y == 0 and x >= 0):
yposi.append([x,y])
else:
ynega.append([x,y])
yposi.sort(key = cmp_to_key(cross_pro))
ynega.sort(key = cmp_to_key(cross_pro))
return yposi+ynega
def quick_sort(lst, comparision, left = 0, right = -1):
"""
(list,比較関数,(l),(r))
input : (p,q)
output : True (p<q)
"""
i = left
if right == -1:
right %= len(lst)
j = right
pivot = (i+j)//2
dpivot = lst[pivot]
while True:
#条件式
while comparision(lst[i],dpivot):
i += 1
while comparision(dpivot,lst[j]):
j -= 1
if i >= j:
break
lst[i],lst[j] = lst[j],lst[i]
i += 1
j -= 1
if left < i - 1:
quick_sort(lst, left, i - 1)
if right > j + 1:
quick_sort(lst, j + 1, right)
def bubble_sort(lst):
"""返り値:転倒数"""
cnt = 0
n = len(lst)
for i in range(n):
for j in reversed(range(i+1),n):
if a[j] > a[j-1]:
a[j],a[j-1] = a[j-1],a[j]
cnt += 1
return cnt
def topological_sort(egde, inedge=None):
n = len(edge)
if inedge == None:
inedge = [0]*n
for v in range(n):
for adj in edge(v):
inedge[adj] += 1
ans = [i for i in range(n) if inedge[i] == 0]
que = deque(ans)
while que:
q = que.popleft()
for e in edge[q]:
inedge[e] -= 1
if inedge[e] == 0:
que.append(e)
ans.append(e)
return ans
"""graph fanctions"""
def dijkstra(edge, start=0, goal=None):
"""計算量 O((node+edge)log(edge))"""
n = len(edge)
dis = [inf]*n
dis[start] = 0
que = [(0, start)]
heapify(que)
while que:
cur_dis,cur_node = heappop(que)
if dis[cur_node] < cur_dis:
continue
for next_node, weight in edge[cur_node]:
next_dis = cur_dis + weight
if next_dis < dis[next_node]:
dis[next_node] = next_dis
heappush(que, (next_dis, next_node))
if goal != None: return dis[goal]
return dis
def warshallfloyd(dis):
n = len(dis)
for i in range(n):
dis[i][i] = 0
for k in range(n):
for i in range(n):
for j in range(n):
dis[i][j] = min(dis[i][j], dis[i][k]+dis[k][j])
return dis
def bellmanford(edge, start=0, goal=None):
"""
始点と終点が決まっている
始点から到達可能かつ、終点に到達可能な閉路のみ検出
"""
n = len(edge)
dis = [inf]*n
pre = [-1]*n #最短経路における直前にいた頂点
negative = [False]*n #たどり着くときに負の閉路があるかどうか
dis[start] = 0
for t in range(2*n):
for u in range(n):
for v, cost in edge[u]:
if dis[v] > dis[u] + cost:
if t >= n-1 and v == goal:
return None #0と衝突しないように
elif i >= n-1:
dis[v] = -inf
else:
dis[v] = dis[u] + cost
pre[v] = u
return dis[goal] #通常はここで終わり
#最短経路の復元
x = goal
path = [x]
while x != start:
x = pre[x]
path.append(x)
#最短経路を含む負の閉路があるかどうか
for i in reversed(range(len(path)-1)):
u, v = path[i+1], path[i]
if dis[v] > dis[u] + cost:
dis[v] = dis[u] + cost
negative[v] = True
if negative[u]:
negative[v] = True
if negative[end]:
return -1
else:
return d[end]
#ループ検出書くの嫌いなので用意しましょう
def loop(g):
pass
"""data stucture"""
#双方向リスト
# https://github.com/tatyam-prime/SortedSet?tab=readme-ov-file
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 = 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)
n = self.size = len(a)
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 "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
class SortedList(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 Deque: #両端以外もO(1)でアクセスできるdeque
def __init__(self, src_arr=[], max_size=300000):
self.N = max(max_size, len(src_arr)) + 1
self.buf = list(src_arr) + [None] * (self.N - len(src_arr))
self.head = 0
self.tail = len(src_arr)
def __index(self, i):
l = len(self)
if not -l <= i < l: raise IndexError('index out of range: ' + str(i))
if i < 0:
i += l
return (self.head + i) % self.N
def __extend(self):
ex = self.N - 1
self.buf[self.tail+1 : self.tail+1] = [None] * ex
self.N = len(self.buf)
if self.head > 0:
self.head += ex
def is_full(self):
return len(self) >= self.N - 1
def is_empty(self):
return len(self) == 0
def append(self, x):
if self.is_full(): self.__extend()
self.buf[self.tail] = x
self.tail += 1
self.tail %= self.N
def appendleft(self, x):
if self.is_full(): self.__extend()
self.buf[(self.head - 1) % self.N] = x
self.head -= 1
self.head %= self.N
def pop(self):
if self.is_empty(): raise IndexError('pop() when buffer is empty')
ret = self.buf[(self.tail - 1) % self.N]
self.tail -= 1
self.tail %= self.N
return ret
def popleft(self):
if self.is_empty(): raise IndexError('popleft() when buffer is empty')
ret = self.buf[self.head]
self.head += 1
self.head %= self.N
return ret
def __len__(self):
return (self.tail - self.head) % self.N
def __getitem__(self, key):
return self.buf[self.__index(key)]
def __setitem__(self, key, value):
self.buf[self.__index(key)] = value
def __str__(self):
return 'Deque({0})'.format(str(list(self)))
class WeightedUnionFind: #重み付きunion-find
def __init__(self, N):
self.N = N
self.parents = [-1] * N
self.rank = [0] * N
self.weight = [0] * N
def root(self, x):
if self.parents[x] == -1:
return x
rx = self.root(self.parents[x])
self.weight[x] += self.weight[self.parents[x]]
self.parents[x] = rx
return self.parents[x]
def get_weight(self, x):
self.root(x)
return self.weight[x]
def unite(self, x, y, d):
'''
A[x] - A[y] = d
'''
w = d + self.get_weight(x) - self.get_weight(y)
rx = self.root(x)
ry = self.root(y)
if rx == ry:
_, d_xy = self.diff(x, y)
if d_xy == d:
return True
else:
return False
if self.rank[rx] < self.rank[ry]:
rx, ry = ry, rx
w = -w
if self.rank[rx] == self.rank[ry]:
self.rank[rx] += 1
self.parents[ry] = rx
self.weight[ry] = w
return True
def is_same(self, x, y):
return self.root(x) == self.root(y)
def diff(self, x, y):
if self.is_same(x, y):
return True, self.get_weight(y) - self.get_weight(x)
else:
return False, 0
"""binary search"""
def bi_int(comparison, ok = 0, ng = inf):
"""
[lowlim,ans)だとTrueで[ans,uplim)だとFalse
のイメージで実装
"""
if not pred(ok):
#条件を満たすことがない
return ok
while abs(ng - ok) > 1:
mid = ok + (ng - ok)//2
if comparison(mid):
ok = mid
else:
ng = mid
return ok
def bi_float(comparison, ok = 0, ng = inf, error = 10**(-9)):
"""
[lowlim,ans)だとTrueで[ans,uplim)だとFalse
のイメージで実装
"""
if not pred(ok):
#条件を満たすことがない
return ok
#相対誤差と絶対誤差のどちらかがerror以下で終了
while abs(ng - ok)/abs(ng) > error and abs(ng - ok) > eroor:
mid = ok + (ng - ok)/2
if comparison(mid):
ok = mid
else:
ng = mid
return ok
"""compress"""
class Compress: #座標圧縮（一次元）
def __init__(self, arr):
values = sorted(set(arr))
self.translator = dict([(values[i], i) for i in range(len(values))])
self.inv_translator = values
self.comp = []
for x in arr:
self.comp.append(self.translator[x])
#圧縮前→圧縮後
def to_comp(self, x):
return self.translator[x]
#圧縮後→圧縮前
def from_comp(self, v):
return self.inv_translator[v]
#lstを変換
def lst_comp(self, lst):
return [self.to_comp(i) for i in lst]
class Compress2D: #２次元リスト[x,y]の座標圧縮
def __init__(self, arr):
self.x = Compress([x for x, y in arr])
self.y = Compress([y for x, y in arr])
self.comp = []
for x,y in arr:
self.comp.append([self.x.translator[x],self.y.translator[y]])
#圧縮前→圧縮後
def to_comp(self, x):
return (self.x.translator[x[0]], self.y.translator[x[1]])
#圧縮後→圧縮前
def from_comp(self, v):
return (self.x.translator[v[0]], self.y.translator[v[1]])
class RollingHash: #hash化
def __init__(self, string, base = 37, mod = 10**9 + 9):
self.mod = mod
l = len(string)
self.hash = [0]*(l+1)
for i in range(1,l+1):
self.hash[i] = ( self.hash[i-1] * base + ord(string[i-1]) ) % mod
self.pw = [1]*(l+1)
for i in range(1,l+1):
self.pw[i] = self.pw[i-1] * base % mod
def get(self, l, r):
"""s[l:r]のhash"""
return (self.hash[r] - self.hash[l] * self.pw[r-l]) % self.mod
class ZobristHash: #多重集合の一致判定
def __init__(self, n, as_list:bool = False, mod = (1<<61)-1):
self.N = n
self.conversion = [random.randint(1, mod - 1) for i in range(n+1)]
self.as_list = as_list #setとして扱うかlistの並び替えか
self.Mod = mod
def makehash(self, a:list):
la = len(a)
hashlst = [0]*(la+1)
if self.as_list:
#listの並び替えとしての一致
for i in range(la):
hashlst[i+1] = (hashlst[i]+self.conversion[a[i]])%self.Mod
return hashlst
else:
#setとしての一致
cnt = {}
for i in range(la):
if a[i] in cnt:
hashlst[i+1] = hashlst[i+1]
continue
cnt.add(a[i])
hashlst[i+1] = hashlst[i]^self.conversion[a[i]]
return hashlst
def get(self, hashedlst:list, l:int, r:int):
"""a[l:r]のhashを返します"""
if self.as_list:
return (hashedlst[r]-hashedlst[l])%self.Mod
else:
return hashedlst[r]^hashedlst[l]
"""畳み込み？？"""
"""graph"""
class GridSearch:
def __init__(self, table):
"""盤面の受取"""
self.table = table
self.H = len(table)
self.W = len(table[0])
self.wall = "#"
self.dist = [[inf]*self.W for _ in range(self.H)]
def find(self, c):
"""始点,終点等の取得"""
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(self, string):
"""壁の設定"""
self.wall = string
def can_start(self, *start):
"""探索済みでないかつ壁でない"""
if len(start) == 1:
i,j = start[0][0],start[0][1]
else:
i,j = start[0],start[1]
if self.dist[i][j] == inf and not self.table[i][j] in self.wall:
return True
else:
return False
def island(self, transition = DIR_4):
"""連結成分の検出"""
H, W = self.H, self.W
self.island_id = [[-1]*W for _ in range(H)]
self.island_size = [[-1]*W for _ in range(H)]
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 DFS(self, start, goal=None, transition = DIR_4):
"""
DFSをします
input : (start,(goal),(transition))
output : dis(table) or goalまでのdis(int)
"""
H, W = self.H, self.W
deq = deque()
deq.append(start)
self.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 self.table[nh][nw] in self.wall:
continue
new_dist = self.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 self.dist[nh][nw] > new_dist:
self.dist[nh][nw] = new_dist
deq.append((nh,nw))
if goal:
return -1
return self.dist
def DFS_break(self, start, goal=None, transition = DIR_4):
"""
壁をcost = 1で破壊できる それ以外の移動はcost = 0
input : (start,(goal),(transition))
output : dis(table) or goalまでのdis(int)
"""
H, W = self.H, self.W
deq = deque()
deq.append(start)
self.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
now_dist = self.dist[h][w]
#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 now_dist
# wallに設定されている文字なら.
if self.table[nh][nw] in self.wall:
if self.dist[nh][nw] > now_dist+1:
self.dist[nh][nw] = now_dist+1
deq.append((nh,nw))
elif self.dist[nh][nw] > now_dist:
self.dist[nh][nw] = now_dist
deq.appendleft((nh,nw))
if goal:
return -1
return self.dist
#バリエーションとして
#方向変換したら距離加算
#壁破壊で距離加算
#壁の種類として他のものがある
#視線が壁になる
#マグネット
#移動に制限がある（エネルギー）
class RootedTree:
"""
__allmethod__
autobuild -> obj : inputから構築
set_root -> None
is_root,is_leaf -> bool
yield_edges -> Iterator
### set_weight -> None : weightのdict生成
get_weight -> int : dictから重さを取得
get_depth -> int : rootからの深さ
### build_depth -> None : 深さの構築
build_des_size -> None :
centroid_decomposition :
build_centroid_dist
is_member_of_centroid_tree
is_id_larger
get_higher_centroids_with_self
yield_centroid_children
find_lowest_common_centroid
"""
@classmethod
def autobuild(cls, N, root = 0, input_index = 1):
"""
(u,v) , (u,v,c)に対応
rootを設定したくないならNone
"""
G = [[] for _ in range(N)]
if N == 1:
obj = RootedTree(G)
if root is not None:
obj.set_root(0)
return obj
line1 = list(map(int, input().split()))
assert 2 <= len(line1) <= 3
# 重み無し.
if len(line1) == 2:
u,v = line1
u,v = u-input_index, v-input_index
G[u].append(v)
G[v].append(u)
for _ in range(N-2):
u,v = map(int, input().split())
u,v = u-input_index, v-input_index
G[u].append(v)
G[v].append(u)
obj = RootedTree(G)
if root is not None:
obj.set_root(0)
return obj
else:
u,v,c = line1
u,v = u-input_index, v-input_index
G[u].append(v)
G[v].append(u)
edge = [(u,v,c)]
for _ in range(N-2):
u,v,c = map(int, input().split())
u,v = u-input_index, v-input_index
G[u].append(v)
G[v].append(u)
edge.append((u,v,c))
obj = RootedTree(G)
obj.set_weight(edge)
if root is not None:
obj.set_root(0)
return obj
def __init__(self, G):
self.N = len(G)
self.G = G
self._rooted = False
self._has_weight = False
self._key = 10**7
def set_root(self, root):
""" DFSついでにトポロジカルソート列も求める """
assert self._rooted == False
self.root = root
n, G = self.N, self.G
par, ch, ts = [-1]*n, [[] for _ in range(n)], []
deq = deque([root])
while deq:
v = deq.popleft()
ts.append(v)
for adj in G[v]:
if adj == par[v]: continue
par[adj] = v
ch[v].append(adj)
deq.append(adj)
self.parent, self.children, self.ts_order = par, ch, ts
self._rooted = True
def encode(self, u, v): #edgte -> int
return u*self._key + v
def decode(self, uv): #int -> edge
return divmod(uv, self._key)
def is_root(self, v) -> bool:
return v == self.root
def is_leaf(self, v) -> bool:
return len(self.children[v]) == 0
def yield_edges(self) -> Iterator[tuple]:
"""rootに近い順にedgeを回すIterator"""
N, ts, ch = self.N, self.ts_order, self.children
if self._has_weight:
wei, en = self.weight, self.encode
for v in ts:
for c in ch[v]:
yield (v,c,wei[en(v,c)])
else:
for v in ts:
for c in ch[v]:
yield (v,c)
""" weight """
#edge->weightにO(1)でアクセスできるようにdictで持つ
def set_weight(self, edge):
assert self._has_weight == False
d = {}
for u,v,c in edge:
d[self.encode(u,v)] = d[self.encode(v,u)] = c
self.weight = d
self._has_weight = True
def get_weight(self, u, v) -> int:
return self.weight[self.encode(u, v)]
"""depth : rootからの深さ"""
def get_depth(self, v) -> int:
# obj.depth[v] と同じ.
if not hasattr(self, "depth"):
self.build_depth()
return self.depth[v]
def build_depth(self):
assert self._rooted
N, ch, ts = self.N, self.children, self.ts_order
depth = [0]*N
for v in ts:
for c in ch[v]:
depth[c] = depth[v] + 1
self.depth = depth
"""subtree_size : 部分木"""
def build_des_size(self):
assert self._rooted
if hasattr(self, "des_size"):
return
N, ts, par = self.N, self.ts_order, self.parent
des = [1]*N
for i in range(N-1,0,-1):
v = ts[i]
p = par[v]
des[p] += des[v]
self.des_size = des
"""centroid : 重心分解"""
def centroid_decomposition(self, build_dist=True):
"""
centroid_id[i] : DFS的に重心分解をしたとき,
頂点iを重心とする重心木が何番目に登場するか.
頂点cenを重心とする重心木の頂点を探索する際は,頂点cenから,
T.is_id_larger(v, cen)==True
な頂点vのみを使って到達可能な頂点vを探索すればいい.
centroid_dfs_order : centroid_id の逆順列.
reveresed(centroid_dfs_order)順に重心木を探索することで
より小さい重心木についての結果を用いたDPが可能.
"""
if hasattr(self, "centroid_id"):
return
# 根に依存しないアルゴリズムなので根0にしていい.
if not self._rooted:
self.set_root(0)
if not hasattr(self, "des_size"):
self.build_des_size()
# sizeは書き換えるのでコピーを使用.
N, G, size = self.N, self.G, self.des_size[:]
c_id, c_depth, c_par, c_dfs_order = [-1]*N, [-1]*N, [-1]*N, []
stack = [(self.root, -1, 0)]
# 重心を見つけたら,「重心分解後のその頂点が重心となる部分木」の
# DFS順の順番, 深さ, 重心木における親にあたる部分木の重心を記録
for order in range(N):
v, prev, d = stack.pop()
while True:
for adj in G[v]:
if c_id[adj] == -1 and size[adj]*2 > size[v]:
# adjを今見ている部分木の根にし,sizeを書き換える.
size[v], size[adj], v = size[v]-size[adj], size[v], adj
break
else:
break
c_id[v], c_depth[v], c_par[v] = order, d, prev
c_dfs_order.append(v)
if size[v] > 1:
for adj in G[v]:
if c_id[adj] == -1:
stack.append((adj, v, d+1))
self.centroid_id, self.centroid_depth, self.centroid_parent, self.centroid_dfs_order = c_id, c_depth, c_par, c_dfs_order
if build_dist == True:
self.build_centroid_dist()
def build_centroid_dist(self):
"""
重心同士を結んだ木を重心分解木と呼ぶことにする.
重心分解木のみを考えて解けるなら楽だが、
「各重心木における重心(根)との距離」
を求めるには元の辺の情報が必要.一方それさえ求めれば、
重心分解木に対する考察だけで足りる問題が多い.
"""
if hasattr(self, "centroid_dist"):
return False
if not hasattr(self, "centroid_id"):
self.centroid_decomposition()
N, G, c_depth = self.N, self.G ,self.centroid_depth
is_id_larger = self.is_id_larger
log = max(c_depth) + 1
# dist[d][v] : vが深さdの重心木に属しているならその重心からの距離.
dist = [[-1]*N for _ in range(log)]
for cen in range(N):
d = c_depth[cen]
stack = [cen]
dist[d][cen] = 0
while stack:
v = stack.pop()
for adj in G[v]:
if dist[d][adj] == -1 and is_id_larger(adj, cen):
if self._has_weight:
dist[d][adj] = dist[d][v] + self.weight[self.encode(v, adj)]
else:
dist[d][adj] = dist[d][v] + 1
stack.append(adj)
self.centroid_log, self.centroid_dist = log, dist
def is_member_of_centroid_tree(self, v, c):
# 頂点vが重心cの重心木に属するかを判定 O(logN)
vs = self.get_higher_centroids_with_self(v)
return c in vs
def is_id_larger(self, u, v):
# 重心cからBFSする時に、is_id_larger(adj, c)とすれば重心木内部を探索できる.
return self.centroid_id[u] > self.centroid_id[v]
def get_higher_centroids_with_self(self, c):
# 頂点cが属する重心木の重心をサイズの昇順に列挙. O(logN)
vs = []
for d in range(self.centroid_depth[c], -1, -1):
vs.append(c)
c = self.centroid_parent[c]
return vs
def yield_centroid_children(self, v):
# 頂点vを重心とする重心木における,
# 「『vの子供を根とした部分木』と構成が同じ重心木の重心」を列挙する.
# 「『重心木』の木」における「『vを重心とする重心木』の子の重心木」の重心 ともいえる.
G, is_id_larger, c_par = self.G, self.is_id_larger, self.centroid_parent
for ch in G[v]:
if is_id_larger(ch, v):
ch_cen = ch
while c_par[ch_cen] != v:
ch_cen = c_par[ch_cen]
yield (ch, ch_cen)
def find_lowest_common_centroid(self, u, v):
# 頂点u,vをどちらも含む最小の重心木を返す. O(logN)
c_depth, c_par = self.centroid_depth, self.centroid_parent
du, dv = c_depth[u], c_depth[v]
if du > dv:
u,v = v,u
du,dv = dv,du
for _ in range(dv - du):
v = c_par[v]
while u != v:
u,v = c_par[u],c_par[v]
return u
def build_the_centroid(self):
""" 全体の重心だけで十分な時用 O(N) """
if not self._rooted:
self.set_root(0)
if hasattr(self, "the_centroid"):
return False
if hasattr(self, "centroid_id"):
self.the_centroid = self.centroid_id[0]
return True
if not hasattr(self, "des_size"):
self.build_des_size()
N, ch, size = self.N, self.children, self.des_size
v = self.root
while True:
for c in ch[v]:
if size[c] > N // 2:
v = c
break
else:
self.the_centroid = v
return True
def get_the_centroid(self):
if hasattr(self, "centroid_id"):
return self.centroid_id[0]
if not hasattr(self, "the_centroid"):
self.build_the_centroid()
return self.the_centroid
""" tree dp """
def dp_from_leaf(self, merge, e, add_root, push=lambda obj,data,dst,src:data):
"""
チートシート
部分木の大きさ : dp_from_leaf(lambda x,y:x+y, 0, lambda x,y,z:y+1)
"""
assert self._rooted
# pushで形整えたデータを親の単位元で初期化されたノードにmerge.
# 子が全部mergeされたらadd_rootで自身の頂点の情報を追加.
N, ts, par = self.N, self.ts_order, self.parent
sub = [e] * N
for i in range(N-1,-1,-1):
v = ts[i]
sub[v] = add_root(self, sub[v], v)
p = par[v]
if p != -1:
sub[p] = merge(sub[p], push(self, sub[v], p, v))
return sub
def rerooting_dp(self, merge, e, add_root, push=lambda obj,data,dst,src:data):
"""全方位木DP 途中で頂点を変更する"""
if self._rooted == False:
self.set_root(0)
sub = self.dp_from_leaf(merge, e, add_root, push)
N = self.N
ts, par, ch = self.ts_order, self.parent, self.children
compl, dp = [e]*N, [e]*N
for i in range(N):
v = ts[i]
p, size = par[v], len(ch[v])
left, right = [e]*size, [e]*size
for j in range(size):
c = ch[v][j]
left[j] = merge(left[j-1] if j>0 else e, push(self, sub[c], v, c))
for j in range(size-1,-1,-1):
c = ch[v][j]
right[j] = merge(right[j+1] if j<size-1 else e, push(self, sub[c], v, c))
for j in range(size):
c = ch[v][j]
compl[c] = merge(compl[c], left[j-1] if j>0 else e)
compl[c] = merge(compl[c], right[j+1] if j<size-1 else e)
if p != -1:
compl[c] = merge(compl[c], push(self, compl[v], v, p))
compl[c] = add_root(self, compl[c], v)
if p != -1:
dp[v] = merge(dp[v], push(self, compl[v], v, p))
dp[v] = merge(dp[v], left[-1] if size else e)
dp[v] = add_root(self, dp[v], v)
return dp
""" dist """
def build_dist_from_root(self, op = lambda x,y : x+y):
assert self._rooted
if hasattr(self, "dist_from_root"):
return
N, ts, ch = self.N, self.ts_order, self.children
dist = [0]*N
if self._has_weight:
wei, en = self.weight, self.encode
else:
wei, en = [1], lambda a,b:0
for v in ts:
for c in ch[v]:
dist[c] = op(dist[v], wei[en(v, c)])
self.dist_from_root = dist
def calc_dist_from_a_node(self, v, op = lambda x,y : x+y):
""" v -> children[v] のdist """
N, G = self.N, self.G
dist, que = [None]*N, [v]
dist[v] = 0
if self._has_weight:
wei, en = self.weight, self.encode
else:
wei, en = [1], lambda a,b:0
while que:
v = que.pop()
for adj in G[v]:
if dist[adj] is None:
dist[adj] = op(dist[v], wei[en(v, adj)])
que.append(adj)
return dist
def build_diameter(self):
"""直径を求める"""
self.build_dist_from_root()
if hasattr(self, "diameter"):
return
dist_r = self.dist_from_root
v = dist_r.index(max(dist_r))
dist_v = self.calc_dist_from_a_node(v)
dia = max(dist_v)
u = dist_v.index(dia)
self.diameter, self.end_points_of_diameter = dia, [v, u]
def get_diameter(self):
"""直径の取得"""
if hasattr(self, "diameter"):
return self.diameter
self.build_diameter()
return self.diameter
main()
"""==================fold line 1800=================="""