結果
| 問題 | No.1614 Majority Painting on Tree |
| ユーザー |
 chineristAC
|
| 提出日時 | 2021-07-22 00:08:57 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 4,135 ms / 5,000 ms |
| コード長 | 15,870 bytes |
| コンパイル時間 | 214 ms |
| コンパイル使用メモリ | 82,520 KB |
| 実行使用メモリ | 179,808 KB |
| 最終ジャッジ日時 | 2024-07-17 20:55:11 |
| 合計ジャッジ時間 | 45,429 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
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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 | 2,755 ms
167,116 KB |
| testcase_01 | AC | 1,117 ms
120,104 KB |
| testcase_02 | AC | 814 ms
116,040 KB |
| testcase_03 | AC | 1,257 ms
120,004 KB |
| testcase_04 | AC | 1,153 ms
124,044 KB |
| testcase_05 | AC | 1,108 ms
123,760 KB |
| testcase_06 | AC | 1,441 ms
127,280 KB |
| testcase_07 | AC | 1,103 ms
125,576 KB |
| testcase_08 | AC | 632 ms
124,040 KB |
| testcase_09 | AC | 898 ms
117,696 KB |
| testcase_10 | AC | 378 ms
114,544 KB |
| testcase_11 | AC | 1,061 ms
117,500 KB |
| testcase_12 | AC | 1,143 ms
118,804 KB |
| testcase_13 | AC | 860 ms
116,664 KB |
| testcase_14 | AC | 1,543 ms
119,872 KB |
| testcase_15 | AC | 1,477 ms
119,272 KB |
| testcase_16 | AC | 514 ms
115,480 KB |
| testcase_17 | AC | 898 ms
117,524 KB |
| testcase_18 | AC | 1,747 ms
125,600 KB |
| testcase_19 | AC | 874 ms
109,948 KB |
| testcase_20 | AC | 3,875 ms
170,508 KB |
| testcase_21 | AC | 3,986 ms
179,808 KB |
| testcase_22 | AC | 4,135 ms
169,020 KB |
| testcase_23 | AC | 661 ms
106,712 KB |
| testcase_24 | AC | 3,765 ms
162,636 KB |
| testcase_25 | AC | 1,143 ms
114,932 KB |
| testcase_26 | AC | 2,293 ms
136,732 KB |
| testcase_27 | AC | 95 ms
82,588 KB |
| testcase_28 | AC | 97 ms
82,544 KB |
| testcase_29 | AC | 96 ms
82,896 KB |
| testcase_30 | AC | 100 ms
82,796 KB |
| testcase_31 | AC | 94 ms
82,428 KB |
| testcase_32 | AC | 95 ms
82,768 KB |
| testcase_33 | AC | 101 ms
82,820 KB |
| testcase_34 | AC | 94 ms
82,904 KB |
| testcase_35 | AC | 97 ms
82,540 KB |
| testcase_36 | AC | 61 ms
71,928 KB |
| testcase_37 | AC | 60 ms
72,592 KB |
| testcase_38 | AC | 61 ms
72,604 KB |
| testcase_39 | AC | 72 ms
78,460 KB |
| testcase_40 | AC | 62 ms
72,376 KB |
| testcase_41 | AC | 61 ms
72,492 KB |
| testcase_42 | AC | 60 ms
73,172 KB |
| testcase_43 | AC | 61 ms
72,356 KB |
| testcase_44 | AC | 60 ms
71,468 KB |
| testcase_45 | AC | 61 ms
72,484 KB |
| testcase_46 | AC | 61 ms
72,776 KB |
| testcase_47 | AC | 61 ms
72,632 KB |
| testcase_48 | AC | 60 ms
73,772 KB |
ソースコード
def divisors(M):
d=[]
i=1
while M>=i**2:
if M%i==0:
d.append(i)
if i**2!=M:
d.append(M//i)
i=i+1
return d
def popcount(x):
x = x - ((x >> 1) & 0x55555555)
x = (x & 0x33333333) + ((x >> 2) & 0x33333333)
x = (x + (x >> 4)) & 0x0f0f0f0f
x = x + (x >> 8)
x = x + (x >> 16)
return x & 0x0000007f
def eratosthenes(n):
res=[0 for i in range(n+1)]
prime=set([])
for i in range(2,n+1):
if not res[i]:
prime.add(i)
for j in range(1,n//i+1):
res[i*j]=1
return prime
def factorization(n):
res=[]
for p in prime:
if n%p==0:
while n%p==0:
n//=p
res.append(p)
if n!=1:
res.append(n)
return res
def euler_phi(n):
res = n
for x in range(2,n+1):
if x ** 2 > n:
break
if n%x==0:
res = res//x * (x-1)
while n%x==0:
n //= x
if n!=1:
res = res//n * (n-1)
return res
def ind(b,n):
res=0
while n%b==0:
res+=1
n//=b
return res
def isPrimeMR(n):
d = n - 1
d = d // (d & -d)
L = [2, 3, 5, 7, 11, 13, 17]
for a in L:
t = d
y = pow(a, t, n)
if y == 1: continue
while y != n - 1:
y = (y * y) % n
if y == 1 or t == n - 1: return 0
t <<= 1
return 1
def findFactorRho(n):
from math import gcd
m = 1 << n.bit_length() // 8
for c in range(1, 99):
f = lambda x: (x * x + c) % n
y, r, q, g = 2, 1, 1, 1
while g == 1:
x = y
for i in range(r):
y = f(y)
k = 0
while k < r and g == 1:
ys = y
for i in range(min(m, r - k)):
y = f(y)
q = q * abs(x - y) % n
g = gcd(q, n)
k += m
r <<= 1
if g == n:
g = 1
while g == 1:
ys = f(ys)
g = gcd(abs(x - ys), n)
if g < n:
if isPrimeMR(g): return g
elif isPrimeMR(n // g): return n // g
return findFactorRho(g)
def primeFactor(n):
i = 2
ret = {}
rhoFlg = 0
while i*i <= n:
k = 0
while n % i == 0:
n //= i
k += 1
if k: ret[i] = k
i += 1 + i % 2
if i == 101 and n >= 2 ** 20:
while n > 1:
if isPrimeMR(n):
ret[n], n = 1, 1
else:
rhoFlg = 1
j = findFactorRho(n)
k = 0
while n % j == 0:
n //= j
k += 1
ret[j] = k
if n > 1: ret[n] = 1
if rhoFlg: ret = {x: ret[x] for x in sorted(ret)}
return ret
def divisors(n):
res = [1]
prime = primeFactor(n)
for p in prime:
newres = []
for d in res:
for j in range(prime[p]+1):
newres.append(d*p**j)
res = newres
res.sort()
return res
def xorfactorial(num):#排他的論理和の階乗
if num==0:
return 0
elif num==1:
return 1
elif num==2:
return 3
elif num==3:
return 0
else:
x=baseorder(num)
return (2**x)*((num-2**x+1)%2)+function(num-2**x)
def xorconv(n,X,Y):
if n==0:
res=[(X[0]*Y[0])%mod]
return res
x=[X[i]+X[i+2**(n-1)] for i in range(2**(n-1))]
y=[Y[i]+Y[i+2**(n-1)] for i in range(2**(n-1))]
z=[X[i]-X[i+2**(n-1)] for i in range(2**(n-1))]
w=[Y[i]-Y[i+2**(n-1)] for i in range(2**(n-1))]
res1=xorconv(n-1,x,y)
res2=xorconv(n-1,z,w)
former=[(res1[i]+res2[i])*inv for i in range(2**(n-1))]
latter=[(res1[i]-res2[i])*inv for i in range(2**(n-1))]
former=list(map(lambda x:x%mod,former))
latter=list(map(lambda x:x%mod,latter))
return former+latter
def merge_sort(A,B):
pos_A,pos_B = 0,0
n,m = len(A),len(B)
res = []
while pos_A < n and pos_B < m:
a,b = A[pos_A],B[pos_B]
if a < b:
res.append(a)
pos_A += 1
else:
res.append(b)
pos_B += 1
res += A[pos_A:]
res += B[pos_B:]
return res
class UnionFindVerSize():
def __init__(self, N):
self._parent = [n for n in range(0, N)]
self._size = [1] * N
self.group = N
def find_root(self, x):
if self._parent[x] == x: return x
self._parent[x] = self.find_root(self._parent[x])
stack = [x]
while self._parent[stack[-1]]!=stack[-1]:
stack.append(self._parent[stack[-1]])
for v in stack:
self._parent[v] = stack[-1]
return self._parent[x]
def unite(self, x, y):
gx = self.find_root(x)
gy = self.find_root(y)
if gx == gy: return
self.group -= 1
if self._size[gx] < self._size[gy]:
self._parent[gx] = gy
self._size[gy] += self._size[gx]
else:
self._parent[gy] = gx
self._size[gx] += self._size[gy]
def get_size(self, x):
return self._size[self.find_root(x)]
def is_same_group(self, x, y):
return self.find_root(x) == self.find_root(y)
class WeightedUnionFind():
def __init__(self,N):
self.parent = [i for i in range(N)]
self.size = [1 for i in range(N)]
self.val = [0 for i in range(N)]
self.flag = True
self.edge = [[] for i in range(N)]
def dfs(self,v,pv):
stack = [(v,pv)]
new_parent = self.parent[pv]
while stack:
v,pv = stack.pop()
self.parent[v] = new_parent
for nv,w in self.edge[v]:
if nv!=pv:
self.val[nv] = self.val[v] + w
stack.append((nv,v))
def unite(self,x,y,w):
if not self.flag:
return
if self.parent[x]==self.parent[y]:
self.flag = (self.val[x] - self.val[y] == w)
return
if self.size[self.parent[x]]>self.size[self.parent[y]]:
self.edge[x].append((y,-w))
self.edge[y].append((x,w))
self.size[x] += self.size[y]
self.val[y] = self.val[x] - w
self.dfs(y,x)
else:
self.edge[x].append((y,-w))
self.edge[y].append((x,w))
self.size[y] += self.size[x]
self.val[x] = self.val[y] + w
self.dfs(x,y)
class Dijkstra():
class Edge():
def __init__(self, _to, _cost):
self.to = _to
self.cost = _cost
def __init__(self, V):
self.G = [[] for i in range(V)]
self._E = 0
self._V = V
@property
def E(self):
return self._E
@property
def V(self):
return self._V
def add_edge(self, _from, _to, _cost):
self.G[_from].append(self.Edge(_to, _cost))
self._E += 1
def shortest_path(self, s):
import heapq
que = []
d = [10**15] * self.V
d[s] = 0
heapq.heappush(que, (0, s))
while len(que) != 0:
cost, v = heapq.heappop(que)
if d[v] < cost: continue
for i in range(len(self.G[v])):
e = self.G[v][i]
if d[e.to] > d[v] + e.cost:
d[e.to] = d[v] + e.cost
heapq.heappush(que, (d[e.to], e.to))
return d
#Z[i]:length of the longest list starting from S[i] which is also a prefix of S
#O(|S|)
def Z_algorithm(s):
N = len(s)
Z_alg = [0]*N
Z_alg[0] = N
i = 1
j = 0
while i < N:
while i+j < N and s[j] == s[i+j]:
j += 1
Z_alg[i] = j
if j == 0:
i += 1
continue
k = 1
while i+k < N and k + Z_alg[k]<j:
Z_alg[i+k] = Z_alg[k]
k += 1
i += k
j -= k
return Z_alg
class BIT():
def __init__(self,n,mod=0):
self.BIT = [0]*(n+1)
self.num = n
self.mod = mod
def query(self,idx):
res_sum = 0
mod = self.mod
while idx > 0:
res_sum += self.BIT[idx]
if mod:
res_sum %= mod
idx -= idx&(-idx)
return res_sum
#Ai += x O(logN)
def update(self,idx,x):
mod = self.mod
while idx <= self.num:
self.BIT[idx] += x
if mod:
self.BIT[idx] %= mod
idx += idx&(-idx)
return
class dancinglink():
def __init__(self,n,debug=False):
self.n = n
self.debug = debug
self._left = [i-1 for i in range(n)]
self._right = [i+1 for i in range(n)]
self.exist = [True for i in range(n)]
def pop(self,k):
if self.debug:
assert self.exist[k]
L = self._left[k]
R = self._right[k]
if L!=-1:
if R!=self.n:
self._right[L],self._left[R] = R,L
else:
self._right[L] = self.n
elif R!=self.n:
self._left[R] = -1
self.exist[k] = False
def left(self,idx,k=1):
if self.debug:
assert self.exist[idx]
res = idx
while k:
res = self._left[res]
if res==-1:
break
k -= 1
return res
def right(self,idx,k=1):
if self.debug:
assert self.exist[idx]
res = idx
while k:
res = self._right[res]
if res==self.n:
break
k -= 1
return res
class SparseTable():
def __init__(self,A,merge_func,ide_ele):
N=len(A)
n=N.bit_length()
self.table=[[ide_ele for i in range(n)] for i in range(N)]
self.merge_func=merge_func
for i in range(N):
self.table[i][0]=A[i]
for j in range(1,n):
for i in range(0,N-2**j+1):
f=self.table[i][j-1]
s=self.table[i+2**(j-1)][j-1]
self.table[i][j]=self.merge_func(f,s)
def query(self,s,t):
b=t-s+1
m=b.bit_length()-1
return self.merge_func(self.table[s][m],self.table[t-2**m+1][m])
class BinaryTrie:
class node:
def __init__(self,val):
self.left = None
self.right = None
self.max = val
def __init__(self):
self.root = self.node(-10**15)
def append(self,key,val):
pos = self.root
for i in range(29,-1,-1):
pos.max = max(pos.max,val)
if key>>i & 1:
if pos.right is None:
pos.right = self.node(val)
pos = pos.right
else:
pos = pos.right
else:
if pos.left is None:
pos.left = self.node(val)
pos = pos.left
else:
pos = pos.left
pos.max = max(pos.max,val)
def search(self,M,xor):
res = -10**15
pos = self.root
for i in range(29,-1,-1):
if pos is None:
break
if M>>i & 1:
if xor>>i & 1:
if pos.right:
res = max(res,pos.right.max)
pos = pos.left
else:
if pos.left:
res = max(res,pos.left.max)
pos = pos.right
else:
if xor>>i & 1:
pos = pos.right
else:
pos = pos.left
if pos:
res = max(res,pos.max)
return res
def solveequation(edge,ans,n,m):
#edge=[[to,dire,id]...]
x=[0]*m
used=[False]*n
for v in range(n):
if used[v]:
continue
y = dfs(v)
if y!=0:
return False
return x
def dfs(v):
used[v]=True
r=ans[v]
for to,dire,id in edge[v]:
if used[to]:
continue
y=dfs(to)
if dire==-1:
x[id]=y
else:
x[id]=-y
r+=y
return r
class slope_trick():
def __init__(self):
self.L = [10**17]
self.R = [10**17]
self.min_f = 0
self.x_move = 0
def move(self,a):
self.x_move += a
def add_right(self,a):
a -= self.x_move
l0 = -self.L[0]
if l0 <= a:
heappush(self.R,a)
else:
heappush(self.L,-a)
heappush(self.R,-heappop(self.L))
self.min_f = self.min_f + max(0,l0-a)
def add_left(self,a):
a -= self.x_move
r0 = self.R[0]
if a <= r0:
heappush(self.L,-a)
else:
heappush(self.R,a)
heappush(self.L,-heappop(self.R))
self.min_f = self.min_f + max(0,a-r0)
def add_abs(self,a):
self.add_left(a)
self.add_right(a)
def change_min_left(self):
self.R = [10**17]
def change_min_right(self):
self.L = [10**17]
import sys,random,bisect
from collections import deque,defaultdict
from heapq import heapify,heappop,heappush
from itertools import permutations
from math import gcd,log
input = lambda :sys.stdin.readline().rstrip()
mi = lambda :map(int,input().split())
li = lambda :list(mi())
def cmb(n, r, mod):
if ( r<0 or r>n ):
return 0
return (g1[n] * g2[r] % mod) * g2[n-r] % mod
mod = 998244353
N = 2*10**5
g1 = [1]*(N+1)
g2 = [1]*(N+1)
inverse = [1]*(N+1)
for i in range( 2, N + 1 ):
g1[i]=( ( g1[i-1] * i ) % mod )
inverse[i]=( ( -inverse[mod % i] * (mod//i) ) % mod )
g2[i]=( (g2[i-1] * inverse[i]) % mod )
inverse[0]=0
N,C = mi()
edge = [[] for v in range(N)]
for _ in range(N-1):
a,b = mi()
edge[a-1].append(b-1)
edge[b-1].append(a-1)
parent = [-1 for v in range(N)]
topo = []
deq = deque([0])
while deq:
v = deq.popleft()
topo.append(v)
for nv in edge[v]:
if parent[v]==nv:
continue
parent[nv] = v
deq.append(nv)
pow_k = [1 for i in range(N+1)]
dp = [0 for v in range(N)]
def solve(k):
for i in range(1,N+1):
pow_k[i] = (k-1) * pow_k[i-1] % mod
for v in topo[::-1]:
m = len(edge[v])//2 + 1
n = len(edge[v])
if v!=0 and n==1:
dp[v] = 1
continue
#all
tmp = 1
ALL = 1
for nv in edge[v]:
if nv==parent[v]:
continue
tmp *= dp[nv]
tmp %= mod
ALL *= k
ALL %= mod
#not 過半数
#過半数: cならm-1以上 そうでないならm以上
minus = 0
for i in range(n):
if m <= i:
minus += cmb(n-1,i,mod) * pow_k[n-1-i] % mod
minus %= mod
dp[v] = 1 + ALL - (minus * k % mod) - (cmb(n-1,m-1,mod) * pow_k[n-1-(m-1)] % mod)
dp[v] %= mod
dp[v] *= tmp
dp[v] %= mod
v = 0
m = len(edge[v])//2 + 1
n = len(edge[v])
#all
tmp = 1
for nv in edge[v]:
tmp *= dp[nv]
tmp %= mod
#not 過半数
minus = 0
for i in range(n+1):
if m <= i:
minus += cmb(n,i,mod) * pow_k[n-i] % mod
minus %= mod
dp[v] = k + pow(k,n,mod) - (minus * k)
dp[v] %= mod
dp[v] *= tmp
dp[v] %= mod
return dp[v]
res = 0
for k in range(1,C+1):
if (C-k)&1:
res -= solve(k) * cmb(C,k,mod)
else:
res += solve(k) * cmb(C,k,mod)
#print(solve(k))
res %= mod
print(res)