結果
| 問題 | No.650 行列木クエリ |
| ユーザー |
 navel_tos
|
| 提出日時 | 2024-02-12 16:37:43 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 1,954 ms / 2,000 ms |
| コード長 | 8,080 bytes |
| コンパイル時間 | 248 ms |
| コンパイル使用メモリ | 82,368 KB |
| 実行使用メモリ | 241,712 KB |
| 最終ジャッジ日時 | 2024-11-16 02:28:11 |
| 合計ジャッジ時間 | 11,868 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
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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 | 47 ms
55,168 KB |
| testcase_01 | AC | 1,257 ms
146,980 KB |
| testcase_02 | AC | 1,871 ms
238,900 KB |
| testcase_03 | AC | 43 ms
57,064 KB |
| testcase_04 | AC | 1,581 ms
154,144 KB |
| testcase_05 | AC | 1,874 ms
241,440 KB |
| testcase_06 | AC | 42 ms
54,528 KB |
| testcase_07 | AC | 42 ms
54,784 KB |
| testcase_08 | AC | 1,145 ms
144,144 KB |
| testcase_09 | AC | 1,954 ms
241,712 KB |
| testcase_10 | AC | 39 ms
54,784 KB |
ソースコード
#yukicoder 650 行列木クエリ
#Heavy-Light decomposition データ構造を使うならbuild必須なので注意
class HL_decomposition:
class SegmentTree: #前提mod1
def __init__(self, n, identity_e, function): self._n = n; self._size = 1 << (n - 1).bit_length(); self._e = e = identity_e; self._f = function; self._node = [e] * 2 * self._size
def build(self, A):
for i,v in enumerate(A, start = self._size): self._node[i] = v
for i in range(self._size - 1, 0, -1): self._node[i] = self._f(self._node[i<<1], self._node[i<<1|1])
def update(self, index, value):
i = self._size + index; self._node[i] = value
while i - 1: i >>= 1; self._node[i] = self._f(self._node[i<<1], self._node[i<<1|1])
def fold(self, Lt, Rt):
Lt, Rt = Lt + self._size, Rt + self._size; vL = vR = self._e
while Lt < Rt:
if Lt & 1: vL = self._f(vL, self._node[Lt]); Lt += 1
if Rt & 1: Rt -= 1; vR = self._f(self._node[Rt], vR)
Lt >>= 1; Rt >>= 1
return self._f(vL, vR)
class SparseTable: #前提mod2
def __init__(self, n, identity_e, function): self._n = n; self._logn = (n - 1).bit_length(); self._size = 1 << self._logn; self._e = e = identity_e; self._f = function; self._T = [[e] * self._logn for _ in range(self._size)]; self._A = [e] * self._size
def build(self, A):
e, f, T = self._e, self._f, self._T; self._A = A = A + [e] * (self._size - self._n)
for x in range(self._logn):
t = 1 << x
for s in range(t, self._size, t << 1):
T[s][x] = A[s]
for j in range(s + 1, s + t, +1): T[j][x] = f(T[j-1][x], A[j])
for s in range(self._size - t - 1, -1, - t << 1):
T[s][x] = A[s]
for j in range(s - 1, s - t, -1): T[j][x] = f(A[j], T[j+1][x])
def fold(self, Lt, Rt): Lt, Rt = max(0, Lt), min(self._size, Rt) - 1; x = (Lt ^ Rt).bit_length() - 1; return self._e if not 0 <= Lt <= Rt < self._size else self._A[Lt] if Lt == Rt else self._f( self._T[Lt][x], self._T[Rt][x] )
def __init__(self, N, G, identity_e = 0, func = 'add'):
#pos[v] = i, order[i] = v 頂点vのDFS順序がi番目
#leader[i]: Heavy edgeの代表値のDFS順序
#depth[i]: 再帰の深さ parent[i]: ひとつ根側のDFS順序
#A[i]: u - vパスの重みw。DFS順序が遅い頂点v側に入れる。pos[u] < pos[v] = i
self._N = N; self._logN = logN = N.bit_length(); self._e = e = identity_e
self._f = f = (lambda x,y: x + y) if func == 'add' else func
self._G = G = [[(v, e) for v in S] for S in G] if N > 1 and isinstance(G[0][0],int) else G
self._A = A = [e for _ in range(N)]; self.pos = pos = [-1] * N
self.order = order = [-1] * N; self.leader = leader = [-1] * N; size = [1] * N
self.depth = depth = [-1] * N; self.parent = parent = [-1] * N; Q = [(0, -1)]
for now,back in Q: #前処理
for nxt,_ in G[now]:
if nxt != back: Q.append((nxt, now))
while Q: now,back = Q.pop(); size[back] += size[now] if back != -1 else 0
Q.append((0, -1, e, 0, -1)) #HL分解
for i in range(N):
now, back, c, d, t = Q.pop(); pos[now], parent[i]= i, pos[back]
order[i], A[i], depth[i] = now, c, d; leader[i] = t = t if t != -1 else i
if size[now] > 1: #部分木のうち最大サイズのものを最後にappend
s, v, x = 0, now, e
for nxt,w in G[now]:
if nxt == back: continue
if s < size[nxt]:
if s > 0: Q.append((v, now, x, d + 1, -1))
s, v, x = size[nxt], nxt, w
else: Q.append((nxt, now, w, d + 1, -1))
Q.append((v, now, x, d, t))
def build(self, use_SegTree = True, A = 'no need to import'):
N, e, f = self._N, self._e, self._f
if A != 'no need to import': self._A = A
self._ST = ST = self.SegmentTree if use_SegTree else self.SparseTable
self._obvST = obvST = ST(N, e, f); obvST.build(self._A)
self._revST = revST = ST(N, e, f); revST.build(self._A[::-1])
def LCA(self, u, v): #O(logN)
i, j = self.pos[u], self.pos[v]; c, d = self.depth[i], self.depth[j]
if c > d: i, j, c, d = j, i, c, d
s, t = self.leader[i], self.leader[j]
for d in range(d - 1, c - 1, -1): j = self.parent[t]; t = self.leader[j]
while s != t: i, j = self.parent[s], self.parent[t]; s, t = self.leader[i], self.leader[j]
return self.order[ min(i,j) ]
def update(self, index_u, value_v, weight = None):
if weight == None: j, w = self.pos[index_u], value_v
else: i, j, w = self.pos[index_u], self.pos[value_v], weight; i, j = (j, i) if i > j else (i, j); assert self.parent[j] == i, 'not connect Tree edge'
self._A[j] = w; self._obvST.update(j, w); self._revST.update(self._N - 1 - j, w)
def fold(self, u, v, path_query = False): #u→vパスの作用値を取得
Lt = Rt = self._e; f = self._f; i, j = self.pos[u], self.pos[v]
c, d = self.depth[i], self.depth[j]; s, t = self.leader[i], self.leader[j]
for c in range(c - 1, d - 1, -1): Lt = f( Lt, self._revST.fold(N - 1 - i, N - s) ); i = self.parent[s]; s = self.leader[i]
for d in range(d - 1, c - 1, -1): Rt = f( self._obvST.fold(t, j + 1), Rt ); j = self.parent[t]; t = self.leader[j]
while s != t: Lt, Rt = f( Lt, self._revST.fold(N-1-i,N-s) ), f( self._obvST.fold(t,j+1), Rt ); i, j = self.parent[s], self.parent[t]; s, t = self.leader[i], self.leader[j]
if i > j: LCA, Lt = j, f( Lt, self._revST.fold(N - i - 1, N - j - 1) )
elif i < j: LCA, Rt = i, f( self._obvST.fold(i + 1, j + 1), Rt )
else: LCA = i
LCA = self._e if path_query else self._A[LCA]; return f( f(Lt, LCA), Rt )
#行列累乗 1行N列の行列は[[1, 2, ...]] と2重括弧に自動変換するので注意
class matrix_pow:
def __init__(self,MOD=998244353): self._MOD=MOD
def eye(self,N): #単位行列の作成
return [[1 if i==j else 0 for j in range(N)] for i in range(N)]
def add(self,A,B): #行列の加算
if isinstance(A[0],int): A=[A]
if isinstance(B[0],int): B=[B]
assert len(A) ==len(B), 'not same size'
assert len(A[0])==len(B[0]), 'not same size'
nG=[[0]*max(len(A[i]) for i in range(len(A))) for _ in range(len(A))]
for h in range(len(nG)):
for w in range(len(nG[h])):
if len(A[h])<w: nG[h][w]+=A[h][w]
if len(B[h])<w: nG[h][w]+=B[h][w]
nG[h][w]%=self._MOD
return nG
def mul(self,A,B): #行列積 L行M列 * M行N列 = L行N列
if isinstance(A[0],int): A=[A]
if isinstance(B[0],int): B=[B]
assert len(A[0])==len(B), 'cannot calcurate'
nG=[[0]*max(len(B[i]) for i in range(len(B))) for _ in range(len(A))]
for h in range(len(nG)):
for w in range(len(nG[0])):
for x in range(len(A[0])):
nG[h][w]+=A[h][x]*B[x][w]%self._MOD; nG[h][w]%=self._MOD
return nG
#入力高速化したらこれでも通るやろ
import sys
input = sys.stdin.readline
#入力受取
N = int(input())
G = [[] for _ in range(N)]
H = []
for _ in range(N - 1):
a,b = map(int,input().split())
G[a].append(b)
G[b].append(a)
H.append((a,b))
#HLDに乗せる 初期値は単位行列
mp = matrix_pow(10 ** 9 + 7)
HLD = HL_decomposition(N, G, [[1,0], [0,1]], mp.mul)
HLD.build(True)
#クエリを処理
for _ in range(int(input())):
t = list(input().split())
if t[0] == 'x':
i,w,x,y,z = map(int, t[1:])
u,v = H[i]
HLD.update(u, v, [[w,x],[y,z]])
if t[0] == 'g':
i,j = map(int, t[1:])
((w,x),(y,z)) = HLD.fold(i, j, True)
print(w,x,y,z)