結果
| 問題 | No.1103 Directed Length Sum |
| ユーザー |
 None
|
| 提出日時 | 2021-03-02 00:04:25 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 10,616 bytes |
| コンパイル時間 | 330 ms |
| コンパイル使用メモリ | 82,304 KB |
| 実行使用メモリ | 503,372 KB |
| 最終ジャッジ日時 | 2024-10-03 01:16:16 |
| 合計ジャッジ時間 | 10,633 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
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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 | 42 ms
59,904 KB |
| testcase_01 | AC | 41 ms
54,400 KB |
| testcase_02 | AC | 1,023 ms
349,508 KB |
| testcase_03 | AC | 1,240 ms
503,372 KB |
| testcase_04 | AC | 1,983 ms
242,760 KB |
| testcase_05 | TLE | - |
| testcase_06 | -- | - |
| testcase_07 | -- | - |
| testcase_08 | -- | - |
| testcase_09 | -- | - |
| testcase_10 | -- | - |
| testcase_11 | -- | - |
| testcase_12 | -- | - |
| testcase_13 | -- | - |
| testcase_14 | -- | - |
| testcase_15 | -- | - |
| testcase_16 | -- | - |
| testcase_17 | -- | - |
| testcase_18 | -- | - |
| testcase_19 | -- | - |
| testcase_20 | -- | - |
| testcase_21 | -- | - |
| testcase_22 | -- | - |
| testcase_23 | -- | - |
ソースコード
class Tree():
def __init__(self, n, decrement=1):
self.n = n
self.edges = [[] for _ in range(n)]
self.root = None
self.size = [1]*n # number of nodes in subtree
self.decrement = decrement
def add_edge(self, u, v, i):
u, v = u-self.decrement, v-self.decrement
self.edges[u].append(v)
self.edges[v].append(u)
def add_edges(self, edges):
for i, p in enumerate(edges):
u, v = p
u, v = u-self.decrement, v-self.decrement
self.edges[u].append(v)
self.edges[v].append(u)
def set_root(self, root):
root -= self.decrement
self.depth = [-1]*self.n
self.root = root
self.par = [-1]*self.n
self.depth[root] = 0
self.order = [root]
next_set = [root]
while next_set:
p = next_set.pop()
for q in self.edges[p]:
if self.depth[q] != -1: continue
self.par[q] = p
self.depth[q] = self.depth[p]+1
self.order.append(q)
next_set.append(q)
for p in self.order[::-1]:
for q in self.edges[p]:
if self.par[p] == q: continue
self.size[p] += self.size[q]
def diameter(self, path=False):
# assert self.root is not None
u = self.depth.index(max(self.depth))
dist = [-1]*self.n
dist[u] = 0
prev = [-1]*self.n
next_set = [u]
while next_set:
p = next_set.pop()
for q in self.edges[p]:
if dist[q] != -1: continue
dist[q] = dist[p]+1
prev[q] = p
next_set.append(q)
d = max(dist)
if path:
v = w = dist.index(d)
path = [v+1]
while w != u:
w = prev[w]
path.append(w+self.decrement)
return d, v+self.decrement, u+self.decrement, path
else: return d
def rerooting(self, op, merge, id):
# assert self.root is not None
dp1 = [id] * self.n
dp2 = [id] * self.n
for p in self.order[::-1]:
t = id
for q in self.edges[p]:
if self.par[p] == q: continue
dp2[q] = t
t = merge(t, op(dp1[q], p, q))
t = id
for q in self.edges[p][::-1]:
if self.par[p] == q: continue
dp2[q] = merge(t, dp2[q])
t = merge(t, op(dp1[q], p, q))
dp1[p] = t
for q in self.order[1:]:
pq = self.par[q]
dp2[q] = op(merge(dp2[q], dp2[pq]), q, pq)
dp1[q] = merge(dp1[q], dp2[q])
return dp1
def heavy_light_decomposition(self):
"""
return flat array of lists of heavy edges (1-indexed if decrement=True)
"""
# assert self.root is not None
self.vid = [-1]*self.n
self.hld = [-1]*self.n
self.head = [-1]*self.n
self.head[self.root] = self.root
self.heavy_node = [-1]*self.n
next_set = [self.root]
for i in range(self.n):
""" for tree graph, dfs ends in N times """
p = next_set.pop()
self.vid[p] = i
self.hld[i] = p+self.decrement
maxs = 0
for q in self.edges[p]:
""" encode direction of Heavy edge into heavy_node """
if self.par[p] == q: continue
if maxs < self.size[q]:
maxs = self.size[q]
self.heavy_node[p] = q
for q in self.edges[p]:
""" determine "head" of heavy edge """
if self.par[p] == q or self.heavy_node[p] == q: continue
self.head[q] = q
next_set.append(q)
if self.heavy_node[p] != -1:
self.head[self.heavy_node[p]] = self.head[p]
next_set.append(self.heavy_node[p])
return self.hld
def lca(self, u, v):
# assert self.head is not None
u, v = u-self.decrement, v-self.decrement
while True:
if self.vid[u] > self.vid[v]: u, v = v, u
if self.head[u] != self.head[v]:
v = self.par[self.head[v]]
else:
return u + self.decrement
def path(self, u, v):
""" return the path array of the shortest path on u-v """
p = self.lca(u, v)
u, v, p = u-self.decrement, v-self.decrement, p-self.decrement
R = []
while u != p:
yield u+self.decrement
u = self.par[u]
yield p+self.decrement
while v != p:
R.append(v)
v = self.par[v]
for v in reversed(R):
yield v+self.decrement
def distance(self, u, v):
# assert self.head is not None
p = self.lca(u, v)
u, v, p = u-self.decrement, v-self.decrement, p-self.decrement
return self.depth[u] + self.depth[v] - 2*self.depth[p]
def find(self, u, v, x):
return self.distance(u,x)+self.distance(x,v)==self.distance(u,v)
def path_to_list(self, u, v, edge_query=False):
"""
transform a half-open interval into segments on the self.hld, which is the heavy edge list
edge_query: map from edge (par,chi) to point (chi)
(note: The root is never updated)
"""
# assert self.head is not None
u, v = u-self.decrement, v-self.decrement
while True:
if self.vid[u] > self.vid[v]: u, v = v, u
if self.head[u] != self.head[v]:
yield self.vid[self.head[v]], self.vid[v] + 1
v = self.par[self.head[v]]
else:
yield self.vid[u] + edge_query, self.vid[v] + 1
return
def ver_to_idx(self, u):
""" return index on self.hld corresponding to vertex u """
return self.vid[u-self.decrement]
def idx_to_ver(self, i):
""" from index i on self.hld to vertex-index """
return self.hld[i]
def idx_to_edge(self, i):
""" from index i on self.hld to edge-index """
return self.edge_label[self.hld[i]-self.decrement]
def subtree_query(self, u):
u -= self.decrement
return self.vid[u], self.vid[u] + self.size[u]
def top_down(self,dp):
def merge(dp_chi,dp_par):
return dp_chi^dp_par
for chi in self.order[1:]:
par=self.par[chi]
dp[chi]=merge(dp[chi], dp[par])
return dp
def top_down_edge_query(self,dp):
def merge(dp_chi,dp_par):
return dp_chi^dp_par
for p in self.order[1+len(self.edges[self.root]):]:
chi,par=self.edge_label[p],self.edge_label[self.par[p]]
dp[chi]=merge(dp[chi], dp[par])
return dp
def bottom_up(self,dp):
def merge(dp_chi,dp_par):
return dp_chi+dp_par
for par in self.order[::-1]:
for chi in self.edges[par]:
if self.par[par] == chi: continue
dp[par]=merge(dp[chi],dp[par])
return dp
def draw(self):
import matplotlib.pyplot as plt
import networkx as nx
G = nx.Graph()
for x in range(self.n):
for y in self.edges[x]:
G.add_edge(x + self.decrement, y + self.decrement)
pos = nx.spring_layout(G)
nx.draw_networkx(G, pos)
plt.axis("off")
plt.show()
#########################################################################################################
def make_tree(N, show=True, decrement=1):
# decrement=True: create 1-indexed tree
def find(x):
tmp = []
while parents[x] >= 0:
tmp.append(x)
x = parents[x]
for y in tmp: parents[y] = x
return x
def union(x, y):
x, y = find(x), find(y)
if x == y: return
if parents[x] > parents[y]: x, y = y, x
parents[x] += parents[y]
parents[y] = x
def same(x, y):
return find(x) == find(y)
import random
# N = random.randint(2, N)
parents = [-1]*N
edges = []
for i in range(N-1):
while True:
j = random.randint(0, N-1)
if same(i,j): continue
union(i,j)
edges.append((i+decrement,j+decrement))
break
if show:
print("#######################")
print(N)
for p in edges:
print(*p)
print("#######################")
return edges
def make_special_tree(N, type, show=True, decrement=1):
edges = []
if type=="path":
for i in range(N-1):
edges.append((i+decrement,i+1+decrement))
if type=="star":
for i in range(N-1):
edges.append((i,i+1+decrement))
if type=="binary":
i = 1
while True:
if (i<<1) >= N: break
edges.append((i-1+decrement, (i<<1)-1+decrement))
if (i<<1)+1 >= N: break
edges.append((i-1+decrement, (i<<1)+decrement))
i += 1
if show:
print("#######################")
print(N)
for p in edges:
print(*p)
print("#######################")
return edges
def draw(edges, decrement=1):
import matplotlib.pyplot as plt
import networkx as nx
N = len(edges)+1
G = nx.Graph()
for x in range(N):
for y in edges[x]:
G.add_edge(x + decrement, y + decrement)
pos = nx.spring_layout(G)
nx.draw_networkx(G, pos)
plt.axis("off")
plt.show()
#########################################################################################################
import sys
input = sys.stdin.readline
# example()
def dfs(start=0,goal=None):
parents={}
p,t=start,0
parents[p]=-2
next_set=[(p,t)]
if not edges[p]:
return p
while next_set:
p,t=next_set.pop()
if not edges[p]:
return p
for q in edges[p]:
if q in parents:
continue
parents[q]=p
next_set.append((q,t+1))
return -1
MOD=10**9+7
N= int(input())
edges=[[] for _ in range(N)]
T = Tree(N,decrement=1)
for i in range(N-1):
x, y = map(int, input().split())
T.add_edge(x,y,i)
edges[y-1].append(x-1)
root=dfs()
T.set_root(root+1)
res=0
for i in range(N):
if i==root: continue
q=i
p=edges[i][0]
a=T.size[q]
b=T.depth[p]+1
res+=a*b
res%=MOD
print(res)