/
013.cr
172 lines (150 loc) · 4.2 KB
/
013.cr
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# ac-library.cr by hakatashi https://github.com/google/ac-library.cr
#
# Copyright 2021 Google LLC
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
module AtCoder
# Implements standard priority queue like [std::priority_queue](https://en.cppreference.com/w/cpp/container/priority_queue).
#
# ```
# q = AtCoder::PriorityQueue(Int64).new
# q << 1_i64
# q << 3_i64
# q << 2_i64
# q.pop # => 3
# q.pop # => 2
# q.pop # => 1
# ```
class PriorityQueue(T)
getter heap : Array(T)
def initialize
initialize(&.itself)
end
# Initializes queue with the custom comperator.
#
# ```
# q = AtCoder::PriorityQueue(Int64).new { |n| -n }
# q << 1_i64
# q << 3_i64
# q << 2_i64
# q.pop # => 1
# q.pop # => 2
# q.pop # => 3
# ```
def initialize(&block : T -> (Int8 | Int16 | Int32 | Int64 | UInt8 | UInt16 | UInt32 | UInt64))
@heap = Array(T).new
@priority_proc = block
end
# Pushes value into the queue.
def push(v : T)
@heap << v
index = @heap.size - 1
while index != 0
parent = (index - 1) // 2
if @priority_proc.call(@heap[parent]) >= @priority_proc.call(@heap[index])
break
end
@heap[parent], @heap[index] = @heap[index], @heap[parent]
index = parent
end
end
# Alias of `push`
def <<(v : T)
push(v)
end
# Pops value from the queue.
def pop
if @heap.size == 0
return nil
end
if @heap.size == 1
return @heap.pop
end
ret = @heap.first
@heap[0] = @heap.pop
index = 0
while index * 2 + 1 < @heap.size
child = if index * 2 + 2 < @heap.size && @priority_proc.call(@heap[index * 2 + 1]) < @priority_proc.call(@heap[index * 2 + 2])
index * 2 + 2
else
index * 2 + 1
end
if @priority_proc.call(@heap[index]) >= @priority_proc.call(@heap[child])
break
end
@heap[child], @heap[index] = @heap[index], @heap[child]
index = child
end
ret
end
# Returns `true` if the queue is empty.
delegate :empty?, to: @heap
# Returns size of the queue.
delegate :size, to: @heap
end
end
struct Edge(T)
include Comparable(Edge(T))
property to : Int32
property cost : T
def initialize(@to : Int32, @cost : T)
end
def <=>(other : Edge(T))
{cost, to} <=> {other.cost, other.to}
end
def to_s(io : IO) : Nil
io << '(' << to << ", " << cost << ')'
end
end
class Graph(T)
getter graph : Array(Array(Edge(T)))
def initialize(size : Int)
@graph = Array.new(size) { Array(Edge(T)).new }
end
def add_edge(i : Int, j : Int, cost : T)
@graph[i] << Edge.new(j, cost)
@graph[j] << Edge.new(i, cost)
end
delegate size, to: @graph
delegate :[], to: @graph
def dijkstra(start : Int32)
queue = AtCoder::PriorityQueue({Int32, T}).new { |(vertex, dist)| -dist }
queue << {start, T.zero}
dist = Array(T?).new(size, nil)
dist[start] = T.zero
until queue.empty?
vertex, d = queue.pop.not_nil!
dist_v = dist[vertex].not_nil!
next if dist_v < d
self[vertex].each do |edge|
if dist[edge.to].nil? || dist[edge.to].not_nil! > dist_v + edge.cost
dist[edge.to] = dist_v + edge.cost
queue << {edge.to, dist_v + edge.cost}
end
end
end
dist
end
def dijkstra!(start : Int32)
dijkstra(start).map(&.not_nil!)
end
end
n, m = read_line.split.map(&.to_i)
g = Graph(Int32).new(n)
m.times do
a, b, c = read_line.split.map(&.to_i)
g.add_edge(a - 1, b - 1, c)
end
dist_1 = g.dijkstra!(0)
dist_n = g.dijkstra!(n - 1)
puts dist_1.zip(dist_n).join('\n') { |d1, dn| d1 + dn }