ac-library.cr

This is not an officially supported Google product.

ac-library.cr is a Crystal port of ac-library.

This library aims to provide the almost-equivalent (and additional) functionality with ac-library but in the manner of Crystal.

Installation

Add the following code to your project's shard.yml.

dependencies:
  atcoder:
    github: google/ac-library.cr
    branch: master

Usage

require "atcoder" # load all libraries
require "atcoder/fenwick_tree" # load FenwickTree

atcoder/mod_int (Implements <atcoder/modint>)

• modint => Unimplemented

• modint998244353 => AtCoder::ModInt998244353

• modint1000000007 => AtCoder::ModInt1000000007

  alias Mint = AtCoder::ModInt1000000007
  Mint.new(30_i64) // Mint.new(7_i64) #=> 285714292

• static_modint => AtCoder.static_modint

  AtCoder.static_modint(ModInt101, 101_i64)
  alias Mint = AtCoder::ModInt101
  Mint.new(80_i64) + Mint.new(90_i64) #=> 89

• dynamic_modint => Unimplemented

atcoder/fenwick_tree (Implements <atcoder/fenwicktree>)

• fenwick_tree<T> fw(n) => AtCoder::FenwickTree(T).new(n)

• fenwick_tree<T> fw(array) => AtCoder::FenwickTree(T).new(array)

  tree = AtCoder::FenwickTree(Int64).new(10)
  tree.add(3, 10)
  tree.add(5, 20)
  tree[3..5] #=> 30
  tree[3...5] #=> 10

  • .add(p, x) => #add(p, x)
  • .sum(l, r) => #[](l...r)

atcoder/seg_tree (Implements <atcoder/segtree>)

• segtree<S, op, e> seg(v) => AtCoder::SegTree(S).new(v, &op?)

  単位元は暗黙的にnilで定義されるため使用する際に定義する必要はありません。逆に言えばモノイドの (単位元以外の) 元にnilを含めることはできません。 The identity element will be implicitly defined as nil, so you don't have to manually define it. In the other words, you cannot include nil into an element of the monoid.

  tree = AtCoder::SegTree.new((0...100).to_a) {|a, b| [a, b].min}
  tree[10...50] #=> 10

  • .set(p, x) => #[]=(p, x)
  • .get(p) => #[](p)
  • .prod(l, r) => #[](l...r)
  • .all_prod() => #all_prod
  • .max_right<f>(l) => #max_right(l, e = nil, &f)
    • 明示的に単位元を与えない場合、f(e: nil) = true として計算します。If the identity element is not given, it computes as f(e: nil) = true.
  • .min_left<f>(r) => #min_left(r, e = nil, &f)
    • 明示的に単位元を与えない場合、f(e: nil) = true として計算します。If the identity element is not given, it computes as f(e: nil) = true.

atcoder/lazy_seg_tree (Implements <atcoder/lazysegtree>)

• lazy_segtree<S, op, e, F, mapping, composition, id> seg(v) => AtCoder::LazySegTree(S, F).new(v, op, mapping, composition)

  単位元は暗黙的にnilで定義されるため使用する際に定義する必要はありません。逆に言えばモノイドの (単位元以外の) 元にnilを含めることはできません。 The identity element will be implicitly defined as nil, so you don't have to manually define it. In the other words, you cannot include nil into an element of the monoid.

  また、恒等写像は暗黙的にnilで定義されるため使用する際に定義する必要はありません。逆に言えばFの (恒等写像以外の) 元にnilを含めることはできません。 Similarly, the identity map of F will be implicitly defined as nil, so you don't have to manually define it. In the other words, you cannot include nil into an element of the set F.

  op = ->(a : Int32, b : Int32) { [a, b].min }
  mapping = ->(f : Int32, x : Int32) { f }
  composition = ->(a : Int32, b : Int32) { a }
  tree = AtCoder::LazySegTree(Int32, Int32).new((0...100).to_a, op, mapping, composition)
  tree[10...50] #=> 10
  tree[20...60] = 0
  tree[50...80] #=> 0

  • .set(p, x) => #set(p, x)
  • .get(p) => #[](p)
  • .prod(l, r) => #[](l...r)
  • .all_prod() => #all_prod
  • .apply(p, f) => #[]=(p, f)
  • .apply(l, r, f) => #[]=(l...r, f)
  • .max_right<f>(l) => #max_right(l, e = nil, &f)
    • 明示的に単位元を与えない場合、f(e: nil) = true として計算します。If the identity element is not given, it computes as f(e: nil) = true.
  • .min_left<f>(r) => #min_left(r, e = nil, &f)
    • 明示的に単位元を与えない場合、f(e: nil) = true として計算します。If the identity element is not given, it computes as f(e: nil) = true.

atcoder/string (Implements <atcoder/string>)

• suffix_array(s) => AtCoder::String.suffix_array(s)
• lcp_array(s) => AtCoder::String.lcp_array(s)
• z_algorithm(s) => AtCoder::String.z_algorithm(s)

atcoder/dsu (Implements <atcoder/dsu>)

• dsu(n) => AtCoder::DSU.new(n)

  dsu = AtCoder::DSU.new(10)
  dsu.merge(0, 2)
  dsu.merge(4, 2)
  dsu.same?(0, 4) #=> true
  dsu.size(4) #=> 3

  • .merge(a, b) => #merge(a, b)

  • .same(a, b) => #same?(a, b)

  • .leader(a) => #leader(a)

  • .size() => #size

  • .groups() => #groups

    • This method returns set instead of list.

atcoder/max_flow (Implements <atcoder/maxflow>)

• mf_graph<Cap> graph(n) => AtCoder::MaxFlow.new(n)

  Cap is always Int64.

  mf = AtCoder::MaxFlow.new(3)
  mf.add_edge(0, 1, 3)
  mf.add_edge(1, 2, 1)
  mf.add_edge(0, 2, 2)
  mf.flow(0, 2) #=> 3

  • .add_edge(from, to, cap) => #add_edge(from, to, cap)
  • .flow(s, t) => #flow(s, t)
  • .min_cut(s) => Unimplemented
  • .get_edge(i) => Unimplemented
  • .edges() => Unimplemented
  • .change_edge(i, new_cap, new_flow) => Unimplemented

atcoder/scc (Impements <atcoder/scc>)

• scc_graph graph(n) => AtCoder::SCC.new(n)

  scc = AtCoder::SCC.new(3_i64)
  scc.add_edge(0, 1)
  scc.add_edge(1, 0)
  scc.add_edge(2, 0)
  scc.scc #=> [Set{2}, Set{0, 1}]

  • .add_edge(from, to) => #add_edge(from, to)
  • .scc() => #scc

atcoder/two_sat (Implements <atcoder/twosat>)

• two_sat graph(n) => AtCoder::SCC.new(n)

  twosat = AtCoder::TwoSat.new(2_i64)
  twosat.add_clause(0, true, 1, false)
  twosat.add_clause(1, true, 0, false)
  twosat.add_clause(0, false, 1, false)
  twosat.satisfiable? #=> true
  twosat.answer #=> [false, false]

  • .add_clause(i, f, j, g) => #add_clause(i, f, j, g)

  • .satisfiable() => #satisfiable?

  • .answer() => #answer

    This method will raise if it's not satisfiable

atcoder/math (Implements <atcoder/math>)

• pow_mod(x, n, m) => AtCoder::Math.pow_mod(x, n, m)
• inv_mod(x, m) => AtCoder::Math.inv_mod(x, m)
• crt(r, m) => AtCoder::Math.crt(r, m)
• floor_sum => AtCoder::Math.floor_sum(n, m, a, b)

atcoder/convolution (Implements <atcoder/convolution>)

• convolution(a, b) => AtCoder::Convolution.convolution(a, b)

  a = [AtCoder::ModInt998244353.new(1_i64)] * 3
  AtCoder::Convolution.convolution(a, a) #=> [1, 2, 3, 2, 1]

• convolution_ll(a, b) => AtCoder::Convolution.convolution_ll(a, b)

  a = [1_000_000_000_i64]
  AtCoder::Convolution.convolution_ll(a, a) #=> [1000000000000000000]

atcoder/min_cost_flow (Implements <atcoder/mincostflow>)

• mcf_graph graph(n) => AtCoder::MinCostFlow.new(n)

  flow = AtCoder::MinCostFlow.new(5)
  flow.add_edge(0, 1, 30, 3)
  flow.add_edge(0, 2, 60, 9)
  flow.add_edge(1, 2, 40, 5)
  flow.add_edge(1, 3, 50, 7)
  flow.add_edge(2, 3, 20, 8)
  flow.add_edge(2, 4, 50, 6)
  flow.add_edge(3, 4, 60, 7)
  flow.flow(0, 4, 70) #=> {70, 1080}

  • .add_edge(from, to, cap, cost) => #add_edge(from, to, cap, cost)
  • .flow(s, t) => #flow(s, t)
  • .flow(s, t, flow_limit) => #flow(s, t, flow_limit)
  • .slope(s, t) => #slope(s, t)
  • .slope(s, t, flow_limit) => #slope(s, t, flow_limit)
  • .get_edge(i) => Unimplemented
  • .edges() => Unimplemented

atcoder/priority_queue (not in ACL)

• AtCoder::PriorityQueue(T).new

  q = AtCoder::PriorityQueue(Int64).new
  q << 1_i64
  q << 3_i64
  q << 2_i64
  q.pop #=> 3
  q.pop #=> 2
  q.pop #=> 1

  • #<<(v : T)

    Push value into the queue.

  • #pop

    Pop value from the queue.

  • #each

    Yields each item in the queue in comparator's order.

    ヒープを破壊せず列挙するため、O(NlogN) の前計算を行っています。ただし、#first は O(1) で動作するように最適化されています。 it pre-calculates in O(NlogN) to enumerate without destroying the heap. Note, however, that #first works for O(1).

    q = AtCoder::PriorityQueue.new(1..n)
    
    # O(n log(n))
    q.each do |x|
      break
    end
    
    # O(n log(n) + n) = O(n log(n))
    q.each do |x|
      # something to do in O(1)
    end
    
    # O(1)
    q.first # => n

  • #size

    Returns size of the queue

  • #empty?

    Returns true if the queue is empty.

atcoder/prime (not in ACL)

• AtCoder::Prime (module)

  Implements Ruby's Prime library.

  AtCoder::Prime.first(7) # => [2, 3, 5, 7, 11, 13, 17]