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: hakatashi/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?)

  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)
    • If the identity element is not given, it computes as f(e: nil) = true.
  • .min_left<f>(r) => #min_left(r, e = nil, &f)
    • 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)

  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.

  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)
    • If the identity element is not given, it computes as f(e: nil) = true.
  • .min_left<f>(r) => #min_left(r, e = nil, &f)
    • 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.

    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]