This documentation is automatically generated by online-judge-tools/verification-helper

:heavy_check_mark: test/math/matrix_product_test.cr

Depends on

Code

# verification-helper: PROBLEM https://judge.yosupo.jp/problem/matrix_product
require "../../src/math/matrix"
require "../../src/math/mint"
require "../../src/scanner"
x, y, z = input(i, i, i)
a, b = input(Matrix.new(Mint2[x, y]), Matrix.new(Mint2[y, z]))
(a * b).join('\n', STDOUT, &.join(' ', STDOUT)); puts
# verification-helper: PROBLEM https://judge.yosupo.jp/problem/matrix_product
# require "../../src/math/matrix"
class Matrix(T)
  include Indexable(Array(T))

  def Matrix.identity(size : Int32) : self
    result = Matrix(T).new(size, size, T.zero)
    (0...size).each do |i|
      result[i][i] = T.new(1)
    end
    result
  end

  macro [](*rows)
    Matrix.new [{{rows.splat}}]
  end

  getter height : Int32, width : Int32, data : Array(Array(T))

  def initialize
    @height = 0
    @width = 0
    @data = Array(Array(T)).new
  end

  def initialize(@height, @width, value : T)
    raise ArgumentError.new("Negative matrix height: #{@height}") unless @height >= 0
    raise ArgumentError.new("Negative matrix width: #{@width}") unless @width >= 0
    @data = Array.new(height) { Array(T).new(width, value) }
  end

  def initialize(@height, @width, &block : Int32, Int32 -> T)
    raise ArgumentError.new("Negative matrix height: #{@height}") unless @height >= 0
    raise ArgumentError.new("Negative matrix width: #{@width}") unless @width >= 0
    @data = Array.new(height) { |i| Array.new(width) { |j| yield i, j } }
  end

  def initialize(@data : Array(Array(T)))
    @height = @data.size
    @width = @data[0].size
    raise ArgumentError.new unless @data.all? { |a| a.size == width }
  end

  def self.from(*rows) : self
    Matrix(T).new rows.map { |row|
      row.map { |value| T.new(value) }.to_a
    }.to_a
  end

  def size : Int32
    @data.size
  end

  def unsafe_fetch(index : Int) : Array(T)
    @data.unsafe_fetch(index)
  end

  private def check_index_out_of_bounds(i, j)
    check_index_out_of_bounds(i, j) { raise IndexError.new }
  end

  private def check_index_out_of_bounds(i, j)
    i += height if i < 0
    j += width if j < 0
    if 0 <= i < height && 0 <= j < width
      {i, j}
    else
      yield
    end
  end

  def fetch(i : Int, j : Int, &)
    i, j = check_index_out_of_bounds(i, j) { return yield i, j }
    unsafe_fetch(i, j)
  end

  def fetch(i : Int, j : Int, default)
    fetch(i, j) { default }
  end

  def [](i : Int, j : Int) : T
    fetch(i, j) { raise IndexError.new }
  end

  def []?(i : Int, j : Int) : T?
    fetch(i, j, nil)
  end

  def unsafe_fetch(i : Int, j : Int) : T
    @data.unsafe_fetch(i).unsafe_fetch(j)
  end

  def +(other : self) : self
    raise IndexError.new unless height == other.height && width == other.width
    Matrix(T).new(height, width) { |i, j|
      unsafe_fetch(i, j) + other.unsafe_fetch(i, j)
    }
  end

  def -(other : self) : self
    raise IndexError.new unless height == other.height && width == other.width
    Matrix(T).new(height, width) { |i, j|
      unsafe_fetch(i, j) - other.unsafe_fetch(i, j)
    }
  end

  def *(other : self) : self
    raise IndexError.new unless width == other.height
    Matrix(T).new(height, other.width) { |i, j|
      (0...width).sum { |k| unsafe_fetch(i, k) * other.unsafe_fetch(k, j) }
    }
  end

  def **(k : Int) : self
    result = Matrix(T).identity(height)
    memo = Matrix.new(data)
    while k > 0
      result *= memo if k.odd?
      memo *= memo
      k >>= 1
    end
    result
  end

  def ==(other : Matrix) : Bool
    return false unless height == other.height && width == other.width
    data == other.data
  end

  def to_s(io) : Nil
    io << data
  end

  def inspect(io) : Nil
    io << "Matrix" << data
  end
end

# require "../../src/math/mint"
struct ModInt(MOD)
  def self.mod
    MOD
  end

  def self.zero
    new
  end

  def self.raw(value : Int64)
    result = new
    result.value = value
    result
  end

  macro [](*nums)
    Array({{@type}}).build({{nums.size}}) do |buffer|
      {% for num, i in nums %}
        buffer[{{i}}] = {{@type}}.new({{num}})
      {% end %}
      {{nums.size}}
    end
  end

  getter value : Int64

  private macro check_mod
    {% if MOD.is_a?(NumberLiteral) %}
      {% raise "can't instantiate ModInt(MOD) with MOD = #{MOD} (MOD must be positive)" unless MOD >= 1 %}
      {% raise "can't instantiate ModInt(MOD) with MOD = #{MOD.kind} (MOD must be Int64)" unless MOD.kind == :i64 %}
    {% else %}
      {% raise "can't instantiate ModInt(MOD) with MOD = #{MOD.class_name.id} (MOD must be an integer)" %}
    {% end %}
  end

  def initialize
    check_mod
    @value = 0i64
  end

  def initialize(value)
    check_mod
    @value = value.to_i64 % MOD
  end

  def initialize(m : ModInt(MOD2)) forall MOD2
    {% raise "Can't create ModInt(#{MOD}) from ModInt(#{MOD2})" if MOD != MOD2 %}
    check_mod
    @value = m.value
  end

  protected def value=(value : Int64)
    @value = value
  end

  def self.scan(scanner, io : IO) : self
    new scanner.i64(io)
  end

  def ==(m : ModInt(MOD2)) forall MOD2
    {% raise "Can't compare ModInt(#{MOD}) and ModInt(#{MOD2})" if MOD != MOD2 %}
    value == m.value
  end

  def ==(m : Int)
    value == m
  end

  def + : self
    self
  end

  def - : self
    self.class.raw(value != 0 ? MOD &- value : 0i64)
  end

  def +(v)
    self + self.class.new(v)
  end

  def +(m : self)
    x = value &+ m.value
    x &-= MOD if x >= MOD
    self.class.raw(x)
  end

  def -(v)
    self - self.class.new(v)
  end

  def -(m : self)
    x = value &- m.value
    x &+= MOD if x < 0
    self.class.raw(x)
  end

  def *(v)
    self * self.class.new(v)
  end

  def *(m : self)
    self.class.new(value &* m.value)
  end

  def /(v)
    self / self.class.new(v)
  end

  def /(m : self)
    raise DivisionByZeroError.new if m.value == 0
    a, b, u, v = m.value, MOD, 1i64, 0i64
    while b != 0
      t = a // b
      a &-= t &* b
      a, b = b, a
      u &-= t &* v
      u, v = v, u
    end
    self.class.new(value &* u)
  end

  def //(v)
    self / v
  end

  def **(exponent : Int)
    t, res = self, self.class.raw(1i64)
    while exponent > 0
      res *= t if exponent & 1 == 1
      t *= t
      exponent >>= 1
    end
    res
  end

  {% for op in %w[< <= > >=] %}
    def {{op.id}}(other)
      raise NotImplementedError.new({{op}})
    end
  {% end %}

  def inv
    self.class.raw(1) // self
  end

  def succ
    self.class.raw(value != MOD &- 1 ? value &+ 1 : 0i64)
  end

  def pred
    self.class.raw(value != 0 ? value &- 1 : MOD &- 1)
  end

  def abs
    self
  end

  def abs2
    self * self
  end

  def to_i64 : Int64
    value
  end

  def to_s(io : IO) : Nil
    value.to_s(io)
  end

  def inspect(io : IO) : Nil
    value.inspect(io)
  end
end

struct Int
  def to_m(type : M.class) forall M
    M.new(self)
  end
end

class String
  def to_m(type : M.class) forall M
    M.new(self)
  end
end

alias Mint = ModInt(1000000007i64)
alias Mint2 = ModInt(998244353i64)

# require "../../src/scanner"
module Scanner
  extend self

  private def skip_to_not_space(io)
    peek = io.peek
    not_space = peek.index { |x| x != 32 && x != 10 } || peek.size
    io.skip(not_space)
  end

  def c(io = STDIN)
    skip_to_not_space(io)
    io.read_char.not_nil!
  end

  private def int(int_type : T.class, io = STDIN) : T forall T
    skip_to_not_space(io)

    value = T.zero
    signed = false
    case x = io.read_byte
    when nil
      raise IO::EOFError.new
    when 45
      signed = true
    when 48..57
      value = T.new 48 &- x
    else
      raise "Unexpected char: #{x.chr}"
    end

    loop do
      peek = io.peek
      return signed ? value : -value if peek.empty?
      i = 0
      while i < peek.size
        c = peek.unsafe_fetch(i)
        if 48 <= c <= 57
          value = value &* 10 &- c &+ 48
          i &+= 1
        elsif c == 32 || c == 10
          io.skip(i &+ 1)
          return signed ? value : -value
        else
          raise "Unexpected char: #{c.chr}"
        end
      end
      io.skip(i)
    end
  end

  private def uint(uint_type : T.class, io = STDIN) : T forall T
    skip_to_not_space(io)
    value = T.zero
    found_digit = false
    loop do
      peek = io.peek
      if peek.empty?
        if found_digit
          return value
        else
          raise IO::EOFError.new
        end
      end
      i = 0
      while i < peek.size
        c = peek.unsafe_fetch(i)
        if 48 <= c <= 57
          found_digit = true
          value = value &* 10 &+ c &- 48
          i &+= 1
        elsif c == 32 || c == 10
          io.skip(i &+ 1)
          return value
        else
          raise "Unexpected char: #{c.chr}"
        end
      end
      io.skip(i)
    end
  end

  def i(io = STDIN)
    int(Int32, io)
  end

  {% for n in [8, 16, 32, 64, 128] %}
    def i{{n}}(io = STDIN)
      int(Int{{n}}, io)
    end

    def u{{n}}(io = STDIN)
      uint(UInt{{n}}, io)
    end
  {% end %}

  {% for method in [:f, :f32, :f64] %}
    def {{method.id}}(io = STDIN)
      s(io).to_{{method.id}}
    end
  {% end %}

  def s(io = STDIN)
    skip_to_not_space(io)

    peek = io.peek
    if peek.empty?
      raise IO::EOFError.new
    end
    if index = peek.index { |x| x == 32 || x == 10 }
      io.skip(index + 1)
      return String.new(peek[0, index])
    end

    String.build do |buffer|
      loop do
        buffer.write peek
        io.skip(peek.size)
        peek = io.peek
        break if peek.empty?
        if index = peek.index { |x| x == 32 || x == 10 }
          buffer.write peek[0, index]
          io.skip(index + 1)
          break
        end
      end
    end
  end
end

macro internal_input(type, else_ast, io)
  {% if Scanner.class.has_method?(type.id) %}
    Scanner.{{type.id}}({{io}})
  {% elsif type.stringify == "String" %}
    Scanner.s({{io}})
  {% elsif type.stringify == "Char" %}
    Scanner.c({{io}})
  {% elsif type.is_a?(Path) %}
    {% if type.resolve.class.has_method?(:scan) %}
      {{type}}.scan(Scanner, {{io}})
    {% else %}
      {{type}}.new(Scanner.s({{io}}))
    {% end %}
  {% elsif String.has_method?("to_#{type}".id) %}
    Scanner.s({{io}}).to_{{type.id}}
  {% else %}
    {{else_ast}}
  {% end %}
end

macro internal_input_array(type, args, io)
  {% for i in 0...args.size %}
    %size{i} = input({{args[i]}}, io: {{io}})
  {% end %}
  {% begin %}
    {% for i in 0...args.size %} Array.new(%size{i}) { {% end %}
      input({{type.id}}, io: {{io}})
    {% for i in 0...args.size %} } {% end %}
  {% end %}
end

# Inputs from *io*.
#
# ### Specifications
#
# ```plain
# AST               | Example             | Expanded code
# ------------------+---------------------+---------------------------------------
# Uppercase string  | Int32, Int64, etc.  | {}.new(Scanner.s)
#                   | s, c, i, iN, uN     | Scanner.{}
#                   | f, big_i, etc.      | Scanner.s.to_{}
# Call []           | type[size]          | Array.new(input(size)) { input(type) }
# TupleLiteral      | {t1, t2, t3}        | {input(t1), input(t2), input(t3)}
# ArrayLiteral      | [t1, t2, t3]        | [input(t1), input(t2), input(t3)]
# HashLiteral       | {t1 => t2}          | {input(t1) => input(t2)}
# NamedTupleLiteral | {a: t1, b: t2}      | {a: input(t1), b: input(t2)}
# RangeLiteral      | t1..t2              | input(t1)..input(t2)
# Expressions       | (exp1; exp2)        | (input(exp1); input(exp2);)
# If                | cond ? t1 : t2      | input(cond) ? input(t1) : input(t2)
# Assign            | target = value      | target = input(value)
# ```
#
# ### Examples
#
# Input:
# ```plain
# 5 3
# foo bar
# 1 2 3 4 5
# ```
# ```
# n, m = input(Int32, Int64) # => {5, 5i64}
# input(String, Char[m])     # => {"foo", ['b', 'a', 'r']}
# input(Int32[n])            # => [1, 2, 3, 4, 5]
# ```
# ```
# n, m = input(i, i64) # => {5, 5i64}
# input(s, c[m])       # => {"foo", ['b', 'a', 'r']}
# input(i[n])          # => [1, 2, 3, 4, 5]
# ```
#
# Input:
# ```plain
# 2 3
# 1 2 3
# 4 5 6
# ```
#
# ```
# h, w = input(i, i) # => {2, 3}
# input(i[h, w])     # => [[1, 2, 3], [4, 5, 6]]
# ```
# ```
# input(i[i, i]) # => [[1, 2, 3], [4, 5, 6]]
# ```
#
# Input:
# ```plain
# 5 3
# 3 1 4 2 5
# 1 2
# 2 3
# 3 1
# ```
# ```
# n, m = input(i, i)       # => {5, 3}
# input(i.pred[n])         # => [2, 0, 3, 1, 4]
# input({i - 1, i - 1}[m]) # => [{0, 1}, {1, 2}, {2, 0}]
# ```
#
# Input:
# ```plain
# 3
# 1 2
# 2 2
# 3 2
# ```
# ```
# input({tmp = i, tmp == 1 ? i : i.pred}[i]) # => [{1, 2}, {2, 1}, {3, 1}]
# ```
#
# Input:
# ```plain
# 3
# 1 1
# 2 1 2
# 5 1 2 3 4 5
# ```
# ```
# n = input(i)   # => 3
# input(i[i][n]) # => [[1], [1, 2], [1, 2, 3, 4, 5]]
# ```
#
# Input:
# ```plain
# 3
# 1 2
# 2 3
# 3 1
# ```
# ```
# n = input(i)
# input_column({Int32, Int32}, n) # => {[1, 2, 3], [2, 3, 1]}
# ```
macro input(ast, *, io = STDIN)
  {% if ast.is_a?(Call) %}
    {% if ast.receiver.is_a?(Nop) %}
      internal_input(
        {{ast.name}},
        {{ast.name}}({% for argument in ast.args %} input({{argument}}, io: {{io}}), {% end %}),
        {{io}},
      )
    {% elsif ast.receiver.is_a?(Path) && ast.receiver.resolve.class.has_method?(ast.name.symbolize) %}
      {{ast.receiver}}.{{ast.name}}(
        {% for argument in ast.args %} input({{argument}}, io: {{io}}) {% end %}
      ) {{ast.block}}
    {% elsif ast.name.stringify == "[]" %}
      internal_input_array({{ast.receiver}}, {{ast.args}}, {{io}})
    {% else %}
      input({{ast.receiver}}, io: {{io}}).{{ast.name}}(
        {% for argument in ast.args %} input({{argument}}, io: {{io}}), {% end %}
      ) {{ast.block}}
    {% end %}
  {% elsif ast.is_a?(TupleLiteral) %}
    { {% for i in 0...ast.size %} input({{ast[i]}}, io: {{io}}), {% end %} }
  {% elsif ast.is_a?(ArrayLiteral) %}
    [ {% for i in 0...ast.size %} input({{ast[i]}}, io: {{io}}), {% end %} ]
  {% elsif ast.is_a?(HashLiteral) %}
    { {% for key, value in ast %} input({{key}}, io: {{io}}) => input({{value}}, io: {{io}}), {% end %} }
  {% elsif ast.is_a?(NamedTupleLiteral) %}
    { {% for key, value in ast %} {{key}}: input({{value}}, io: {{io}}), {% end %} }
  {% elsif ast.is_a?(RangeLiteral) %}
    Range.new(
      input({{ast.begin}}, io: {{io}}),
      input({{ast.end}}, io: {{io}}),
      {{ast.excludes_end?}},
    )
  {% elsif ast.is_a?(SymbolLiteral) %}
    {{ast.id}}
  {% elsif ast.is_a?(Expressions) %}
    ( {% for exp in ast.expressions %} input({{exp}}, io: {{io}}); {% end %} )
  {% elsif ast.is_a?(If) %}
    input({{ast.cond}}, io: {{io}}) ? input({{ast.then}}, io: {{io}}) : input({{ast.else}}, io: {{io}})
  {% elsif ast.is_a?(Assign) %}
    {{ast.target}} = input({{ast.value}}, io: {{io}})
  {% else %}
    internal_input({{ast}}, {{ast}}, io: {{io}})
  {% end %}
end

macro input(*asts, io = STDIN)
  { {% for ast in asts %} input({{ast}}, io: {{io}}), {% end %} }
end

macro input_column(types, size, *, io = STDIN)
  %size = {{size}}
  {% for type, i in types %}
    %array{i} = Array({{type}}).new(%size)
  {% end %}
  %size.times do
    {% for type, i in types %}
      %array{i} << input({{type}}, io: {{io}})
    {% end %}
  end
  { {% for type, i in types %} %array{i}, {% end %} }
end

x, y, z = input(i, i, i)
a, b = input(Matrix.new(Mint2[x, y]), Matrix.new(Mint2[y, z]))
(a * b).join('\n', STDOUT, &.join(' ', STDOUT)); puts
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