#688122 (Crystal) No.891 隣接3項間の漸化式

提出ソース

結果

問題	No.891 隣接3項間の漸化式
ユーザー	te-sh
提出日時	2021-08-11 23:41:48
言語	Crystal (1.11.2)
結果	AC
実行時間	2 ms / 2,000 ms
コード長	9,997 bytes
コンパイル時間	19,049 ms
コンパイル使用メモリ	293,508 KB
実行使用メモリ	4,356 KB
最終ジャッジ日時	2023-10-26 01:43:40
合計ジャッジ時間	21,540 ms
ジャッジサーバーID （参考情報）	judge15 / judge13

このコードへのチャレンジ
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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	2 ms 4,324 KB
testcase_01	AC	1 ms 4,356 KB
testcase_02	AC	2 ms 4,356 KB
testcase_03	AC	1 ms 4,356 KB
testcase_04	AC	2 ms 4,356 KB
testcase_05	AC	2 ms 4,356 KB
testcase_06	AC	1 ms 4,356 KB
testcase_07	AC	2 ms 4,356 KB
testcase_08	AC	1 ms 4,356 KB
testcase_09	AC	2 ms 4,356 KB
testcase_10	AC	2 ms 4,356 KB
testcase_11	AC	2 ms 4,356 KB
testcase_12	AC	2 ms 4,356 KB
testcase_13	AC	2 ms 4,356 KB
testcase_14	AC	1 ms 4,356 KB
testcase_15	AC	2 ms 4,356 KB
testcase_16	AC	2 ms 4,356 KB
testcase_17	AC	2 ms 4,356 KB
testcase_18	AC	2 ms 4,356 KB
testcase_19	AC	2 ms 4,356 KB
testcase_20	AC	2 ms 4,356 KB
testcase_21	AC	2 ms 4,356 KB
testcase_22	AC	2 ms 4,356 KB
testcase_23	AC	1 ms 4,356 KB
testcase_24	AC	2 ms 4,356 KB
testcase_25	AC	2 ms 4,356 KB
testcase_26	AC	2 ms 4,356 KB
testcase_27	AC	2 ms 4,356 KB
testcase_28	AC	2 ms 4,356 KB
testcase_29	AC	2 ms 4,356 KB
testcase_30	AC	2 ms 4,356 KB
testcase_31	AC	2 ms 4,356 KB
testcase_32	AC	2 ms 4,356 KB
testcase_33	AC	2 ms 4,356 KB
testcase_34	AC	2 ms 4,356 KB
testcase_35	AC	2 ms 4,356 KB
testcase_36	AC	2 ms 4,356 KB
testcase_37	AC	2 ms 4,356 KB
testcase_38	AC	1 ms 4,356 KB
testcase_39	AC	2 ms 4,356 KB
testcase_40	AC	1 ms 4,356 KB
testcase_41	AC	2 ms 4,356 KB

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ソースコード

raw source code

def solve(io)
  a, b, n = io.get3
  m = Matrix.new([[a, b], [1, 0]].map { |mi| mi.map { |mij| Mint.new(mij) } })
  r = m ** n * Vector.new([1, 0].map { |vi| Mint.new(vi) })
  io.put r[1]
end

class ProconIO
  def initialize(@ins : IO = STDIN, @outs : IO = STDOUT)
    @buf = IO::Memory.new("")
  end

  def get(k : T.class = Int32) forall T
    get_v(k)
  end

  macro define_get
    {% for i in (2..9) %}
      def get({{ *(1..i).map { |j| "k#{j}".id } }})
        { {{ *(1..i).map { |j| "get(k#{j})".id } }} }
      end
    {% end %}
  end
  define_get

  macro define_getn
    {% for i in (2..9) %}
      def get{{i}}(k : T.class = Int32) forall T
        get({{ *(1..i).map { "k".id } }})
      end
    {% end %}
  end
  define_getn

  def get_a(n : Int, k : T.class = Int32) forall T
    Array.new(n) { get_v(k) }
  end

  def get_c(n : Int, k : T.class = Int32) forall T
    get_a(n, k)
  end

  macro define_get_c
    {% for i in (2..9) %}
      def get_c(n : Int, {{ *(1..i).map { |j| "k#{j}".id } }})
        a = Array.new(n) { get({{ *(1..i).map { |j| "k#{j}".id } }}) }
        { {{ *(1..i).map { |j| "a.map { |e| e[#{j-1}] }".id } }} }
      end
    {% end %}
  end
  define_get_c

  macro define_getn_c
    {% for i in (2..9) %}
      def get{{i}}_c(n : Int, k : T.class = Int32) forall T
        get_c(n, {{ *(1..i).map { "k".id } }})
      end
    {% end %}
  end
  define_getn_c

  def get_m(r : Int, c : Int, k : T.class = Int32) forall T
    Array.new(r) { get_a(c, k) }
  end

  macro define_put
    {% for i in (1..9) %}
      def put({{ *(1..i).map { |j| "v#{j}".id } }}, *, delimiter = " ")
        {% for j in (1..i) %}
          print_v(v{{j}}, delimiter)
          {% if j < i %}@outs << delimiter{% end %}
        {% end %}
        @outs.puts
      end
    {% end %}
  end
  define_put

  def put_e(*vs)
    put(*vs)
    exit
  end

  def put_f(*vs)
    put(*vs)
    @outs.flush
  end


  private def get_v(k : Int32.class); get_token.to_i32; end
  private def get_v(k : Int64.class); get_token.to_i64; end
  private def get_v(k : UInt32.class); get_token.to_u32; end
  private def get_v(k : UInt64.class); get_token.to_u64; end
  private def get_v(k : Float64.class); get_token.to_f64; end
  private def get_v(k : String.class); get_token; end

  private def get_token
    loop do
      token = @buf.gets(' ', chomp: true)
      break token unless token.nil?
      @buf = IO::Memory.new(@ins.read_line)
    end
  end

  private def print_v(v, dlimiter)
    @outs << v
  end

  private def print_v(v : Enumerable, delimiter)
    v.each_with_index do |e, i|
      @outs << e
      @outs << delimiter if i < v.size - 1
    end
  end
end

struct Int
  def cdiv(b : Int)
    (self + b - 1) // b
  end

  def bit?(i : Int)
    bit(i) == 1
  end

  def set_bit(i : Int)
    self | (self.class.new(1) << i)
  end

  def reset_bit(i : Int)
    self & ~(self.class.new(1) << i)
  end

  
  {% if compare_versions(env("CRYSTAL_VERSION") || "0.0.0", "0.35.0") < 0 %}
    def digits(base = 10)
      raise ArgumentError.new("Invalid base #{base}") if base < 2
      raise ArgumentError.new("Can't request digits of negative number") if self < 0
      return [0] if self == 0

      num = self
      digits_count = (Math.log(self.to_f + 1) / Math.log(base)).ceil.to_i
      ary = Array(Int32).new(digits_count)
      while num != 0
        ary << num.remainder(base).to_i
        num = num.tdiv(base)
      end
      ary
    end
  {% end %}

  {% if compare_versions(env("CRYSTAL_VERSION") || "0.0.0", "0.34.0") < 0 %}
    def bit_length : Int32
      x = self < 0 ? ~self : self

      if x.is_a?(Int::Primitive)
        Int32.new(sizeof(self) * 8 - x.leading_zeros_count)
      else
        to_s(2).size
      end
    end
  {% end %}
end

struct Float64
  def near?(x)
    (self - x).abs <= (self.abs < x.abs ? x.abs : self.abs) * EPSILON
  end
end

struct Number
  {% if compare_versions(env("CRYSTAL_VERSION") || "0.0.0", "1.1.0") < 0 %}
    def zero?
      self == 0
    end

    def positive?
      self > 0
    end

    def negative?
      self < 0
    end
  {% end %}

  {% if compare_versions(env("CRYSTAL_VERSION") || "0.0.0", "0.36.0") < 0 %}
    def self.additive_identity
      zero
    end

    def self.multiplicative_identity
      new(1)
    end
  {% end %}
end

class Array
  macro new_md(*args, &block)
    {% if !block %}
      {% for arg, i in args[0...-2] %}
        Array.new({{arg}}) {
      {% end %}
      Array.new({{args[-2]}}, {{args[-1]}})
      {% for arg in args[0...-2] %}
        }
      {% end %}
    {% else %}
      {% for arg, i in args %}
        Array.new({{arg}}) { |_i{{i}}|
      {% end %}
      {% for block_arg, i in block.args %}
        {{block_arg}} = _i{{i}}
      {% end %}
      {{block.body}}
      {% for arg in args %}
        }
      {% end %}
    {% end %}
  end
end

module Math
  {% if compare_versions(env("CRYSTAL_VERSION") || "0.0.0", "1.2.0") < 0 %}
    def isqrt(value : Int::Primitive)
      raise ArgumentError.new "Input must be non-negative integer" if value < 0
      return value if value < 2
      res = value.class.zero
      bit = res.succ << (res.leading_zeros_count - 2)
      bit >>= value.leading_zeros_count & ~0x3
      while (bit != 0)
        if value >= res + bit
          value -= res + bit
          res = (res >> 1) + bit
        else
          res >>= 1
        end
        bit >>= 2
      end
      res
    end
  {% end %}
end

macro min_u(a, b)
  {{a}} = Math.min({{a}}, {{b}})
end

macro max_u(a, b)
  {{a}} = Math.max({{a}}, {{b}})
end

macro zip(a, *b, &block)
  {{a}}.zip({{*b}}) {{block}}
end

def powr(a : T, n : Int, i : T = T.multiplicative_identity) forall T
  powr(a, n, i) { |a, b| a * b }
end

def powr(a : T, n : Int, i : T = T.multiplicative_identity, &block) forall T
  return i if n == 0
  r, b = i, a
  while n > 0
    r = yield r, b if n.bit(0) == 1
    b = yield b, b
    n >>= 1
  end
  r
end

def ext_gcd(a : T, b : T) forall T
  if a == 0
    {b, T.new(0), T.new(1)}
  else
    g, x, y = ext_gcd(b % a, a)
    {g, y - (b // a) * x, x}
  end
end

def bit_subsets(a : Int, includes_zero = false)
  n = i = a
  if includes_zero
    while i >= 0
      yield i & n
      i = (i & n) - 1
    end
  else
    while i > 0
      yield i
      i = (i - 1) & n
    end
  end
end

def bit_zeta_trans_subset(n : Int, f : Array(T), &compose : (T, T) -> T) forall T
  g = Array.new(1 << n) { |i| f[i] }
  n.times do |i|
    (1 << n).times do |j|
      if j >> i & 1 != 0
        g[j] = compose.call(g[j], g[j ^ (1 << i)])
      end
    end
  end
  g
end

def bit_zeta_trans_superset(n : Int, f : Array(T), &compose : (T, T) -> T) forall T
  g = Array.new(1 << n) { |i| f[i] }
  n.times do |i|
    (1 << n).times do |j|
      if j >> i & 1 == 0
        g[j] = compose.call(g[j], g[j ^ (1 << i)])
      end
    end
  end
  g
end

class Vector(T)
  include Indexable(T)

  def initialize(n : Int32)
    @b = Array.new(n, T.zero)
  end

  def initialize(@b : Array(T))
  end

  def ==(r : self)
    @b == r.to_a
  end

  def to_a
    @b
  end

  delegate size, to: @b

  delegate unsafe_fetch, to: @b

  delegate :[]=, to: @b

  def +(r : self)
    raise "Size mismatch" if size != r.size
    Vector.new(@b.zip(r.to_a).map { |vi, ri| vi + ri })
  end

  def -(r : self)
    raise "Size mismatch" if size != r.size
    Vector.new(@b.zip(r.to_a).map { |vi, ri| vi - ri })
  end

  def *(r : T)
    Vector.new(@b.map { |vi| vi * r })
  end

  def *(r : self)
    raise "Size mismatch" if size != r.size
    @b.zip(r.to_a).map { |vi, ri| vi * ri }.sum
  end
end

class Matrix(T)
  include Indexable(T)

  def initialize(@rows : Int32, @cols : Int32)
    @b = Array.new(@rows) { Array.new(@cols, T.zero) }
  end

  def initialize(@b : Array(Array(T)))
    @rows = @b.size
    @cols = @b[0].size
  end

  def self.unit(n : Int32)
    new(Array.new(n) { |i| Array.new(n) { |j| i == j ? T.multiplicative_identity : T.zero } })
  end

  def ==(r : self)
    @b == r.to_a
  end

  def to_a
    @b
  end

  getter rows : Int32

  getter cols : Int32

  def size
    rows
  end

  delegate unsafe_fetch, to: @b

  def +(r : self)
    raise "Size mismatch" if rows != r.rows || cols != r.cols
    Matrix.new(Array.new(rows) { |i| Array.new(cols) { |j| self[i][j] + r[i][j] } })
  end

  def -(r : self)
    raise "Size mismatch" if rows != r.rows || cols != r.cols
    Matrix.new(Array.new(rows) { |i| Array.new(cols) { |j| self[i][j] - r[i][j] } })
  end

  def *(r : T)
    Matrix.new(Array.new(rows) { |i| Array.new(cols) { |j| self[i][j] * r } })
  end

  def *(r : Vector(T))
    raise "Size mismatch" if cols != r.size
    Vector.new(Array.new(rows) { |i| (0...cols).map { |j| self[i][j] * r[j] }.sum })
  end

  def *(r : self)
    raise "Size mismatch" if cols != r.rows
    Matrix.new(Array.new(rows) { |i| Array.new(r.cols) { |j| (0...cols).map { |k| self[i][k] * r[k][j] }.sum } })
  end

  def **(r : Int)
    raise "Size mismatch" if rows != cols
    powr(self, r, Matrix(T).unit(rows))
  end
end

abstract struct ModInt < Number
  macro new_type(name, mod)
    struct {{name}} < ModInt
      @@mod : Int32 = {{mod}}
    end
  end

  def initialize(v : Int)
    @v = (v % @@mod).to_i64
  end

  def_hash @@mod, @v

  def to_s
    @v.to_s
  end

  def to_s(io : IO) : Nil
    @v.to_s(io)
  end

  getter v : Int64

  delegate to_i, to: @v

  def ==(r : self)
    @v == r.v
  end

  def ==(r : Int)
    @v == (r % @@mod)
  end

  def - : self
    m(-@v)
  end

  def +(r : self)
    m(@v + r.v)
  end

  def +(r : Int)
    self + m(r)
  end

  def -(r : self)
    m(@v - r.v)
  end

  def -(r : Int)
    self - m(r)
  end

  def *(r : self)
    m(@v * r.v)
  end

  def *(r : Int)
    self * m(r)
  end

  def //(r : self)
    self * r.inv
  end

  def //(r : Int)
    self // m(r)
  end

  def **(n : Int)
    powr(self, n)
  end

  def inv
    m(ext_gcd(@v.to_i32, @@mod)[1])
  end


  private def m(v : Int)
    self.class.new(v)
  end
end
ModInt.new_type(Mint, 10**9+7)

solve(ProconIO.new)

yukicoder

結果

テストケース

ソースコード