This documentation is automatically generated by online-judge-tools/verification-helper
test/math/matrix_test.cr
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- Last update: 2022-03-28 10:35:50+09:00
- Problem: https://yukicoder.me/problems/no/997
Depends on
Code
# verification-helper: PROBLEM https://yukicoder.me/problems/no/997
require "../../src/math/mint"
require "../../src/math/matrix"
require "../../src/scanner"
n, w, k = input(i, i, i64)
a = input(i[n])
dp = Array.new(2 * w + 1) { Mint[0, 0] }
dp[0][0] = Mint.new(1)
(1..2 * w).each do |i|
(0...n).each do |j|
i2 = i - a[j]
dp[i][0] += dp[i2][0] if 0 <= i2
dp[i][1] += dp[i2][1] if 0 <= i2
dp[i][1] += dp[i2][0] if 0 <= i2 < w < i
end
end
val1, val2 = dp[w][0], dp[2 * w][1]
x = Matrix(Mint).from [val1, val2], [1, 0]
y = Matrix(Mint).from [val1], [1]
puts (x**k * y)[1][0]# verification-helper: PROBLEM https://yukicoder.me/problems/no/997
# 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/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/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
n, w, k = input(i, i, i64)
a = input(i[n])
dp = Array.new(2 * w + 1) { Mint[0, 0] }
dp[0][0] = Mint.new(1)
(1..2 * w).each do |i|
(0...n).each do |j|
i2 = i - a[j]
dp[i][0] += dp[i2][0] if 0 <= i2
dp[i][1] += dp[i2][1] if 0 <= i2
dp[i][1] += dp[i2][0] if 0 <= i2 < w < i
end
end
val1, val2 = dp[w][0], dp[2 * w][1]
x = Matrix(Mint).from [val1, val2], [1, 0]
y = Matrix(Mint).from [val1], [1]
puts (x**k * y)[1][0]