結果

問題 No.718 行列のできるフィボナッチ数列道場 (1)
コンテスト
ユーザー むらため
提出日時 2019-01-27 03:14:02
言語 Nim
(2.2.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 3,743 bytes
記録
記録タグの例:
初AC ショートコード 純ショートコード 純主流ショートコード 最速実行時間
コンパイル時間 2,619 ms
コンパイル使用メモリ 60,836 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-07-01 11:00:06
合計ジャッジ時間 3,109 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 20
権限があれば一括ダウンロードができます
コンパイルメッセージ
/home/judge/data/code/Main.nim(1, 8) Warning: imported and not used: 'sequtils' [UnusedImport]
/home/judge/data/code/Main.nim(1, 17) Warning: imported and not used: 'math' [UnusedImport]

ソースコード

diff #
raw source code 

import sequtils,math

proc getchar_unlocked():char {. importc:"getchar_unlocked",header: "<stdio.h>" .}
proc scan(): int =
  while true:
    let k = getchar_unlocked()
    if k < '0': break
    result = 10 * result + k.ord - '0'.ord
#[
const MOD = 1000000007

template useMatrix =
  type Matrix = ref object
    w,h:int
    data: seq[int]
  proc `[]`(m:Matrix,x,y:int):int = m.data[x + y * m.w]
  proc `[]=`(m:var Matrix,x,y,val:int) = m.data[x + y * m.w] = val
  proc newMatrix(w,h:int):Matrix =
    new(result)
    result.w = w
    result.h = h
    result.data = newSeq[int](w * h)
  proc identityMatrix(n:int):Matrix =
    result = newMatrix(n,n)
    for i in 0..<n: result[i,i] = 1
  proc newMatrix(arr:seq[seq[int]]):Matrix =
    new(result)
    result.w = arr[0].len
    result.h = arr.len
    result.data = newSeqUninitialized[int](result.w * result.h)
    for x in 0..<result.w:
      for y in 0..<result.h:
        result[x,y] = arr[y][x]

  proc `$`(m:Matrix) : string =
    result = ""
    for y in 0..<m.h:
      result &= "["
      for x in 0..<m.w:
        result &= $m[x,y]
        if x != m.w - 1 : result &= ","
      result &= "]"
      if y != m.h - 1 : result &= "\n"
    result &= ""

  proc `*`(a,b:Matrix): Matrix =
    assert a.w == b.h
    result = newMatrix(a.h,b.w)
    for y in 0..<a.h:
      for x in 0..<b.w:
        var n = 0
        for k in 0..<a.w:
          when declared(MOD):
            n = (n + (a[k,y] * b[x,k]) mod MOD) mod MOD
          else:
            n += a[k,y] * b[x,k]
        result[y,x] = n

  proc `*`(a:Matrix,b:seq[int]):seq[int] =
    assert a.w == b.len
    result = newSeq[int](b.len)
    for x in 0..<a.h:
      var n = 0
      for k in 0..<a.w:
        when declared(MOD):
          n = (n + (a[k,x] * b[k]) mod MOD) mod MOD
        else:
          n += a[k,x] * b[k]
      result[x] = n

  proc `^`(m:Matrix,n:int) : Matrix =
    assert m.w == m.h
    if n <= 0 : return identityMatrix(m.w)
    if n == 1 : return m
    let m2 = m^(n div 2)
    if n mod 2 == 0 : return m2 * m2
    return m2 * m2 * m
useMatrix()
]#
# proc calcFib(n:int):int = (newMatrix(@[@[1,1],@[1,0]])^(n-1)*(@[1,0]))[0]
# F(n) = f(n+1) * f(n)
# let n = scan()
# echo (calcFib(n) * calcFib(n+1)) mod MOD

# mod
# template useModulo =
const MOD = 1000000007
type ModInt = object
  v:int # 0~MODに収まる
proc toModInt*(a:int) : ModInt =
  if a < -MOD : result.v = ((a mod MOD) + MOD) mod MOD
  elif a < 0 : result.v = a + MOD
  elif a >= MOD: result.v = a mod MOD
  else: result.v = a
proc `+`*(a,b:ModInt) : ModInt =
  result.v = a.v + b.v
  if result.v >= MOD : result.v = result.v mod MOD
proc `*`*(a,b:ModInt) : ModInt =
  result.v = a.v * b.v
  if result.v >= MOD : result.v = result.v mod MOD
proc `^`*(a:ModInt,b:int) : ModInt =
  if b == 0 : return 1.toModInt()
  if b == 1 : return a
  let pow = a^(b div 2)
  if b mod 2 == 0 : return pow * pow
  return pow * pow * a
proc `+`*(a:int,b:ModInt) : ModInt = a.toModInt() + b
proc `+`*(a:ModInt,b:int) : ModInt = a + b.toModInt()
proc `-`*(a:ModInt,b:int) : ModInt = a + (-b)
proc `-`*(a,b:ModInt) : ModInt = a + (-b.v)
proc `-`*(a:int,b:ModInt) : ModInt = a.toModInt() + (-b.v)
proc `*`*(a:int,b:ModInt) : ModInt = a.toModInt() * b
proc `*`*(a:ModInt,b:int) : ModInt = a * b.toModInt()
proc `/`*(a,b:ModInt) : ModInt = a * b^(MOD-2)
proc `$`*(a:ModInt) : string = $a.v

# useModulo()

proc calcFib(n:int) : tuple[x:ModInt,y:ModInt] =
  if n == 0 : return (0.toModInt(),1.toModInt())
  let (fn,fn1) = calcFib(n div 2)
  let fnx1 = fn1 - fn
  let f2n = (fn1 + fnx1) * fn
  let f2nx1 = fn * fn + fnx1 * fnx1
  let f2n1 = f2n + f2nx1
  if n mod 2 == 0 : return (f2n,f2n1)
  else: return (f2n1,f2n1 + f2n)

let n = scan()
echo calcFib(n)[0] * calcFib(n+1)[0]
0