結果

問題 No.376 立方体のN等分 (2)
ユーザー 👑 obakyan
提出日時 2019-05-09 08:59:59
言語 Lua
(LuaJit 2.1.1734355927)
結果
AC  
実行時間 2,743 ms / 5,000 ms
コード長 3,092 bytes
コンパイル時間 43 ms
コンパイル使用メモリ 6,944 KB
実行使用メモリ 143,112 KB
最終ジャッジ日時 2024-07-02 00:46:52
合計ジャッジ時間 25,196 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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 * 2
other AC * 38
権限があれば一括ダウンロードができます

ソースコード

diff # 

local n = io.read("*n")
local mce, mfl, msq, mmi = math.ceil, math.floor, math.sqrt, math.min
local tbli = table.insert

local function getprimes(x)
  local primes = {}
  local allnums = {}
  for i = 1, x do allnums[i] = true end
  for i = 2, x do
    if(allnums[i]) then
      tbli(primes, i)
      local lim = mfl(x / i)
      for j = 2, lim do
        allnums[j * i] = false
      end
    end
  end
  return primes
end

local function getdivisorparts(x, primes)
  local prime_num = #primes
  local tmp = {}
  local lim = mce(msq(x))
  local primepos = 1
  local dv = primes[primepos]
  while(primepos <= prime_num and dv <= lim) do
    if(x % dv == 0) then
      local asdf = {}
      asdf.p = dv
      asdf.cnt = 1
      x = x / dv
      while(x % dv == 0) do
        x = x / dv
        asdf.cnt = asdf.cnt + 1
      end
      tbli(tmp, asdf)
      lim = mce(msq(x))
    end
    if(primepos == prime_num) then break end
    primepos = primepos + 1
    dv = primes[primepos]
  end
  if(x ~= 1) then
    local asdf = {}
    asdf.p, asdf.cnt = x, 1
    tbli(tmp, asdf)
  end
  return tmp
end

local function getdivisor(divisorparts, minlim)
  local t = {}
  local pat = 1
  local len = #divisorparts
  local allpat = 1
  for i = 1, len do
    allpat = allpat * (divisorparts[i].cnt + 1)
  end
  for t_i_pat = 0, allpat - 1 do
    local div = allpat
    local i_pat = t_i_pat
    local ret = 1
    for i = 1, len do
      div = mfl(div / (divisorparts[i].cnt + 1))
      local mul = mfl(i_pat / div)
      i_pat = i_pat % div
      for j = 1, mul do ret = ret * divisorparts[i].p end
    end
    if minlim == nil or minlim <= ret then
      tbli(t, ret)
    end
  end
  table.sort(t)
  return t
end
local retmin, retmax = n - 1, n - 1
local primes = getprimes(mce(msq(n)))
local divisorparts = getdivisorparts(n, primes)
local divisor = getdivisor(divisorparts)
local dmax = mce(n^(1/3))
local numdivisorparts = #divisorparts
local numdivisor = #divisor

for i = 1, numdivisor do
  if(dmax < divisor[i]) then break end
  local divpart = getdivisorparts(divisor[i], primes)
  local k = 1
  local numdivpart = #divpart
  for j = 1, numdivpart do
    while(k <= numdivisorparts) do
      if divpart[j].p == divisorparts[k].p then
        divisorparts[k].cnt = divisorparts[k].cnt - divpart[j].cnt
        k = k + 1
        break
      else
        k = k + 1
      end
    end
    if(numdivisorparts < k) then break end
  end

  local rem = mfl(n / divisor[i])
  local remdiv = getdivisor(divisorparts, divisor[i])
  local remlim = mce(msq(rem))
  local numremdiv = #remdiv
  for j = 1, numremdiv do
    if(remlim < remdiv[j]) then break end
    local last = mfl(rem / remdiv[j])
    retmin = mmi(retmin, divisor[i] + remdiv[j] + last - 3)
  end

  k = 1
  for j = 1, numdivpart do
    while(k <= numdivisorparts) do
      if divpart[j].p == divisorparts[k].p then
        divisorparts[k].cnt = divisorparts[k].cnt + divpart[j].cnt
        k = k + 1
        break
      else
        k = k + 1
      end
    end
    if(numdivisorparts < k) then break end
  end

end
print(retmin .. " " .. retmax)
0