結果

問題 No.766 金魚すくい
ユーザー tottoripaper
提出日時 2018-12-25 17:38:50
言語 OCaml
(5.2.1)
結果
AC  
実行時間 274 ms / 1,500 ms
コード長 2,313 bytes
コンパイル時間 385 ms
コンパイル使用メモリ 21,580 KB
実行使用メモリ 9,600 KB
最終ジャッジ日時 2024-10-09 00:33:24
合計ジャッジ時間 7,008 ms
ジャッジサーバーID
(参考情報)
judge1 / judge5
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 * 42
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 #
プレゼンテーションモードにする

let rec expt ( * ) e a n =
if n = 0 then
e
else if n land 1 = 1 then
a * expt ( * ) e (a * a) (n / 2)
else
expt ( * ) e (a * a) (n / 2)
let mod_expt a n mo = expt (fun x y -> x * y mod mo) 1 a n
let mod_inv a p = mod_expt a (p - 2) p
module Combination : sig
type t
val init : n:int -> modulo:int -> t
val fact : int -> t -> int
val inv_fact : int -> t -> int
val nPk : int -> int -> t -> int
val nCk : int -> int -> t -> int
val nHk : int -> int -> t -> int
end = struct
type t = int * int array * int array
let init ~n ~modulo =
let f = Array.make (n + 1) 0 in
let () =
f.(0) <- 1;
for i = 1 to n do
f.(i) <- f.(i - 1) * i mod modulo
done in
let inv_f = Array.make (n + 1) 0 in
let () =
inv_f.(n) <- mod_inv f.(n) modulo;
for i = n - 1 downto 0 do
inv_f.(i) <- inv_f.(i + 1) * (i + 1) mod modulo
done in
(modulo, f, inv_f)
let fact n (_, f, _) = f.(n)
let inv_fact n (_, _, inv_f) = inv_f.(n)
let nPk n k ((mo, _, _) as c) =
if n < k then
0
else
fact n c * inv_fact (n - k) c mod mo
let nCk n k ((mo, _, _) as c) =
if n < k then
0
else
fact n c * inv_fact k c mod mo * inv_fact (n - k) c mod mo
let nHk n k c = if n = 0 && k = 0 then 1 else nCk (n + k - 1) k c
end
let id x = x
let mo = 1_000_000_007
let c = Combination.init ~n:200100 ~modulo:mo
let (n, m, p) = Scanf.scanf "%d %d %d" (fun n m p -> (n, m, p))
let (p, q) = (p * mod_inv 100 mo mod mo, (100 - p) * mod_inv 100 mo mod mo)
let v = Array.init n (fun _ -> Scanf.scanf " %d" id)
let () =
Array.sort (fun x y -> - compare x y) v;
for i = 1 to n - 1 do
v.(i) <- (v.(i) + v.(i - 1)) mod mo
done
let cnt = ref 0
let () =
for i = 1 to n - 1 do (* i *)
let prob = Combination.nHk (i + 1) (m - 1) c mod mo * mod_expt p m mo mod mo * mod_expt q i mo mod mo in
cnt := (!cnt + v.(i - 1) * prob mod mo) mod mo
done;
for j = 0 to m - 1 do (* N j *)
let prob = Combination.nHk n j c mod mo * mod_expt p j mo mod mo * mod_expt q n mo mod mo in
cnt := (!cnt + v.(n - 1) * prob mod mo) mod mo
done;
print_int !cnt;
print_newline ()
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