Project Euler Problem 16

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Problem 16

累乗の各桁の和

http://odz.sakura.ne.jp/projecteuler/index.php?cmd=read&page=Problem%2016

$2^{15}=32768$ であり, これの各桁の和は $3+2+7+6+8=26$ となる.

同様にして, $2^{1000}$ の各桁の和を求めよ.

Power digit sum

http://projecteuler.net/problem=16

$2^{15}=32768$ and the sum of its digits is $3+2+7+6+8=26$ .

What is the sum of the digits of the number $2^{1000}$ ?

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Scala

更新日 : 2013.01.31

scala> BigInt(2).pow(15)
res11: scala.math.BigInt = 32768

scala> BigInt(2).pow(100)
res12: scala.math.BigInt = 1267650600228229401496703205376

scala> BigInt(2).pow(100).toString.toCharArray
res14: Array[Char] = Array(1, 2, 6, 7, 6, 5, 0, 6, 0, 0, 2, 2, 8, 2, 2, 9, 4, 0, 1, 4, 9, 6, 7, 0, 3, 2, 0, 5, 3, 7, 6)

scala> BigInt(2).pow(100).toString.toCharArray.map(_.toInt)
res18: Array[Int] = Array(49, 50, 54, 55, 54, 53, 48, 54, 48, 48, 50, 50, 56, 50, 50, 57, 52, 48, 49, 52, 57, 54, 55, 48, 51, 50, 48, 53, 51, 55, 54)

scala> BigInt(2).pow(100).toString.toCharArray.map(_.toInt - 48)
res19: Array[Int] = Array(1, 2, 6, 7, 6, 5, 0, 6, 0, 0, 2, 2, 8, 2, 2, 9, 4, 0, 1, 4, 9, 6, 7, 0, 3, 2, 0, 5, 3, 7, 6)

scala> BigInt(2).pow(100).toString.toCharArray.map(_.toInt - 48).sum
res20: Int = 115

scala> BigInt(2).pow(1000).toString.toCharArray.map(_.toInt - 48).sum
res21: Int = 1366

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F#

更新日 : 2013.01.30

> System.Numerics.BigInteger.Pow(2I,15);;
val it : System.Numerics.BigInteger = 32768I
> System.Numerics.BigInteger.Pow(2I,100);;
val it : System.Numerics.BigInteger = 1267650600228229401496703205376I

> System.Convert.ToString (System.Numerics.BigInteger.Pow(2I,100));;
val it : string = "1267650600228229401496703205376"

> (System.Convert.ToString (System.Numerics.BigInteger.Pow(2I,100))).ToCharArray();;
val it : char [] =
  [|'1'; '2'; '6'; '7'; '6'; '5'; '0'; '6'; '0'; '0'; '2'; '2'; '8'; '2'; '2';
    '9'; '4'; '0'; '1'; '4'; '9'; '6'; '7'; '0'; '3'; '2'; '0'; '5'; '3'; '7';
    '6'|]

> (System.Convert.ToString (System.Numerics.BigInteger.Pow(2I,100))).ToCharArray() |> Array.map(int);;
val it : int [] =
  [|49; 50; 54; 55; 54; 53; 48; 54; 48; 48; 50; 50; 56; 50; 50; 57; 52; 48; 49;
    52; 57; 54; 55; 48; 51; 50; 48; 53; 51; 55; 54|]

> (System.Convert.ToString (System.Numerics.BigInteger.Pow(2I,100))).ToCharArray() |> Array.map(int) |> Array.map(fun n -> n - 48);;
val it : int [] =
  [|1; 2; 6; 7; 6; 5; 0; 6; 0; 0; 2; 2; 8; 2; 2; 9; 4; 0; 1; 4; 9; 6; 7; 0; 3;
    2; 0; 5; 3; 7; 6|]

> (System.Convert.ToString (System.Numerics.BigInteger.Pow(2I,100))).ToCharArray() |> Array.map(int) |> Array.map(fun n -> n - 48) |> Array.sum;;
val it : int = 115

> (System.Convert.ToString (System.Numerics.BigInteger.Pow(2I,1000))).ToCharArray() |> Array.map(int) |> Array.map(fun n -> n - 48) |> Array.sum;;
val it : int = 1366