Problem:
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Problem A:
Bit String Reordering

You have to reorder a given bit string as specified. The only operation allowed is swapping adjacent bit pairs. Please write a program that calculates the minimum number of swaps required.

The initial bit string is simply represented by a sequence of bits, while the target is specified by a run-length code. The run-length code of a bit string is a sequence of the lengths of maximal consecutive sequences of zeros or ones in the bit string. For example, the run-length code of "011100" is "1 3 2". Note that there are two different bit strings with the same run-length code, one starting with zero and the other starting with one. The target is either of these two.

In Sample Input 1, bit string "100101" should be reordered so that its run-length code is "1 3 2", which means either "100011" or "011100". At least four swaps are required to obtain "011100". On the other hand, only one swap is required to make "100011". Thus, in this example, 1 is the answer.

Input

The input consists of a single test case. The test case is formatted as follows.

$N$ $M$

$b_1$ $b_2$ . . . $b_N$

$p_1$ $p_2$ . . . $p_M$

The first line contains two integers $N$ ($1 \leq N \leq 15$) and $M$ ($1 \leq M \leq N$). The second line
specifies the initial bit string by $N$ integers. Each integer $b_i$ is either 0 or 1. The third line contains the run-length code, consisting of $M$ integers. Integers $p_1$ through $p_M$ represent the lengths of consecutive sequences of zeros or ones in the bit string, from left to right. Here, $1 \leq p_j$ for $1 \leq j \leq M$ and $\sum^{M}_{j=1} p_j = N$ hold. It is guaranteed that the initial bit string can be reordered into a bit string with its run-length code $p_1, . . . , p_M$.

Output

Output the minimum number of swaps required

Sample Input 1

6 3
1 0 0 1 0 1
1 3 2

Sample Output 1

1

Sample Input 2

7 2
1 1 1 0 0 0 0
4 3

Sample Output 2

12

Sample Input 3

15 14
1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
1 1 1 1 1 1 1 1 1 1 1 1 1 2

Sample Output 3

7

Sample Input 4

1 1
0
1

Sample Output 4

0

Solution in Scala (judge verdict: Accepted)

import scala.io.StdIn._
object Main extends App {

  val Array(n, m) = readLine.trim.split(' ').map(_.toInt)
  val bits = readLine.trim.split(' ').map(_.toInt).toRunLength
  val target = readLine.trim.split(' ').map(_.toInt).toList
  println(solve(bits, target))

  def solve(from: List[Int], to: List[Int]): Int = {
    def swap(from: List[Int], to: List[Int]): Option[Int] = {
      (from, to) match {
        case (Nil, Nil) ⇒ Some(0)
        case (0::t, _) ⇒ straight(t, to)
        case (_, 0::t) ⇒ straight(from, t)
        case (ff::fs::ft, tf::tt) if tf < fs ⇒ straight(ff::fs-tf::ft, tt).map(_ + tf * ff)
        case (ff::fs::ft::fr, tf::tt) ⇒ swap(ff+ft::fr, tf-fs::tt).map(_ + fs * ff)
        case (ff::fs::Nil, tf::tt) ⇒ swap(ff::Nil, tf-fs::tt).map(_ + fs * ff)
        case _ ⇒ None
      }
    }
    def straight(from: List[Int], to: List[Int]): Option[Int] = {
      (from, to) match {
        case (Nil, Nil) ⇒ Some(0)
        case (0::t, _) ⇒ swap(t, to)
        case (_, 0::t) ⇒ swap(from, t)
        case (ff::ft, tf::tt) if ff <= tf ⇒ swap(ft, tf - ff::tt)
        case (ff::ft, tf::tt) ⇒ swap(ff-tf::ft, tt)
        case _ ⇒ None
      }
    }
    List(swap(from, to), straight(from, to)).flatten.min
  }
  implicit class ArrayWrapper(val value: Array[Int]) {
    def toRunLength: List[Int] = {
      var last = 0
      var result = Nil: List[Int]
      for (i ← value.indices.tail){
        if (value(i) != value(i - 1)) {
          result ::= i - last
          last = i
        }
      }
      (value.size - last::result).reverse
    }
  }
  implicit class Wrapper[T](val value: List[T]) {
    def minOption(implicit ord: Ordering[T]): Option[T] = {
      if (value.isEmpty) None
      else Some(value.min)
    }
  }
  implicit class Extension[T](val value: T) extends AnyVal {
    @inline def let[A](@inline func: T ⇒ A): A = func(value)
    @inline def also(@inline func: T ⇒ Unit): T = {func(value); value}
  }
}