Problem:
海苔(のり)

　
ヒバラ海の浜辺の集落では海苔の生産が盛んです。海苔はすべて長方形に成型されます。海苔を天日干しするときは、２枚の海苔を同じ敷物の上に乗せて、１枚目の上辺と２枚目の上辺が平行になるように置きます。アルバイトのゲンムさんは平行に置くことはできるのですが、まだ慣れていないため重なった部分ができてしまうことがあります。重なった部分は売り物にならないので、重なっていない部分の海苔の面積を求めておく必要があります。

同じ敷物の上に置いた２枚の海苔それぞれの左下端の位置と幅と高さが与えられたとき、重なっていない部分の海苔の面積を出力するプログラムを作成せよ。

入力

入力は以下の形式で与えられる。

$x_1$ $y_1$ $w_1$ $h_1$
$x_2$ $y_2$ $w_2$ $h_2$

１行目に１枚目の海苔の左下端の座標$x_1,y_1$ ($0 \leq x_1,y_1 \leq 1,000$)と幅と高さ$w_1,h_1$ ($1 \leq w_1,h_1 \leq 1,000$)が与えられる。２行目に２枚目の海苔の左下端の座標$x_2,y_2$ ($0 \leq x_2,y_2 \leq 1,000$)と幅と高さ$w_2,h_2$ ($1 \leq w_2,h_2 \leq 1,000$)が与えられる。入力はすべて整数で与えられる。

出力

重なっていない部分の海苔の面積を整数で１行に出力する。

入出力例

入力例１

0 0 4 5
2 2 3 6

出力例１

26

入力例２

1 2 2 1
2 0 2 2

出力例２

6

入力例３

0 0 1 1
0 0 1 1

出力例３

0

Solution in Scala (judge verdict: Accepted)

//import java.util.Scanner

import java.io._
import java.nio.file.Files._
import java.nio.file.Path
import java.util.StringTokenizer

import scala.collection.immutable._
import scala.io.Codec

/**
  * Scala implementation of a faster java.util.Scanner
  * See: http://codeforces.com/blog/entry/7018
  */

class Scanner(reader: LineNumberReader) extends Iterable[String] with AutoCloseable {
  def this(reader: BufferedReader) = this(new LineNumberReader(reader))

  def this(reader: Reader) = this(new BufferedReader(reader))

  def this(inputStream: InputStream)(implicit codec: Codec) = this(new InputStreamReader(inputStream, codec.charSet))

  def this(path: Path)(implicit codec: Codec) = this(newBufferedReader(path, codec.charSet))

  def this(file: File)(implicit codec: Codec) = this(file.toPath)(codec)

  def this(str: String) = this(new StringReader(str))

  override def iterator: Iterator[String] = for {
    line <- Iterator.continually(reader.readLine()).takeWhile(_ != null)
    tokenizer = new StringTokenizer(line)
    tokens <- Iterator.continually(tokenizer).takeWhile(_.hasMoreTokens)
  } yield tokens.nextToken()

  private[this] var current = iterator

  def hasNext: Boolean = current.hasNext

  @inline def next(): String = current.next()

  /**
    * This is different from Java's scanner.nextLine
    * The Java one is a misnomer since it actually travel to end of current line
    * This one actually does fetch the next line
    */
  def nextLine(): String = {
    val line = reader.readLine()
    current = iterator
    line
  }

  def lineNumber: Int = reader.getLineNumber

  def nextString(): String = next()

  def nextBoolean(): Boolean = next().toBoolean

  def nextByte(radix: Int = 10): Byte = java.lang.Byte.parseByte(next(), radix)

  def nextShort(radix: Int = 10): Short = java.lang.Short.parseShort(next(), radix)

  def nextInt(radix: Int = 10): Int = java.lang.Integer.parseInt(next(), radix)

  def nextLong(radix: Int = 10): Long = java.lang.Long.parseLong(next(), radix)

  def nextBigInt(radix: Int = 10): BigInt = BigInt(next(), radix)

  def nextFloat(): Float = next().toFloat

  def nextDouble(): Double = next().toDouble

  def nextBigDecimal(): BigDecimal = BigDecimal(next())

  override def close(): Unit = reader.close()
}


class IUnionFind(val size: Int) {

  private case class Node(var parent: Option[Int], var treeSize: Int)

  private val nodes = Array.fill[Node](size)(Node(None, treeSize = 1))

  def union(t1: Int, t2: Int): IUnionFind = {
    if (t1 == t2) return this

    val root1 = root(t1)
    val root2 = root(t2)
    if (root1 == root2) return this

    val node1 = nodes(root1)
    val node2 = nodes(root2)

    if (node1.treeSize < node2.treeSize) {
      node1.parent = Some(t2)
      node2.treeSize += node1.treeSize
    } else {
      node2.parent = Some(t1)
      node1.treeSize += node2.treeSize
    }
    this
  }

  def connected(t1: Int, t2: Int): Boolean = t1 == t2 || root(t1) == root(t2)

  def root(t: Int): Int = nodes(t).parent match {
    case None => t
    case Some(p) =>
      nodes(t).parent = Some(root(p))
      nodes(t).parent.get
  }
}


object Main {
  def solve(sc: => Scanner): Unit = {
    val x1, y1, w1, h1 = sc.nextLong()
    val x2, y2, w2, h2 = sc.nextLong()
    println(w1 * h1 + w2 * h2
      - 2 * Math.max(0, Math.min(x1 + w1, x2 + w2) - Math.max(x1, x2)) * Math.max(0, Math.min(y1 + h1, y2 + h2) - Math.max(y1, y2)))
  }

  def flip(A: Array[Boolean], B: Array[(Int, Long)]): Array[(Int, Long)] = {
    B.map { case (index, _) =>
      (index, (if (0 < index && A(index - 1)) B(index - 1)._2 else 0L) + (if (index + 1 < B.length && !A(index + 1)) B(index + 1)._2 else 0L))
    }
  }

  val mod: Long = (1e9 + 7).toLong

  @scala.annotation.tailrec
  def recursive(sum: Long, ans: Array[Long]): Array[Long] = {
    if (sum == 0) ans ++ Array.fill(50 - ans.length)(49L)
    else {
      val one: Long = Math.min(Math.pow(10, 16).toLong + 800, sum)
      recursive(sum - one, ans :+ (one + 49))
    }
  }

  @scala.annotation.tailrec
  def factorial(now: Long, ans: Long = 1): Long = {
    if (now == 0) 0 else if (now == 1) ans else factorial(now - 1, now * ans)
  }

  implicit class implicitInt(val N: Int) {
    def times[B](function: Int => B): IndexedSeq[B] = (0 until N).map(function)
  }

  def calc(input: (Long, Long, Long, Long, Long, Long)): Long = {
    input match {
      case (a, b, c, x, y, z) =>
        var ans: Long = Long.MaxValue
        if (b >= 3 && (a >= 2 || c >= 2)) {
          ans = Math.min(ans, Math.max(a - (b - 1), 0) * x + Math.max(c - Math.min(a - 1, b - 2), 0) * z)
          ans = Math.min(ans, Math.max(a - Math.min(c - 1, b - 2), 0) * x + Math.max(c - (b - 1), 0) * z)
        }
        //        println(ans)
        if (b >= 2 && (a >= b && c >= b + 1)) {
          ans = Math.min(ans, y + Math.max(0, a - (c - 1)) * x)
        }
        //        println(ans)
        if (b >= 2 && (a >= b + 1 && c >= b)) {
          ans = Math.min(ans, y + Math.max(0, c - (a - 1)) * z)
        }
        //        println(ans)
        if (a >= 2 && c >= 2)
          if (a != c)
            ans = Math.min(ans, Math.max(0, b - (Math.min(a, c) - 1)) * y)
          else if (a >= 3 && c >= 3)
            ans = Math.min(ans, Math.max(0, b - (Math.min(a, c) - 2)) * y + Math.min(x, z))
        //        println(ans)
        if (ans == Long.MaxValue) ans = -1
        ans
    }
  }

  def time(s: String): Int =
    s.substring(0, 2).toInt * 60 + s.substring(3, 5).toInt

  /*
  def getPermutation(begin: Long = 0): LazyList[Long] =
    LazyList.cons(begin, getPermutation(begin + 1))

  def getFibonacci(prevprev: Long = 0, prev: Long = 1): LazyList[Long] =
    LazyList.cons(prevprev, getFibonacci(prev, prevprev + prev))

  @scala.annotation.tailrec
  def recursive2(X: Set[Long], Y: LazyList[Long]): Long = if (X.contains(Y.head)) X.size else recursive2(X + Y.head, Y.tail)
*/
  def check(i: Int, X: String): Long = {
    if (X == "") 0 else check(i, X.tail) * i + X.head.toString.toLong
  }

  def shift(n: Long): Long = {
    if (n == 0) 0
    else if (n == 1) 1
    else shift(n - 1) << 1
  }

  def unShift(n: Long): Long = {
    if (n == 0) 0
    else unShift(n >> 1) + 1
  }

  @scala.annotation.tailrec
  def gcd(i: Long, j: Long): Long = {
    if (i < j) gcd(j, i)
    else if (j == 0) i
    else gcd(j, i % j)
  }

  def primeFactors(i: Long): List[Long] = primeFactors_(i, 1).sorted


  def primeFactors_(i: Long, j: Long): List[Long] = {
    if (j * j > i) List.empty else if (i % j == 0) primeFactors_(i, j + 1) ++ List[Long](j, i / j) else primeFactors_(i, j + 1)
  }

  def main(args: Array[String]): Unit = {
    val sc: Scanner = new Scanner(System.in)
    solve(sc)
  }
}

/*
object Util {
  def getPermutation(begin: Long = 0): LazyList[Long] =
    LazyList.cons(begin, getPermutation(begin + 1))

  def getPrimeList: LazyList[Long] =
    getPrimeListRecursive(getPermutation(begin = 2))

  private def getPrimeListRecursive(A: LazyList[Long]): LazyList[Long] =
    LazyList.cons(A.head, getPrimeListRecursive(A.tail.filter(_ % A.head != 0)))

  def fib(a: Long = 0, b: Long = 1, mod: Long = Long.MaxValue): LazyList[Long] = a #:: fib(b % mod, (a + b) % mod, mod)
}

 */

object ArabicRoman {

  type =?>[A, B] = PartialFunction[A, B]

  private val codeTable: List[(Int, String)] = List(
    (1000, "M"), (900, "CM"), (500, "D"), (400, "CD"), (100, "C"),
    (90, "XC"), (50, "L"), (40, "XL"), (10, "X"), (9, "IX"), (5, "V"), (4, "IV"), (1, "I"))

  val arabicToRoman: Int =?> String = {
    case src if src >= 1 && src <= 3999 =>

      @scala.annotation.tailrec
      def convert(left: Int, cont: String = "", code: List[(Int, String)] = codeTable): String = {
        val (unitVal, unitChar) = code.head
        left - unitVal match {
          case n if n == 0 => cont + unitChar
          case n if n > 0 => convert(n, cont + unitChar, code)
          case _ => convert(left, cont, code.tail)
        }
      }

      convert(src)
  }

  val romanToArabic: String =?> Int = {
    case src if Option(src).exists { s => {
      s.nonEmpty && """[^MDCLXVI]""".r.findFirstMatchIn(s.toUpperCase).isEmpty
    }
    } =>

      @scala.annotation.tailrec
      def convert(left: String, cont: Int = 0, code: List[(Int, String)] = codeTable): Int = {
        val (unitVal, unitChar) = code.head
        left.splitAt(unitChar.length) match {
          case ("", _) => cont
          case (`unitChar`, tail) => convert(tail, cont + unitVal, code)
          case _ => convert(left, cont, code.tail)
        }
      }

      convert(src.toUpperCase())
  }
}

object PowMod {
  def naivePowMod(a: Long, k: Long, m: Long): Long = {
    var t: Long = 1
    val aMod: Long = a % m

    for (_ <- 1L to k) {
      t = ((t % m) * aMod) % m
    }
    t.toInt
  }

  def powMod(a: Long, k: Long, m: Long): Long = {
    if (k == 0) 1
    else {
      val t = powMod(a, k / 2, m)
      if ((k % 2) == 0) (t * t) % m else (((t * t) % m) * a) % m
    }
  }
}