Problem:
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Minimum Spanning Tree

For a given weighted graph $G = (V, E)$, find the minimum spanning tree (MST) of $G$ and print total weight of edges belong to the MST.

Input

In the first line, an integer $n$ denoting the number of vertices in $G$ is given. In the following $n$ lines, a $n \times n$ adjacency matrix $A$ which represents $G$ is given.
$a_{ij}$ denotes the weight of edge connecting vertex $i$ and vertex $j$. If there is no edge between $i$ and $j$, $a_{ij}$ is given by -1.

Output

Print the total weight of the minimum spanning tree of $G$.

Constraints

$1 \leq n \leq 100$

$0 \leq a_{ij} \leq 2,000$ (if $a_{ij} \neq -1$)

$a_{ij} = a_{ji}$

$G$ is a connected graph

Sample Input 1

5
-1 2 3 1 -1
2 -1 -1 4 -1
3 -1 -1 1 1
1 4 1 -1 3
-1 -1 1 3 -1

Sample Output 1

5

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in Scala (judge verdict: Accepted)

//import java.util.Scanner

import scala.collection.Searching._
import scala.annotation.tailrec
import scala.collection.mutable
import scala.collection.immutable._
import scala.io.StdIn.readLine

import java.io._
import java.nio.file.{Files, Path}
import java.util.StringTokenizer

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(Files.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 = 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 = current.hasNext

  @inline def next() = 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() = 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)(new Node(None, 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 N = sc.nextInt()
    val A = Array.fill(N)(Array.fill(N)(sc.nextLong()))
    val pq = new mutable.PriorityQueue[(Long, Int)]()(Ordering.by(v => -v._1))
    pq.enqueue((0L, 0))
    println(recursive(A, pq, Set[Int]()))
  }

  def recursive(A: Array[Array[Long]], pq: mutable.PriorityQueue[(Long, Int)], used: Set[Int]): Long = {
    if (pq.length == 0) (0) else {
      val now = pq.dequeue()
      (if (used.contains(now._2)) (0) else {
        for (i <- 0 until A(now._2).size) {
          if (A(now._2)(i) != -1) (pq.enqueue((A(now._2)(i), i)))
        }
        now._1
      }) + recursive(A, pq, used + now._2)
    }
  }

  def recursive2(N: Long): String = {
    if (N == 0) ("") else (('a'.toInt + (N % 26)).toChar + recursive2(N / 26))
  }

  def check(A: Array[List[Int]]): Boolean = {
    A.map(_.size == 0).fold(true)((a, b) => a & b)
  }

  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)
  }

  def gcd(i: Long, j: Long): Long = {
    if (i < j) (gcd(j, i)) else (if (j == 0) (i) else (gcd(j, i % j)))
  }

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

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

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

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

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

object ArabicRoman {

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

  val codeTable = 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) => {

      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) == None)
    }
    }) => {

      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())
    }
  }
}