Problem:
Score : 900 points

Problem Statement

Joisino has a formula consisting of N terms: A_1 op_1 A_2 ... op_{N-1} A_N.
Here, A_i is an integer, and op_i is an binary operator either + or -.
Because Joisino loves large numbers, she wants to maximize the evaluated value of the formula by inserting an arbitrary number of pairs of parentheses (possibly zero) into the formula.
Opening parentheses can only be inserted immediately before an integer, and closing parentheses can only be inserted immediately after an integer.
It is allowed to insert any number of parentheses at a position.
Your task is to write a program to find the maximum possible evaluated value of the formula after inserting an arbitrary number of pairs of parentheses.

Constraints

1≦N≦10^5

1≦A_i≦10^9

op_i is either + or -.

Input

The input is given from Standard Input in the following format:

N
A_1 op_1 A_2 ... op_{N-1} A_N

Output

Print the maximum possible evaluated value of the formula after inserting an arbitrary number of pairs of parentheses.

Sample Input 1

3
5 - 1 - 3

Sample Output 1

7

The maximum possible value is: 5 - (1 - 3) = 7.

Sample Input 2

5
1 - 2 + 3 - 4 + 5

Sample Output 2

5

The maximum possible value is: 1 - (2 + 3 - 4) + 5 = 5.

Sample Input 3

5
1 - 20 - 13 + 14 - 5

Sample Output 3

13

The maximum possible value is: 1 - (20 - (13 + 14) - 5) = 13.

Solution in Scala (2.11.7) (judge verdict: Runtime Error)

import scala.collection.mutable
import scala.collection.mutable.ListBuffer

/**
 * Created by Rahul on 1/5/17.
 */
class AdditionAndSubstraction {

  val cache = new mutable.HashMap[(Int,Int),Tuple2[Long,Long]]()
  def maxSum(arr : Array[Long],start : Int,end : Int,depth : Int) : Tuple2[Long,Long] = {
//    for (i <- 0 to depth-1) {
//      print(" ")
//    }
//    println("start = " + start + "  end " + end)
    if (cache.contains((start,end))) {
      //println("Cache hit " + (start,end))
      cache.get((start,end)).get
    }else {
      if (start == end) {
        (arr(start),arr(end))
      } else {
        val lstBuffer = new mutable.HashSet[Long]
        var maxSumObserved : Long = Int.MinValue
        var minSumObserved : Long = Int.MaxValue
        for (i <- start + 1 to end) {
          val current = arr(i)
          if (current < 0) {
            //Negate the value
            arr(i) = -current
            val lst1 : Tuple2[Long,Long] = maxSum(arr, start, i - 1, depth + 1)
            val lst2 : Tuple2[Long,Long] = maxSum(arr, i, end, depth + 1)
            val comb = new Array[Long](4)
            comb(0) = lst1._1 - lst2._1
            comb(1) = lst1._1 - lst2._2
            comb(2) = lst1._2 - lst2._1
            comb(3) = lst1._2 - lst2._2
            val localMax = comb.max
            val localMin = comb.min
            if (localMax > maxSumObserved) {
              //println(i  + " " + maxSumObserved)
              maxSumObserved = localMax
            }

            if (localMin < minSumObserved) {
              minSumObserved = localMin
            }
            //minSumObserved = comb.min

//            lst1.foreach(s1 => {
//              lst2.foreach(s2 => {
//                lstBuffer.+=(s1 - s2)
//              })
//            })
            //reset back
            arr(i) = current

          } else {
            val lst1 = maxSum(arr, start, i - 1, depth + 1)
            val lst2 = maxSum(arr, i, end, depth + 1)
//            lst1.foreach(s1 => {
//              lst2.foreach(s2 => {
//                lstBuffer.+=(s1 + s2)
//              })
//            })
            val comb = new Array[Long](4)
            comb(0) = lst1._1 + lst2._1
            comb(1) = lst1._1 + lst2._2
            comb(2) = lst1._2 + lst2._1
            comb(3) = lst1._2 + lst2._2
            val localMax = comb.max
            val localMin = comb.min
            if (localMax > maxSumObserved) {
              //println(i  + " " + maxSumObserved)
              maxSumObserved = localMax
            }

            if (localMin < minSumObserved) {
              minSumObserved = localMin
            }
          }
        }

        var currentSum : Long = 0
        for (i <- start to end) {
          currentSum += arr(i)
        }

        //lstBuffer.+=(currentSum)
        if (currentSum > maxSumObserved) {
          //println("Here ")
          maxSumObserved = currentSum
        }

        if (currentSum < minSumObserved) {
          //println("Here")
          minSumObserved = currentSum
        }


        //val s = lstBuffer.toSet
        cache.put((start,end),(maxSumObserved,minSumObserved))
//        for (i <- 0 to depth-1) {
//          print(" ")
//        }
        //println("Start = " + start + " End = " + end + " " + (maxSumObserved,minSumObserved))
        (maxSumObserved,minSumObserved)


      }
    }
  }

}


object Main extends App {
  val addSub = new AdditionAndSubstraction
  val count = scala.io.StdIn.readLine().toInt
  val exprArr = scala.io.StdIn.readLine().split(" ")
  var state = 1
  val exprIntArr = new Array[Long](count)
  exprIntArr(0) = exprArr(0).toLong
  var j = 1
  var totalAdd = 1
  var totalSub = 0
  for (i <- 1 to count-1) {

    exprArr(j) match {
      case "+" => {
        totalAdd = totalAdd + 1
        state = 1
        exprIntArr(i) = exprArr(j+1).toLong * state
        j = j + 2
      }
      case "-" => {
        totalSub = totalSub + 1
        state = -1
        exprIntArr(i) = exprArr(j+1).toLong * state
        j = j + 2
      }
      case num => {
        println("Error")
      }
    }



  }

  //println(exprIntArr.deep.mkString(" "))

  if (totalSub == 0) {
    println(exprIntArr.sum)
  }else {
    println(addSub.maxSum(exprIntArr,0,exprIntArr.length-1,0)._1)
  }

}