function isOperator(value){
 var operatorString = "+-*/()";
 return operatorString.indexOf(value) > -1
}

function getPrioraty(value){
 switch(value){
  case '+':
  case '-':
   return 1;
  case '*':
  case '/':
   return 2;
  default:
   return 0;
 }
}

function prioraty(o1, o2){
 return getPrioraty(o1) <= getPrioraty(o2);
}

function dal2Rpn(exp){
 var inputStack = [];
 var outputStack = [];
 var outputQueue = [];

 for(var i = 0, len = exp.length; i < len; i++){
  var cur = exp[i];
  if(cur != ' ' ){
   inputStack.push(cur);
  }
 }
 console.log('step one');
 while(inputStack.length > 0){
  var cur = inputStack.shift();
  if(isOperator(cur)){
   if(cur == '('){
    outputStack.push(cur);
   }else if(cur == ')'){
    var po = outputStack.pop();
    while(po != '(' && outputStack.length > 0){
     outputQueue.push(po);
     po = outputStack.pop();
    }
    if(po != '('){
     throw "error: unmatched ()";
    }
   }else{
    while(prioraty(cur, outputStack[outputStack.length - 1]) && outputStack.length > 0){
     outputQueue.push(outputStack.pop());
    }
    outputStack.push(cur);
   }
  }else{
   outputQueue.push(new Number(cur));
  }
 }
 console.log('step two');
 if(outputStack.length > 0){
  if(outputStack[outputStack.length - 1] == ')' || outputStack[outputStack.length - 1] == '('){
   throw "error: unmatched ()";
  }
  while(outputStack.length > 0){
   outputQueue.push(outputStack.pop());
  }
 }
 console.log('step three');
 return outputQueue;

}

console.log(dal2Rpn('1 + 2'));
console.log(dal2Rpn('1 + 2 + 3'));
console.log(dal2Rpn('1 + 2 * 3'));
console.log(dal2Rpn('1 + 2 * 3 - 4 / 5'));
console.log(dal2Rpn('( 1 + 2 )'));

console.log(dal2Rpn('( 1 + 2 ) * ( 3 - 4 ) / 5'));
console.log(dal2Rpn('( 1 + 2 ) * (( 3 - 4 ) / 5)'));

function evalRpn(rpnQueue){
 var outputStack = [];
 while(rpnQueue.length > 0){
  var cur = rpnQueue.shift();

  if(!isOperator(cur)){
   outputStack.push(cur);
  }else{
   if(outputStack.length < 2){
    throw "unvalid stack length";
   }
   var sec = outputStack.pop();
   var fir = outputStack.pop();

   outputStack.push(getResult(fir, sec, cur));
  }
 }

 if(outputStack.length != 1){
  throw "unvalid expression";
 }else{
  return outputStack[0];
 }
}