## Basic Calculator II

Implement a basic calculator to evaluate a simple expression string.
The expression string contains only non-negative integers, +-*/ operators and empty spaces . The integer division should truncate toward zero.
You may assume that the given expression is always valid.
Some examples:

"3+2*2" = 7
" 3/2 " = 1
" 3+5 / 2 " = 5


### Analysis:

This is a straightforward question that only requires basic string operations.
Note that, there is no brackets "(" or ")" in the string, there is no negative numbers in the string. All we have is a string with +, -, *, / and numbers, and spaces.

Note that, the numbers in the string is not constrained to be 0 to 9, in other words, the first step is to split those numbers and operators from the string.  We can keep every digits of the number in a temporary string, until meet one of the operators. Then convert the number string into int and save it, don't forget to reset the tmp string.

Now we have a list of numbers as well as a list of operators. Since * and / operations have higher priorities, and there is no "( )", we can first compute those operations using the two adjacent numbers. After all the * and / operations are "removed" from the list, the last step is to compute all the remaining + and - in its original order.

Finally, the first number in the number list is the result.

Misc. In python, remove element from list is pretty easy by using .pop(index) method. In C++, this can be done by using the vec.erase(vec.begin() + index) method, where vec is of type stl vector.  In python, string to int can be easily done by call the constructor of int: int(str). In C++, I choose to use a stringstream variable to do this convention. Remember to clear the string stream for new numbers.

### Code(C++):

class Solution {
public:
int calculate(string s) {

vector<int> num;  //vector of ints
vector<char> ops; //vector of operators

//Convert string into ints and operators
string n = ""; // string to store digits
stringstream ss;
for (int i=0;i<s.size();i++){
if (s[i] == ' '){
continue; //remove spaces
}else{
if (s[i]>='0' && s[i]<='9'){
n = n + s[i];
} else{
ss.clear();
ss << n;
int tmp;
ss >> tmp;
num.push_back(tmp);
n = "";
ops.push_back(s[i]);
}
}
}
//don't forget the last number
if (n.size()!=0){
ss.clear();
ss << n;
int tmp;
ss >> tmp;
num.push_back(tmp);
}

//compute all the * and / operations
int i = 0;
while (i<ops.size()){
if (ops[i] == '*'){
num[i] = num[i] * num[i+1];
num.erase(num.begin()+i+1);
ops.erase(ops.begin()+i);
}else if (ops[i] == '/'){
num[i] = num[i] / num[i+1];
num.erase(num.begin()+i+1);
ops.erase(ops.begin()+i);
}else{
i++;
}
}

//compute all the + and - operations
i = 0;
while (i<ops.size()){
if (ops[i] == '+'){
num[i] = num[i] + num[i+1];
num.erase(num.begin()+i+1);
ops.erase(ops.begin()+i);
}else if (ops[i] == '-'){
num[i] = num[i] - num[i+1];
num.erase(num.begin()+i+1);
ops.erase(ops.begin()+i);
}else{
i++;
}
}

return num[0];
}
};


### Code(Python):

class Solution(object):
def calculate(self, s):
"""
:type s: str
:rtype: int
"""

# remove spaces
s = s.replace(" ","")

num = [] # list of numbers
ops = [] # list of operators

# read numbers and operators from string
i = 0
n = ""
while i < len(s):
if '9'>= s[i] >= '0':
n = n + s[i]
else:
num.append(int(n))
n = ""
ops.append(s[i])
i+=1
if len(n) != 0:
num.append(int(n))

# compute all the * and / operations
i = 0
while i < len(ops):
if ops[i] == '*':
num[i] = num[i] * num[i+1]
num.pop(i+1)
ops.pop(i)
elif ops[i] == '/':
num[i] = num[i] / num[i+1]
num.pop(i+1)
ops.pop(i)
else:
i += 1

# compute all the + and - operations
i = 0
while i < len(ops):
if ops[i] == '+':
num[i] = num[i] + num[i+1]
num.pop(i+1)
ops.pop(i)
elif ops[i] == '-':
num[i] = num[i] - num[i+1]
num.pop(i+1)
ops.pop(i)

return num[0]