# 772 Basic Calculator III

## 1. Question

Implement a basic calculator to evaluate a simple expression string.
The expression string may contain open`(`and closing parentheses`)`, the plus`+`or minus sign`-`,non-negativeintegers and empty spaces.
The expression string contains only non-negative integers,`+`,`-`,`*`,`/`operators , open`(`and closing parentheses`)`and empty spaces. The integer division should truncate toward zero.
You may assume that the given expression is always valid. All intermediate results will be in the range of`[-2147483648, 2147483647]`.
Some examples:
"1 + 1" = 2
" 6-4 / 2 " = 4
"2*(5+5*2)/3+(6/2+8)" = 21
"(2+6* 3+5- (3*14/7+2)*5)+3"=-12
Note:Do not use the`eval`built-in library function.

## 2. Implementation

(1) Stack
class Solution {
public int calculate(String s) {
if (s == null || s.length() == 0) {
return 0;
}
Stack<Integer> nums = new Stack();
Stack<Character> operators = new Stack();
int i = 0;
int num = 0;
int n = s.length();
while (i < n) {
char c = s.charAt(i);
if (Character.isDigit(c)) {
num = c - '0';
while ((i + 1) < n && Character.isDigit(s.charAt(i + 1))) {
num = 10 * num + s.charAt(i + 1) - '0';
++i;
}
nums.push(num);
}
else if (isOperator(c)) {
while (!operators.isEmpty() && hasPrecedence(c, operators.peek())) {
nums.push(calculate(operators.pop(), nums.pop(), nums.pop()));
}
operators.push(c);
}
else if (c == '(') {
operators.push(c);
}
else if (c == ')') {
while (!operators.isEmpty() && operators.peek() != '(') {
nums.push(calculate(operators.pop(), nums.pop(), nums.pop()));
}
operators.pop();
}
++i;
}
while (!operators.isEmpty()) {
nums.push(calculate(operators.pop(), nums.pop(), nums.pop()));
}
return nums.isEmpty() ? 0 : nums.pop();
}
public boolean isOperator(char c) {
return c == '+' || c == '-' || c == '*' || c == '/';
}
public int calculate(char operator, int num1, int num2) {
int res = 0;
switch(operator) {
case '+':
res = num1 + num2;
break;
case '-':
res = num2 - num1;
break;
case '*':
res = num1 * num2;
break;
case '/':
res = num2 / num1;
break;
}
return res;
}
// check if op2 has higher precendence than op1
public boolean hasPrecedence(char op1, char op2) {
if (op2 == ')' || op2 == '(') {
return false;
}
if ((op1 == '*' || op1 == '/') && (op2 == '+' || op2 == '-')) {
return false;
}
return true;
}
}

## 3. Time & Space Complexity

Stack: 时间复杂度: O(n), 空间复杂度: O(n)