http://www.geeksforgeeks.org/expression-evaluation/

Mistakes

if ')', don't forget to peek at the top of operators to check whether it is '(' in the while condition

public class Solution {
    /**
     * @param expression: an array of strings;
     * @return: an integer
     */
    public int evaluateExpression(String[] expression) {
        //two stacks, one is for operands, one is for operators
        Stack<Integer> operands = new Stack<>();
        Stack<Character> operators = new Stack<>();

        //loop through each string in the input array, 
        for (String str : expression) {
            char[] c = str.toCharArray();
            //if numbers, push to value stack
            if (c.length >= 2 || Character.isDigit(c[0])) {
                operands.push(Integer.valueOf(str));
            } else if (c[0] == '(') {
                //if "(", push to stack
                operators.push(c[0]);
            } else if (c[0] == ')') {
                //if ")", pop two operands, and one operator, do the operation, push result back to value stack, keep doing this until reach to "("
                while (!operators.isEmpty() && operators.peek() != '(') {
                    char operator = operators.pop();
                    int num2 = operands.pop();
                    int num1 = operands.pop();
                    operands.push(calculate(operator, num1, num2));
                }
                operators.pop();
            } else {
                //if operators, if not empty and the top operator has equal or high prioity than this one, let prev operators do the operation with top two operands
                if (operators.isEmpty() || hasPrecedence(c[0], operators.peek())) {
                    operators.push(c[0]);
                } else {
                    char operator = operators.pop();
                    int num2 = operands.pop();
                    int num1 = operands.pop();
                    operands.push(calculate(operator, num1, num2));
                    operators.push(c[0]);
                }
            }
        }

        //loop throught the rest in two stacks
        while (!operators.isEmpty()) {
            char operator = operators.pop();
            int num2 = operands.pop();
            int num1 = operands.pop();
            operands.push(calculate(operator, num1, num2));
        }


        //return result
        return operands.isEmpty() ? 0 : operands.pop();
    }


    private int calculate(char operator, int operand1, int operand2){
        int result = 0;

        switch (operator) {
            case '+':
                result = operand1 + operand2;
                break;
            case '-':
                result = operand1 - operand2;
                break;
            case '/':
                result = operand1 / operand2;
                break;
            case '*':
                result = operand1 * operand2;
                break;
        }

        return result;

    }

    //return true, if operator1 is higher than opertor2
    private boolean hasPrecedence(char operator1, char operator2) {
        if (operator2 == '(' || operator2 == ')') {
            return true;
        }

        if ((operator1 == '*' || operator1 == '/') && (operator2 == '+' || operator2 == '-')) {
            return true;
        }

        return false;
    }
};