Different Ways to Add Parentheses(Medium)

Given a string of numbers and operators, return all possible results from computing all the different possible ways to group numbers and operators. The valid operators are +, - and *.

Example 1
Input: "2-1-1".

((2-1)-1) = 0
(2-(1-1)) = 2
Output: [0, 2]


Example 2
Input: "2*3-4*5"

(2*(3-(4*5))) = -34
((2*3)-(4*5)) = -14
((2*(3-4))*5) = -10
(2*((3-4)*5)) = -10
(((2*3)-4)*5) = 10
Output: [-34, -14, -10, -10, 10]

分治法（Divide and conquer），递归地将表达式按照运算符拆分为左右两半

public List<Integer> diffWaysToCompute(String input) {
    List<Integer> result = new ArrayList<>();
    if (input == null || input.length() == 0) {
        return result;
    }

    for (int i = 0; i < input.length(); i++) {
        char c = input.charAt(i);

        if (!isOperator(c)) {
            continue;
        }

        List<Integer> left = diffWaysToCompute(input.substring(0, i));
        List<Integer> right = diffWaysToCompute(input.substring(i + 1));

        for (int num1 : left) {
            for (int num2 : right) {
                int val = calculate(num1, num2, c);
                result.add(val);
            }
        }
    }

    // only contains one number
    if (result.isEmpty()) {
        result.add(Integer.parseInt(input));
    }

    return result;
}

private int calculate(int num1, int num2, char operator) {
    int result = 0;

    switch(operator) {
        case '+' : result = num1 + num2;
            break;

        case '-' : result = num1 - num2;
            break;

        case '*' : result = num1 * num2;
            break;
    }

    return result;
}

private boolean isOperator(char operator) {
    return (operator == '+') || (operator == '-') || (operator == '*');
}