Different Ways to Add Parentheses

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]

分析：

加了括号以后，每一个operator在某种情况下都会被最后执行。

    public List<Integer> diffWaysToCompute(String input) {
        List<Integer> list = new ArrayList<Integer>();
        for (int i = 0; i < input.length(); i++) {
            if (input.charAt(i) == '+' || input.charAt(i) == '-' || input.charAt(i) == '*') {
                List<Integer> left = diffWaysToCompute(input.substring(0, i));
                List<Integer> right = diffWaysToCompute(input.substring(i + 1));
                for (int l : left) {
                    for (int r : right) {
                        if (input.charAt(i) == '+') {
                            list.add(l + r);
                        } else if (input.charAt(i) == '-') {
                            list.add(l - r);
                        } else if (input.charAt(i) == '*') {
                            list.add(l * r);
                        }
                    }
                }
            }
        }
        if (list.size() == 0) {
            list.add(Integer.parseInt(input));
        }
        return list; 
    }