241. Different Ways to Add Parentheses

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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

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

Example 2

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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]

解法1：

用Divide & Conquer的思想，按照每一个运算符号分成左右两边。每边计算一下结果然后按照运算符号结合起来。当只有数字的时候所生成的res一定为空，这个时候就把数字加入res即可。

lang: java
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class Solution {
    public List<Integer> diffWaysToCompute(String input) {
        List<Integer> res = new ArrayList<>();
        for (int i = 0; i < input.length(); i++) {
            if (input.charAt(i) == '+' || input.charAt(i) == '-' || input.charAt(i) == '*') {
                String left = input.substring(0, i);
                String right = input.substring(i + 1);
                List<Integer> leftRes = diffWaysToCompute(left);
                List<Integer> rightRes = diffWaysToCompute(right);
                for (int l : leftRes) {
                    for (int r : rightRes) {
                        switch (input.charAt(i)) {
                            case '+' :
                                res.add(l + r);
                                break;
                            case '-':
                                res.add(l - r);
                                break;
                            case '*':
                                res.add( l * r);
                                break;
                        }
                    }
                }
            }
        }
        if (res.size() == 0) {
            res.add(Integer.parseInt(input));
        }
        return res;
    }
}