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”.

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((2-1)-1) = 0
(2-(1-1)) = 2

Output: [0, 2]

Example 2
Input: “23-45”

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(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]

乍一看还以为是backtracking呢，原来是Divide and Conquer。

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