# parentheses - 241. Different Ways to Add Parentheses

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

Example 2:

``````Input: "2*3-4*5"
Output: [-34, -14, -10, -10, 10]
Explanation:  (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
``````

java：

``````class Solution {

private Map<String, List<Integer>> mem = new HashMap<>();

public List<Integer> diffWaysToCompute(String input) {
if (mem.containsKey(input)) return mem.get(input);

List<Integer> res = new ArrayList<>();

for (int i = 0; i < input.length(); i++) {
char c = input.charAt(i);
if (!(c == '+' || c == '-' || c == '*')) continue;

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

// 笛卡尔积
for (Integer l : left) {
for (Integer r : right) {
int temp = 0;
if (c == '+') temp = r + l;
else if (c == '-') temp = l - r;
else /*(c == '*')*/ temp = l * r;
}
}
}

mem.put(input, res);
return res;
}
}
``````

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