<p>Given a string <code>expression</code> of numbers and operators, return <em>all possible results from computing all the different possible ways to group numbers and operators</em>. You may return the answer in <strong>any order</strong>.</p>

<p>The test cases are generated such that the output values fit in a 32-bit integer and the number of different results does not exceed <code>10<sup>4</sup></code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;2-1-1&quot;
<strong>Output:</strong> [0,2]
<strong>Explanation:</strong>
((2-1)-1) = 0 
(2-(1-1)) = 2
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;2*3-4*5&quot;
<strong>Output:</strong> [-34,-14,-10,-10,10]
<strong>Explanation:</strong>
(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
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= expression.length &lt;= 20</code></li>
	<li><code>expression</code> consists of digits and the operator <code>&#39;+&#39;</code>, <code>&#39;-&#39;</code>, and <code>&#39;*&#39;</code>.</li>
	<li>All the integer values in the input expression are in the range <code>[0, 99]</code>.</li>
</ul>

class Solution:
    dic = {} # memoise each expression to the list of results

    def diffWaysToCompute(self, expression: str) -> List[int]:

        if expression in self.dic: # work has already been done before 
            return self.dic[expression]
 
        if expression.isdigit():
            return [int(expression)]

        res_list = []
        for i, c in enumerate(expression):
            if c in ['+', '-', '*']:
                left_res = self.diffWaysToCompute(expression[:i])
                right_res = self.diffWaysToCompute(expression[i+1:])

                for left in left_res:
                    for right in right_res:
                        if c == "+":
                            res = left + right
                        elif c == "-":
                            res = left - right
                        else:
                            res = left * right

                        res_list.append(res)

        self.dic[expression] = res_list
        return res_list
16700