Different Ways to Add Parentheses
<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>
	<li>The integer values in the input expression do not have a leading <code>&#39;-&#39;</code> or <code>&#39;+&#39;</code> denoting the sign.</li>
</ul>
Recursion; Memoization; Math; String; Dynamic Programming
var memo = map[string][]int{}

func diffWaysToCompute(expression string) []int {
	return dfs(expression)
}

func dfs(exp string) []int {
	if v, ok := memo[exp]; ok {
		return v
	}
	if len(exp) < 3 {
		v, _ := strconv.Atoi(exp)
		return []int{v}
	}
	ans := []int{}
	for i, c := range exp {
		if c == '-' || c == '+' || c == '*' {
			left, right := dfs(exp[:i]), dfs(exp[i+1:])
			for _, a := range left {
				for _, b := range right {
					if c == '-' {
						ans = append(ans, a-b)
					} else if c == '+' {
						ans = append(ans, a+b)
					} else {
						ans = append(ans, a*b)
					}
				}
			}
		}
	}
	memo[exp] = ans
	return ans
}