<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 {
public:
    unordered_map<string, vector<int>> dp;

    vector<int> helper(string &s, int i, int j) {
        string key = to_string(i) + "," + to_string(j);
        if (dp.find(key) != dp.end()) return dp[key];  // Return cached result if it exists
        
        if (i > j) return {};
        
        string num = s.substr(i, j - i + 1);
        if (num.find_first_not_of("0123456789") == string::npos) {
            return {stoi(num)};
        }

        vector<int> ans;
        for (int k = i; k < j; k++) {
            if (s[k] == '+' || s[k] == '-' || s[k] == '*') {
                vector<int> left = helper(s, i, k - 1);
                vector<int> right = helper(s, k + 1, j);
                
                for (auto x : left) {
                    for (auto y : right) {
                        if (s[k] == '+') ans.push_back(x + y);
                        else if (s[k] == '-') ans.push_back(x - y);
                        else if (s[k] == '*') ans.push_back(x * y);
                    }
                }
            }
        }
        return dp[key] = ans;  // Store the result in the map
    }

    vector<int> diffWaysToCompute(string expression) {
        return helper(expression, 0, expression.size() - 1);
    }
};

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