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

    vector<int> helper(string &expression, int st, int ed) {
        vector<int> ans;

        bool hasSymbol = false;

        for(int k=st+1;k<ed;k++) {
            if (isSymbol(expression[k])) {
                if (dp[st][k-1].empty()) {
                    dp[st][k-1] = helper(expression, st, k-1);
                }
                if (dp[k+1][ed].empty()) {
                    dp[k+1][ed] = helper(expression, k+1, ed);
                }
                for(auto p: dp[st][k-1]) {
                    for(auto q: dp[k+1][ed]) {
                        ans.push_back(performOperation(expression[k], p, q));
                    }
                }
                hasSymbol = true;
            }
        }

        if (!hasSymbol) {
            return {stoi(expression.substr(st, ed-st+1))};
        }

        return ans;
    }

    int performOperation(char c, int a, int b) {
        switch(c) {
            case '-': return a-b;
            case '+': return a+b;
            case '*': return a*b;
            default : return -1;
        }
    }

    bool isSymbol(char c) {
        return c=='-' || c == '+' || c =='*';
    }

    vector<int> dp[20][20];
};

/**



*/
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