<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 Partition(expression, 0, expression.size());
    }

    std::vector<int> Partition(std::string &exp, int left, int right) {
        int first_v = exp[left] - '0'; int left_front = left;
        if (std::isdigit(exp[left+1])) { first_v = first_v * 10 + exp[left+1] - '0'; left_front++; }
        if (left_front + 1 == right) return {first_v};

        int last_v = exp[right-1] - '0'; int right_tail = right;
        if (std::isdigit(exp[right-2])) { last_v = last_v + (exp[right-2] - '0') * 10; right_tail--; }
        if (left_front + 3 == right_tail) return {Calc(first_v, last_v, exp[left_front+1])};

        std::vector<int> retv;
        for (int i = left_front + 1; i < right;) {
            std::vector<int> left_val = Partition(exp, left, i);
            std::vector<int> right_val = Partition(exp, i+1, right);
            for (auto &l_v : left_val) {
                for (auto &r_v : right_val) {
                    retv.emplace_back(Calc(l_v, r_v, exp[i]));
                }
            }
            if (std::isdigit(exp[i + 2])) {
                i = i + 3;
            } else {
                i = i + 2;
            }
        }
        return retv;
    }

    int Calc(int i, int j, char expr) {
        switch(expr) {
        case '+':
            return i + j;
        case '-':
            return i - j;
        case '*':
            return i * j;
        }
        return 0;
    }
};
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