<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:
    int evaluate(const int left, const int right, const char op) {
        switch (op) {
            case '+': return left + right;
            case '-': return left - right;
            default: return left * right;
        }
    }

    vector<int> helper(const int n, const vector<int> &nums, const vector<char>& ops, const int left, const int right, vector<vector<int>> &cache) {
        if (left == right)
            return {nums[left]};
        if (right - left == 1)
            return {evaluate(nums[left], nums[right], ops[left])};
        const int idx = left * n + right;
        if (!cache[idx].empty())
            return cache[idx];
        vector<int> ret;
        for (int i = left; i < right; ++i) {
            auto prefix = helper(n, nums, ops, left, i, cache);
            auto suffix = helper(n, nums, ops, i + 1, right, cache);
            for (const auto p : prefix)
                for (const auto s : suffix)
                    ret.push_back(evaluate(p, s, ops[i]));
        }
        return cache[idx] = ret;
    }

    vector<int> diffWaysToCompute(const string& expression) {
        vector<int> nums;
        vector<char> ops;
        int num = 0;
        for (char c : expression)
            if (isdigit(c))
                num = num * 10 + (c - '0');
            else {
                nums.push_back(num);
                ops.push_back(c);
                num = 0;
            }
        nums.push_back(num);
        const int n = (int)nums.size();
        vector<vector<int>> cache(n * n);
        return helper(n, nums, ops, 0, n - 1, cache);
    }
};
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