<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 {
private:
    std::unordered_map<std::string, std::vector<int>> memo;

    void parseExpression(const std::string& expression, std::vector<int>& numbers, std::vector<char>& operators) {
        int currentNumber = 0;
        for (char c : expression) {
            if (std::isdigit(c)) {
                currentNumber = currentNumber * 10 + (c - '0');
            } else {
                numbers.push_back(currentNumber);
                currentNumber = 0;
                operators.push_back(c);
            }
        }
        numbers.push_back(currentNumber);
    }

    int computeOperation(int left, int right, char op) {
        switch (op) {
            case '+': return left + right;
            case '-': return left - right;
            case '*': return left * right;
            default: throw std::invalid_argument("Invalid operator: " + std::string(1, op));
        }
    }

    std::vector<int> computeResults(const std::vector<int>& numbers, const std::vector<char>& operators, int start, int end) {
        std::string key = std::to_string(start) + "," + std::to_string(end);
        if (memo.find(key) != memo.end()) {
            return memo[key];
        }

        std::vector<int> results;
        if (start == end) {
            results.push_back(numbers[start]);
        } else {
            for (int i = start; i < end; ++i) {
                std::vector<int> leftResults = computeResults(numbers, operators, start, i);
                std::vector<int> rightResults = computeResults(numbers, operators, i + 1, end);
                char op = operators[i];

                for (int left : leftResults) {
                    for (int right : rightResults) {
                        results.push_back(computeOperation(left, right, op));
                    }
                }
            }
        }

        memo[key] = results;
        return results;
    }

public:
    std::vector<int> diffWaysToCompute(std::string expression) {
        std::vector<int> numbers;
        std::vector<char> operators;
        parseExpression(expression, numbers, operators);
        
        memo.clear();  
        return computeResults(numbers, operators, 0, numbers.size() - 1);
    }
};

//KDS
10600