241. Different Ways to Add Parentheses

Given a string of numbers and operators, return all possible results from computing all the different possible ways to group numbers and operators. The valid operators are +, - and *.

Example 1:

Input: "2-1-1"
Output: [0, 2]
Explanation: 
((2-1)-1) = 0 
(2-(1-1)) = 2

Example 2:

Input: "2*3-4*5"
Output: [-34, -14, -10, -10, 10]
Explanation: 
(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

Approach #1: 

namespace studycat {
    int add(int x, int y) { return x + y; }
    int sub(int x, int y) { return x - y; }
    int mul(int x, int y) { return x * y; }
}

class Solution {
public:
    vector<int> diffWaysToCompute(string input) {
        return helper(input);
    }
    
private:
    unordered_map<string, vector<int>> memo;
    
    const vector<int>& helper(const string& input) {
        if (memo.count(input)) return memo[input];
        
        vector<int> ans;
        
        for (int i = 0; i < input.length(); ++i) {
            char op = input[i];
            
            if (op == '+' || op == '-' || op == '*') {
                const string left = input.substr(0, i);
                const string right = input.substr(i+1);

                const vector<int>& l = helper(left);
                const vector<int>& r = helper(right);
                
                std::function<int(int, int)> f;

                switch(op) {
                    case '+': f = studycat::add; break;
                    case '-': f = studycat::sub; break;
                    case '*': f = studycat::mul; break;
                }
                
                for (int i : l) 
                    for (int j : r) 
                        ans.push_back(f(i, j));
     
            }
        }
        if (ans.empty())
            ans.push_back(std::stoi(input));
        
        memo[input].swap(ans);
        return memo[input];
    }
};

　　

Analysis:

http://zxi.mytechroad.com/blog/leetcode/leetcode-241-different-ways-to-add-parentheses/