2017-09-13 LeetCode_282 Expression Add Operators

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本文介绍了一种算法，用于解决给定一个仅包含0-9数字的字符串和一个目标值，如何在数字间插入+、-、*运算符使得表达式结果等于目标值的问题。通过递归地构建所有可能的算术表达式，并使用栈来跟踪当前计算状态。

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282. Expression Add Operators

Given a string that contains only digits 0-9 and a target value, return all possibilities to add binary operators (not unary) +, -, or * between the digits so they evaluate to the target value.

Examples:

"123", 6 -> ["1+2+3", "1*2*3"] 
"232", 8 -> ["2*3+2", "2+3*2"]
"105", 5 -> ["1*0+5","10-5"]
"00", 0 -> ["0+0", "0-0", "0*0"]
"3456237490", 9191 -> []

Credits:
Special thanks to @davidtan1890 for adding this problem and creating all test cases.

solution:

 
         #include <stack> 
        
class Solution {
public:
    void divides(vector<string>& ans, string& num, int target, string str, int d, bool flag, stack<long long> nums, stack<char> syms, int state) {
        if (state == 0) {
            nums.top() = nums.top()*10+num[d-1]-'0';
        } else if (state == 1 || state == 2) {
            while (syms.size()) {
                long long x = nums.top(); nums.pop();
                if (syms.top() == '+') nums.top() += x;
                else if (syms.top() == '-') nums.top() -= x;
                else nums.top() *= x;
                syms.pop();
            }
            if (state == 1) syms.push('+');
            else syms.push('-');
            nums.push(num[d-1]-'0');
        } else {
            while (syms.size() && syms.top() == '*') {
                long long x = nums.top(); nums.pop();
                nums.top() *= x; syms.pop();
            }
            syms.push('*');
            nums.push(num[d-1]-'0');
        }
        if (d == num.length()) {
            while (syms.size()) {
                long long x = nums.top(); nums.pop();
                if (syms.top() == '+') nums.top() += x;
                else if (syms.top() == '-') nums.top() -= x;
                else nums.top() *= x;
                syms.pop();
            }
            if (target == nums.top()) ans.push_back(str);
            return;
        }
        if (flag) divides(ans, num, target, str+num[d], d+1, true, nums, syms, 0);
        divides(ans, num, target, str+"+"+num[d], d+1, num[d]-'0', nums, syms, 1);
        divides(ans, num, target, str+"-"+num[d], d+1, num[d]-'0', nums, syms, 2);
        divides(ans, num, target, str+"*"+num[d], d+1, num[d]-'0', nums, syms, 3);
    }
    vector<string> addOperators(string num, int target) {
        vector<string> ans;
        if (num.length() == 0) return ans;
        string str; str += num[0];
        stack<long long> nums; nums.push(0);
        stack<char> syms;
        divides(ans, num, target, str, 1, num[0]-'0', nums, syms, 0);
        return ans;
    }
 
         
};
 
   