给定一个仅包含数字 0-9 的字符串和一个目标值，在数字之间添加二元运算符（不是一元）+、- 或 * ，返回所有能够得到目标值的表达式。
示例 1:
输入: num = "123", target = 6
输出: ["1+2+3", "1*2*3"]
示例 2:
输入: num = "232", target = 8
输出: ["2*3+2", "2+3*2"]
示例 3:
输入: num = "105", target = 5
输出: ["1*0+5","10-5"]
示例 4:
输入: num = "00", target = 0
输出: ["0+0", "0-0", "0*0"]
示例 5:
输入: num = "3456237490", target = 9191
输出: []
代码
class Solution {
public:
vector addOperators(string num, int target) {
vector res;
addOperatorsDFS(num, target, 0, 0, "", res);
return res;
}
void addOperatorsDFS(string num, int target, long long diff, long long curNum, string out, vector &res) {
if (num.size() == 0 && curNum == target) {
res.push_back(out);
}
for (int i = 1; i <= num.size(); ++i) {
string cur = num.substr(0, i);
if (cur.size() > 1 && cur[0] == '0') return;
string next = num.substr(i);
if (out.size() > 0) {
addOperatorsDFS(next, target, stoll(cur), curNum + stoll(cur), out + "+" + cur, res);
addOperatorsDFS(next, target, -stoll(cur), curNum - stoll(cur), out + "-" + cur, res);
addOperatorsDFS(next, target, diff * stoll(cur), (curNum - diff) + diff * stoll(cur), out + "*" + cur, res);
} else {
addOperatorsDFS(next, target, stoll(cur), stoll(cur), cur, res);
}
}
}
};