282. 给表达式添加运算符（回溯）

class Solution {
    List<String> res = new ArrayList<>();

    public List<String> addOperators(String num, int target) {
        dfs(num,0,"",target,0,0);
        return res;
    }

    public void dfs(String num, int index, String s, int target, long sum, long pre) {
        if(index == num.length()) {
            if(target == sum) {
                res.add(s);
            }
            return;
        }
         // 枚举当前数可能的所有取值
        for(int i = index; i < num.length(); i++) {
             // 当前数位大于1且以0开头直接返回
            if(num.charAt(index) == '0' && i > index) return;
            long cur = Long.parseLong(num.substring(index,i+1));
            if(index == 0) { // index==0说明是第一个数，特殊处理
                dfs(num,i+1,s+cur,target,sum+cur,cur);
            } else {  // 三种情况回溯
                dfs(num,i+1,s+'+'+cur,target,sum+cur,cur);
                dfs(num,i+1,s+'-'+cur,target,sum-cur,-cur);
                dfs(num,i+1,s+'*'+cur,target,sum-pre+pre*cur,pre*cur);
            }
        }
    }
}