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// @Title: 给表达式添加运算符 (Expression Add Operators)
// @Author: 15816537946@163.com
// @Date: 2021-10-16 23:32:08
// @Runtime: 80 ms
// @Memory: 9 MB
import (
    "strconv"
)

func addOperators(num string, target int) []string {
    out := []string{}

    var backtrack func(string, string, int,int) 

    backtrack = func(num, prefix string, val, last int) {
        if len(num) == 0 {
            if val == target {
                out = append(out, prefix)
            }
            return
        }

        for i :=1;i<=len(num);i++ {
            str := num[:i]
            digit, _ := strconv.Atoi(str)

            // prevent number starting with 0 except the number 0 itself
            if num[0] == '0' && i != 1 {
                continue
            }

            // for the first call 
            if prefix == "" {
                backtrack(num[i:],str, digit, digit)
            } else {
                backtrack(num[i:],prefix+"+"+str, val+digit, digit)
                backtrack(num[i:],prefix+"-"+str,val-digit,-digit)
                backtrack(num[i:],prefix+"*"+str,val-last+last*digit, last*digit)
            }
        }
    }

    backtrack(num,"", 0,0)

    return out

}