记一道面试题

Write a function that given a string of digits and a target value, prints where to put +'s and *'s between the digits so they combine exactly to the target value. Note there may be more than one answer, it doesn't matter which one you print.
Examples:
"1231231234",11353 -> "12*3+1+23*123*4"
"3456237490",1185 -> "3*4*56+2+3*7+490"

"3456237490",9191 -> "no solution"

方案一：（不是俺想出）可供参考（用了穷举法）

[] args)
        {
            Check("22", 1/*Should start from 1*/, 4);
            Check("3456237490", 1/*Should start from 1*/, 1185); 
            Check("3456237490", 1/*Should start from 1*/, 9191); 
        }

        public static void Check(string str,int index, int expectedResult)
        {
            string testStr = string.Empty;
            
            for (int i = index; i < str.Length; i++)
            {          
                //Check index +
                testStr = str.Insert(i, "+");
                if (Evaluate(testStr) == expectedResult)
                    Console.WriteLine(testStr + "=" + expectedResult);
                Check(testStr, i + 2, expectedResult);
                //Check index * 
                testStr = str.Insert(i, "*");
                if (Evaluate(testStr) == expectedResult)
                    Console.WriteLine(testStr + "=" + expectedResult);
                Check(testStr, i + 2, expectedResult);
            }
        }

        public static long Evaluate(string expression)
        {
            List<string> strs = new List<string>();
            string str = string.Empty;
            foreach (char ch in expression.ToCharArray())
            {
                switch (ch)
                {
                    case '*':
                        if (str != string.Empty)
                            strs.Add(str);
                        str = string.Empty;
                        strs.Add("*");
                        break;
                    case '+':
                        if (str != string.Empty)
                            strs.Add(str);
                        str = string.Empty;
                        strs.Add("+");
                        break;
                    default:
                        str += ch.ToString();
                        break;
                }
            }
            if (str != string.Empty)
                strs.Add(str);
            Stack<long> intStack = new Stack<long>();
            for (int i = 0; i < strs.Count; i++ )
            {
                switch (strs[i])
                {
                    case "+":
                        break;
                    case "*":
                        long before = intStack.Pop();
                        long next = long.Parse(strs[++i]);
                        intStack.Push(before * next);
                        break;
                    default:
                        intStack.Push(long.Parse(strs[i]));
                        break;
                }
            }
            long result = 0;
            while (intStack.Count > 0)
                result += intStack.Pop();
            return result;
        }
    }