The most important job is recruiting.
Yes, it’s totally true. I have spent about a quarter of my time for finding the good guys and got both success and failure in seeing how good a candidate looks like. Then I have tried to create a question that’s possible to use in all my interviews with candidates of developer position.
The interview question is:
Writing continuously the non-negative numbers by skipping the number which is built by only one digit (11, 22, 33… 111, 222, …), we have a sequence:
0123456789101213…19202123…
You can see the 10th digit is 1. So let’s say 10th 1. Compute:
10th + 100th + 1.000th + …
My question is “What is your approach to solve this problem? Don’t need to give the final result”.
It’s so easy? Not sure – as it’s a kind of a problem that its difficulty increases so fast by the data limitation. Could you find 100th? 1000th? 100.000.000.000th? Yes, it’s much more different.
OK, let see some possible solutions that are described below:
Solution 1: Natural thinking
It seems we can build up and store the sequence of digits in a string. And it’s so easy to get the digit by the index then. The code should be
StringBuilder sequence = new StringBuilder();
for (int number = 0; number < 1000; number++) {
if (!BuiltByOneDigit(number)) {
sequence = sequence.Append(number.ToString());
}
}
int result = (int)sequence[1] + (int)sequence[10] + (int)sequence[100] + (int)sequence[1000];
But how about the 100.000.000.000th?
Solution 2: Optimisation
We can consider to stop the loop as soon as possible. For example, to generate a string with length 100.000.000.000, the maximum value of number in the loop should be less than 10.000.000.000 (why? could it be a smaller number?).
But it’s still too large. How much of memory it takes to store 10.000.000.000 characters? 10.000.000.000 bytes > 9GB. But wait, why do we need to store whole the string? How many meaning digit in the string? They are 10th, 100th, 1.000th.. digits. Yes, so just count to get the meaning digit and skip storing others. The code should look like
long length = 0;
long index = 1;
int result = 0;
for (int number = 0; number < 1000000000; number++) {
if (!BuiltByOneDigit(number)) {
string numberInString = number.ToString();
if (length + numberInString.Length < index) {
result += (int)numberInString[index - length];
index *= 10;
}
length += numberInString.Length;
}
}
// output: result
This approach can reduce the memory usage to nearly 0. But 10.000.000.000 seems too big for reaching in loop.
Solution 3: Math approach
Let’s see another approach by math
- How many digits do we have by writing a sequence from 0 to 9? 10
- How many digits do we have by writing a sequence from 10 to 99? 162 = (99 – 10 + 1 – 9) * 2. Skipping 9 numbers: 11, 22, …
- How many digits do we have by writing a sequence from 100 to 999? 2673 = (999 – 100 + 1 – 9) * 3. Skipping 9 numbers: 111, 222, …
- …
OK, so what 4.321th digit? 4321 – 10 – 162 – 2673 = 1476 > 0, this digit belongs to a number that falls in (1.000, 9.999) which has 4 digits. So its index from 1.000 = 1476 / 4 = 369. Then the finding digit should be 1 (in 1.369).
It’s not much easy but not difficult to implement in code and the process time is going to be 0.
It’s just a problem itself but how people approach or solve it can tell much about them.
After about hundred interviews, I had a lot of data and classify the candidates by the common feedback questions:
- I cannot understand this question. I get no information because some of developers are super in building software by tools but have never faced this kind of problem. Just explain or give them another question.
- I cannot solve this. Say goodbye to him, at least easy giving up is not my style or at least he should ask me like #1.
- I think there is a rule here. 10th is 1 so I guess 100th, 1.000th, 10.000th.. are 1 as well. Life is not easy man. The interview question is for testing the logical not tricky thought.
- What is its input? How to input data, from console? Why 10th is 1, it is 9?… I usually don’t waste my time for answering these questions. He just focuses on the minor things and forget the real problem.
- We can generate this string and get the digit by index after that. Yes, it’s the first solution, right? He looks like a normal developer. I usually go ahead with him by some questions depending on how he structure the program. “How many functions or methods you have?”, “How do we check a number that is built by 1 digit?” etc. And of course, some suggestion to optimize the solution, “What should you choose, optimize memory or speed?”, “How many meaning digits we have?” etc, and the story begins.
- Ah yes, we should not maintain the whole string, we can remove the unnecessary parts. Sure, the second solution. He seems a good developer.
- Yeah, we remove 9 numbers in 2-digit numbers that equals to 18 digits. We also remove 9 numbers in 3-digit numbers that equals to 27 digits. And the actual position of 1.0000 should be minused… He is a must-have guy at least in the talent aspect.
It just a common test for his IQ, but the specific code should shows his knowledge and skills in a specific language or platform. For example, good C# developer should use StringBuilder to build the sequence instead of using string. C++ developer should check the number that is built by 1 digit by operations instead of by converting it to string. Putting the condition like if (sequence.Length > 10.000.000.000) in the loop is not the good way in any language.
The guy who can show off the solution 3 in the first time – he is really intelligent or he has solved a thousand problems like that, maybe a code challenger, also a right man we would hire.
The guy who cannot pose the best solution at the first time but can come to the solution 3 after the advises has potential to become a great developer.
The guy who cannot come to the optimized solution after the advises just be a normal developer – not a smart guy. I have never hired him even though he has a lot of experience or certificated.
In my opinion, Java, .NET or what common technologies is so easy for a talent guy learns in a short time but technology-master cannot go far with a week algorithm coding background.
So far, I think it’s a good question to see the developer’s IQ that I used in a long time. Now I’m creating another :).
