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# Solving Google Interview Questions

24 Nov 2017 · 6 mins read Edit PostA simple technical algorithm question, asked at Google interviews taken from a user on Glassdoor.

### Question:

```
Find all string combinations consisting only of 0, 1, where ? can be either 0 or 1
```

Input: string containing characters 0, 1 and ?, where ? is a wildcard for 0 or 1. Output: print all possible combinations of the string.

**Example Input**

β011?0β

**Example Output**

[β01100β, β01110β]

### Worst Case

To solve problems like these, a good method is to think of *any* solution you can think of. This is likely to be the *worst case solution*.

For this problem, my worst case solution is this:

**Setup Code**

```
var output = [];
var input = "011?0";
print(input);
console.log(output);
```

**Algorithm**

```
function print(input) {
var str = "";
for(var i = 0; i < input.length; i++) {
var c = input.charAt(i);
if (c == "?") {
c = 1;
print(
str + '0' + input.substring(i + 1)
);
}
str = str + c;
}
output.push(str);
}
```

This algorithm loops over the string and builds a new one without the β?β character. When it gets to a β?β character, it builds a new string using a 0 instead of this β?β and continues with this run, and re-calls the algorithm with the same string but with the β?β replaced with a 1.

**Complexity:**

`O(2^n)`

, where N is the number of wildcards `?`

. 2 because there are 2 options the wildcard could be.

The positives and negatives of this solution are:

**Pros:**

- Simple

**Cons:**

- Performs unnecessary calculations - every time a ? appears, the function calls itself and starts at the beginning of the string again, re-checking each character to see if it is a β?β.
- Uses recursion? (is this even a con?)
- Requires a global variable
`output`

### Better Case

- Improved function to take in start position:
`print(str, 0)`

,`i`

is set to start pos. When we call it again, we use:`print(str, i + 1)`

```
function print(input, output, start) {
var str = input.substring(0, start);
for (var i = start; i < input.length; i++) {
var c = input.charAt(i);
if (c == "?") {
c = 1;
print(
str + '0' + input.substring(i + 1),
output,
i
);
}
str = str + c;
}
output.push(str);
}
```

**Complexity:**

`O(2^n)`

, where N is the number of wildcards `?`

. 2 because there are 2 options the wildcard could be.

**Pros:**

- Uses less computations
- Doesnβt require a global variable
`output`

**Cons:**

- Uses recursion (is this even a con?)

### Measuring Computations

I initially thought the better case used less computations than the worst case. I decided to test this theory by adding up a counter for each line I thought needed a computation. See the source code on CodePen.

```
Input: ? - Worst Case: Total Computations: 21
Input: ? - Better Case: Total Computations: 19 (3 less computations)
Input: ?? - Worst Case: Total Computations: 65
Input: ?? - Better Case: Total Computations: 57 (8 less computations)
Input: ??? - Worst Case: Total Computations: 181
Input: ??? - Better Case: Total Computations: 129 (52 less computations)
Input: ???? - Worst Case: Total Computations: 461
Input: ???? - Better Case: Total Computations: 273 (188 less computations)
```

**Better Case counting computations**

```
function print(input, output, start) {
var str = input.substring(0, start); ct += 2;
for (var i = start; i < input.length; i++) { ct += 2;
var c = input.charAt(i); ct += 2;
ct++;
if (c == "?") {
c = 1; ct++;
print(
str + '0' + input.substring(i + 1),
output,
i
); ct += 2;
}
str = str + c; ct++;
}
output.push(str); ct++;
}
```

I also discovered I had a bug in my worst case algorithm after counting these computations and debugging the function using Chrome dev tools JavaScript debugger.

Chromeβs JavaScript debugger revealed my error and I fixed it.

I found two solutions to this problem, one slightly better than the other.

## Solution

```
function print(input, output, start) {
var str = input.substring(0, start);
for (var i = start; i < input.length; i++) {
var c = input.charAt(i);
if (c == "?") {
c = 1;
print(
str + '0' + input.substring(i + 1),
output,
i
);
}
str = str + c;
}
output.push(str);
}
```

## Suggested

- The First Website I Built
*— 15 November 2017* - Solving Google Interview Questions
*— 27 November 2017*