bhuvesh - 5 months ago 34

Java Question

today i heard about this website called codility where a user can give various programming test to check their code's performance.

When I started, they presented me with this sample test,

Task description A small frog wants to get to the other side of the

road. The frog is currently located at position X and wants to get to

a position greater than or equal to Y. The small frog always jumps a

fixed distance, D. Count the minimal number of jumps that the small

frog must perform to reach its target.

Write a function:

`class Solution { public int solution(int X, int Y, int D); }`

that, given three integers,`X`

and`Y`

, returns the minimal number of jumps from position`D`

to a position equal to or greater than`X`

.`Y`

For example,

given:

`X = 10`

`Y = 85`

the function should return`D = 30`

,`3`

because the frog will be positioned as follows:

after the first jump,

at position 10 + 30 = 40

after the second jump, at position 10 + 30 + 30 = 70

after the third jump, at position 10 + 30 + 30 + 30 = 100

Assume that: X, Y and D are integers within the range

[1..1,000,000,000]; X ≤ Y. Complexity: expected worst-case time

complexity is O(1); expected worst-case space complexity is O(1).

The question was pretty straight forward and it took me like 2 minutes to write the solution, which is following,

`class Solution {`

public int solution(int X, int Y, int D) {

int p = 0;

while (X < Y){

p++;

X = X + D;

}

return p;

}

}

However, the test result shows that the performance of my code is just

`20%`

`55%`

Here is the link to result, https://codility.com/demo/results/demo66WP2H-K25/

That was so simple code, where I have just used a single

`while`

Answer

Basic math:

```
X + nD >= Y
nD >= Y - X
n >= (Y - X) / D
```

The minimum value for n will be the result of rounding up the division of (Y - X) by D.

Big O analysis for this operation:

- Complexity: O(1). It's a difference, a division and a round up
- Worst-case space complexity is O(1): you can have at most 3 more variables:
- Difference for Y - X, let's assign this into Z.
- Division between Z by D, let's assign this into E.
- Rounding E up, let's assign this into R (from result).