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`

,`Y`

and`D`

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

to a position equal to or greater than`Y`

.For example, given:

`X = 10`

`Y = 85`

`D = 30`

the function should return`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%`

and I scored just `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`

loop, how could it possibly be make much faster ?

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).

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