Definitions:

   

   

Problem:
Define a function solution with input A, B and K, such that solution returns the number of integers divisible by K , belonging to the interval [A, B].

• Expected worst-case time complexity is O(1);
• Expected worst-case space complexity is O(1);

Elements of input arrays can be modified. 

Analysis:

The solution to this problem is pretty simple, the integers divisible by K, are the ones described by

   

.

   

 gives us all divisible integers from 1 to B,

   

.
Now we just have to subtract the integers that dot not belong to the interval [A, B]. We have to be careful here, since A belongs to the interval, if A is divisible we have count it, so when excluding, we are going to do

   

. And the solution is

   

We are doing only one operation to solve this problem, so this gives us, time complexity and space complexity of O(1);

Complete Solution:

Count

Python

# Name: CountDiv # Link: https://codility.com/demo/take-sample-test/count_div/ def solution(A, B, K): # B//K Al numbers divisible by K from 0 to B, (A - 1)//K # all number divisible by K except A if A is divisible return B//K - (A - 1)//K

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# Name: CountDiv # Link: https://codility.com/demo/take-sample-test/count_div/     def solution(A, B, K):     # B//K Al numbers divisible by K from 0 to B, (A - 1)//K     # all number divisible by K except A if A is divisible     return B//K - (A - 1)//K

Time Complexity O(1)
Space Complexity O(1)

Link to GitHub solution here .
Link to Codility problem here .