Number of Managers

Question

A company is arranged in a heirarchical structure, with a layer of workers at the bottom. Each worker is managed by a manager. Consequently, each manager is managed by another manager until there is a company "boss". Each manager is restricted to managing, at most, x workers. For a company of size y calculate the number of managers required (including the boss)

Function should take two inputs. Eg non-golfed definition: calc_num_managers(num_workers, num_workers_per_manager)

You can assume that the number of workers per manager will be greater than 1.

Examples:

• A company with 0 workers needs 0 managers
• If the company has 4 workers, and each manager can manage 8 workers, then there is 1 manager.
• If the company has 4 workers, and each manager can manage 4 workers, then you need 1 manager
• If the company has 12 workers, and each manager can manage 8 workers, then there are 3 managers:

Answer 1

C, C++, Java, C#, D : 73 69 bytes

-4 bytes thanks to Zacharý

Due to the similarities between theses languages, this answer works for each.
Maybe it works in processing too, but i can't test

int c(int w,int p){int r=0;do{w=(w+p-1)/p;r+=w;}while(w>1);return r;}

Here is an optimized version in D : 62 bytes thanks to Zacharý

T c(T)(T w,T p){T r;do{w=(w+p-1)/p;r+=w;}while(w>1);return r;}

T here is a type for template metaprogramming. This function is callable with c(4,8);

Answer 2

Jelly, 14 bytes

Ṃ÷⁴Ċ0Ṃ’$?µÐĿḊS

Try it online!

Answer 3

JavaScript, 46 43 bytes

If scheme isn't solvable, there will be stack exeeded error

-3 bytes ceil trick inspired by Cows quack

f=(w,m)=>(r=0|(w+m-1)/m,r>1&&(r+=f(r,m)),r)

//test
;[[0,1],[4,8],[4,4],[12,8],[8,3],[10,3]]//0;1;1;3;4;7
.map(e=>console.log("w="+e[0]+" m="+e[1]+" result="+f(e[0],e[1])))

Requirements

w count of workers, non-negative integer

m count of max workers per manager, positive integer

Answer 4

Perl 5, 44 + 1 (-n) = 45bytes

$t=<>;$m+=$_=1+int$_/$t while($_>1);say$m|$_

Try it online!

Answer 5

Husk, 7 bytes

ΣtU¡(⌈/

Try it online!

Repeatedly (¡) takes the ceiling (⌈) of the division (/) of the number of workers by the number of workers per manager and sums (Σ) all the unique results (U).