puzzle_06

Analysis

The growing of the school of fishs could be somewhat exponential, but for now we do not know it's growth rate yet.

Design

First - and straight - idea was to simulate the Lanternfish's life and school of (linked) fishs.

type Lanternfish_Ptr is access all Lanternfish;

type Lanternfish is record
    Timer   : Life_Timer      := BabyFish;
    Sibling : Lanternfish_Ptr := null;
end record;

A new baby fish can be created easily throught the use of dynamic allocation when one comes at it's life-timer of 0.

procedure New_Fish (Timer : Life_Timer) is
    (...)
begin
    (...)
    Last_fish := new Lanternfish;
    (...)
    Previous_Last_Fish.Sibling := Last_fish;
    (...)
end New_Fish;

First results

Population

Running the simulation for 18 or 80 days of a school of Lanternfish was cool 😎 ... in the begining

Going further became a nightmare 😫 ... of over-population 🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟🐟!

Day	🐟 Population	🐟 Population
0	5	300
18	26	1_563
20	34	1_959
80	5_934	350_605
120	191_336	11_301_761
150	2_621_894	154_900_658
160	6_311_710	372_489_150
170	14_979_958	883_463_328
180	35_890_123	2_120_130_781
185	55_653_352	3_285_743_983
210	490_587_171	Out of memory
256	Out of memory	Out of memory

Some charting shows clearly that growth is a 10 exponential here, with a factor depending on the initial data (5🐟 ou 300🐟) : respectively 24 or 20.

One can then extrapolate what the population would be after 256 days.

Day	5 Initial Population	300 Initial Population
256	39_300_000_000	3_070_000_000_000
256	39 Giga	3 Tera

Execution time

Execution time (sec) ... on a Ryzen 3900 @ 4.3 GHz equiped with 64 GB of RAM.

Day	5 🐟 at init.	300 🐟 at init.
18	0.005	0.01
20	0.005	0.01
80	0.005	0.01
120	0.015	0.32
150	0.15	4.72
158	0.31	9.24
160	0.195	11.08
170	0.447	26.59
180	2.202	63.76
185	1.80	105.76
199	11.25	Out of memory 162 GB
210	29.25	Out of memory
256	Out of memory	Out of memory 284 GB

Clearly, have to find another simulation algorithm 🧞‍♂️

💡 New solution pattern 💡

Lets consider the fish population as counting in the pyramid of age.

Mature : constant := 0;
Young  : constant := 6;
BabyFish : constant := 8;

type Life_Timer is new Natural range Mature .. BabyFish;

type Pyramid_of_Age is array (Life_Timer) of Population;

This is now actually efficient!

Main loop

   -- Time and Life is passing by
    for D in 1 .. Run_Args.Nb_of_Days loop
        Fish_Count := Next_Day;
    end loop;

Applying an aging function

function Next_Day return Population is
(...)
    -- General population aging
    for T in Life_Timer loop
        case T is
            when Mature => -- 0
                New_Young      := Fish_Population (Mature);
                New_Generation := Fish_Population (Mature);
            when others =>
                Fish_Population (T - 1) := Fish_Population (T);
        end case;
    end loop;

    -- New Babies and add youngsters
    Fish_Population (BabyFish) := Next_Generation_Count;
    Fish_Population (Young)    := @ + New_Young;

    Next_Generation_Count := Fish_Population (Mature);
(...)