How to resolve the algorithm Abundant, deficient and perfect number classifications step by step in the Prolog programming language

Published on 12 May 2024 09:40 PM
#Prolog

How to resolve the algorithm Abundant, deficient and perfect number classifications step by step in the Prolog programming language

Table of Contents

Problem Statement

These define three classifications of positive integers based on their   proper divisors. Let   P(n)   be the sum of the proper divisors of   n   where the proper divisors are all positive divisors of   n   other than   n   itself.

6   has proper divisors of   1,   2,   and   3. 1 + 2 + 3 = 6,   so   6   is classed as a perfect number.

Calculate how many of the integers   1   to   20,000   (inclusive) are in each of the three classes. Show the results here.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Abundant, deficient and perfect number classifications step by step in the Prolog programming language

Source code in the prolog programming language

proper_divisors(1, []) :- !.
proper_divisors(N, [1|L]) :-
	FSQRTN is floor(sqrt(N)),
	proper_divisors(2, FSQRTN, N, L).

proper_divisors(M, FSQRTN, _, []) :-
	M > FSQRTN,
	!.
proper_divisors(M, FSQRTN, N, L) :-
	N mod M =:= 0, !,
	MO is N//M, % must be integer
	L = [M,MO|L1], % both proper divisors
	M1 is M+1,
	proper_divisors(M1, FSQRTN, N, L1).
proper_divisors(M, FSQRTN, N, L) :-
	M1 is M+1,
	proper_divisors(M1, FSQRTN, N, L).

dpa(1, [1], [], []) :-
	!.
dpa(N, D, P, A) :-
	N > 1,
	proper_divisors(N, PN),
	sum_list(PN, SPN),
	compare(VGL, SPN, N),
	dpa(VGL, N, D, P, A).

dpa(<, N, [N|D], P, A) :- N1 is N-1, dpa(N1, D, P, A).
dpa(=, N, D, [N|P], A) :- N1 is N-1, dpa(N1, D, P, A).
dpa(>, N, D, P, [N|A]) :- N1 is N-1, dpa(N1, D, P, A).


dpa(N) :-
	T0 is cputime,
	dpa(N, D, P, A),
	Dur is cputime-T0,
	length(D, LD),
	length(P, LP),
	length(A, LA),
	format("deficient: ~d~n abundant: ~d~n  perfect: ~d~n",
		   [LD, LA, LP]),
	format("took ~f seconds~n", [Dur]).

You may also check:How to resolve the algorithm Van Eck sequence step by step in the VTL-2 programming language
You may also check:How to resolve the algorithm Simple windowed application step by step in the EchoLisp programming language
You may also check:How to resolve the algorithm Draw a cuboid step by step in the PicoLisp programming language
You may also check:How to resolve the algorithm Distributed programming step by step in the Go programming language
You may also check:How to resolve the algorithm Topological sort step by step in the Sidef programming language