How to resolve the algorithm Narcissistic decimal number step by step in the Prolog programming language

Published on 12 May 2024 09:40 PM
#Prolog

How to resolve the algorithm Narcissistic decimal number step by step in the Prolog programming language

Table of Contents

Problem Statement

A   Narcissistic decimal number   is a non-negative integer,

n

{\displaystyle n}

,   that is equal to the sum of the

m

{\displaystyle m}

-th   powers of each of the digits in the decimal representation of

n

{\displaystyle n}

,   where

m

{\displaystyle m}

is the number of digits in the decimal representation of

n

{\displaystyle n}

.

Narcissistic (decimal) numbers are sometimes called   Armstrong   numbers, named after Michael F. Armstrong. They are also known as   Plus Perfect   numbers.

Generate and show here the first   25   narcissistic decimal numbers.

Note:

0

1

= 0

{\displaystyle 0^{1}=0}

,   the first in the series.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Narcissistic decimal number step by step in the Prolog programming language

Source code in the prolog programming language

digits(0, []):-!.
digits(N, [D|DList]):-
	divmod(N, 10, N1, D),
	digits(N1, DList).

combi(0, _, []).
combi(N, [X|T], [X|Comb]):-
	N > 0,
	N1 is N - 1,
	combi(N1, [X|T], Comb).
combi(N, [_|T], Comb):-
	N > 0,
	combi(N, T, Comb).

powSum([], _, Sum, Sum).
powSum([D|DList], Pow, Acc, Sum):-
	Acc1 is Acc + D^Pow,
	powSum(DList, Pow, Acc1, Sum).

armstrong(Exp, PSum):-
	numlist(0, 9, DigList),
	(Exp > 1 ->
	  Min is 10^(Exp - 1)
	  ; Min is 0
	),
	Max is 10^Exp - 1,
	combi(Exp, DigList, Comb),
	powSum(Comb, Exp, 0, PSum),
	between(Min, Max, PSum),
	digits(PSum, DList),
	sort(0, @=<, DList, DSort),	% hold equal digits
	( DSort = Comb;
      PSum =:= 0,	% special case because
	  Comb = [0]	% DList in digits(0, DList) is [] and not [0]
	).
	
do:-between(1, 7, Exp),
	findall(ArmNum, armstrong(Exp, ArmNum), ATemp),
	sort(ATemp, AList),
	writef('%d -> %w\n', [Exp, AList]),
	fail.
do.

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