How to resolve the algorithm Smith numbers step by step in the CLU programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Smith numbers step by step in the CLU programming language
Table of Contents
Problem Statement
Smith numbers are numbers such that the sum of the decimal digits of the integers that make up that number is the same as the sum of the decimal digits of its prime factors excluding 1. By definition, all primes are excluded as they (naturally) satisfy this condition! Smith numbers are also known as joke numbers.
Using the number 166 Find the prime factors of 166 which are: 2 x 83 Then, take those two prime factors and sum all their decimal digits: 2 + 8 + 3 which is 13 Then, take the decimal digits of 166 and add their decimal digits: 1 + 6 + 6 which is 13 Therefore, the number 166 is a Smith number.
Write a program to find all Smith numbers below 10000.
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Smith numbers step by step in the CLU programming language
Source code in the clu programming language
% Get all digits of a number
digits = iter (n: int) yields (int)
while n > 0 do
yield(n // 10)
n := n / 10
end
end digits
% Get all prime factors of a number
prime_factors = iter (n: int) yields (int)
% Take factors of 2 out first (the compiler should optimize)
while n // 2 = 0 do yield(2) n := n/2 end
% Next try odd factors
fac: int := 3
while fac <= n do
while n // fac = 0 do
yield(fac)
n := n/fac
end
fac := fac + 2
end
end prime_factors
% See if a number is a Smith number
smith = proc (n: int) returns (bool)
dsum: int := 0
fac_dsum: int := 0
% Find the sum of the digits
for d: int in digits(n) do dsum := dsum + d end
% Find the sum of the digits of all factors
nfac: int := 0
for fac: int in prime_factors(n) do
nfac := nfac + 1
for d: int in digits(fac) do fac_dsum := fac_dsum + d end
end
% The number is a Smith number if these two are equal,
% and the number is not prime (has more than one factor)
return(fac_dsum = dsum cand nfac > 1)
end smith
% Yield all Smith numbers up to a limit
smiths = iter (max: int) yields (int)
for i: int in int$from_to(1, max-1) do
if smith(i) then yield(i) end
end
end smiths
% Display all Smith numbers below 10,000
start_up = proc ()
po: stream := stream$primary_output()
count: int := 0
for s: int in smiths(10000) do
stream$putright(po, int$unparse(s), 5)
count := count + 1
if count // 16 = 0 then stream$putl(po, "") end
end
stream$putl(po, "\nFound " || int$unparse(count) || " Smith numbers.")
end start_up
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