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Project Euler Problem 33

on project euler, erlang, python

Digit cancelling fractions

The fraction 49/98 is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that 49/98 = 4/8, which is correct, is obtained by cancelling the 9s.

We shall consider fractions like, 30/50 = 3/5, to be trivial examples.

There are exactly four non-trivial examples of this type of fraction, less than one in value, and containing two digits in the numerator and denominator.

If the product of these four fractions is given in its lowest common terms, find the value of the denominator.

Link to original description
Source code examples on Github

Erlang version

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#!/usr/bin/env escript
%% -*- erlang -*-
%%! -smp enable -sname p33
% vim:syn=erlang

-mode(compile).

main(_) ->
    {N,M} = lists:foldl(fun({A,B}, {C,D})-> {A*C,B*D} end, {1,1}, 
        [{X,Y}||X<-lists:seq(10,99), Y<-lists:seq(10,99), isPhr(X,Y), X < Y]),
    io:format("Answer ~p ~n", [ round(M / N) ]).

isPhr(X,X) -> false;
isPhr(X,_) when X rem 10 == 0 -> false;
isPhr(_,Y) when Y rem 10 == 0 -> false;
isPhr(X,Y) ->
    case sets:to_list(sets:intersection(sets:from_list(integer_to_list(X)),
                                           sets:from_list(integer_to_list(Y)))) of
        []    -> false;
        Inter ->
            XX = [X1 || X1<- integer_to_list(X), lists:member(X1,Inter) == false],            
            YY = [Y1 || Y1<- integer_to_list(Y), lists:member(Y1,Inter) == false],
            case {XX,YY} of
                {"", _} -> false;
                {_, ""} -> false;
                {"0",_} -> false;
                {_,"0"} -> false;
                _ ->
                    case X/Y == list_to_integer(XX)/list_to_integer(YY) of
                        true -> true
                        ;_   -> false
                    end
            end
    end.

Python version

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#!/usr/bin/python3

def isPhr(x, y):
    if x == y: return False
    if x % 10 == 0 and y % 10 == 0: return False

    inter = [i for i in str(y) if i in str(x)]
    if  inter != []:
       x1 = "".join([i for i in str(x) if i not in inter])
       y1 = "".join([i for i in str(y) if i not in inter])
       if x1 == "" or y1 == "": return False
       if x1 == "0" or y1 == "0": return False
       if x / y == int(x1) / int(y1):
           return True
       else:
           return False
    else:
       return False

am, bm = 1,1
for (a,b) in [(x,y) for x in range(10,100) for y in range(10,100) if x < y and isPhr(x,y)]:
        am *= a
        bm *= b 

print("Answer %s" % (bm // am))