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Prolog : Project Euler 1-9
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problem1(Answer) :- aggregate(sum(N),num(N),Answer). | |
num(N) :- between(1,999,N), answer(N). | |
answer(N) :- N rem 3 =:= 0, !. | |
answer(N) :- N rem 5 =:= 0. |
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:- use_module(library(fibonacci), [fib/2]). | |
problem2(Answer) :- aggregate(sum(N),fibEven(N),Answer). | |
fibEven(X) :- | |
between(1,inf,M), N is M*3, fib(N,X), | |
(X < 4000000 -> true; !, false). |
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problem3(Answer) :- prime_factors(600851475143,L), max_list(L,Answer). | |
prime_factors(N,X) :- prime_factors(N,2,X). | |
prime_factors(N,P,[N]) :- N < P*P, !. | |
prime_factors(N,P,[P|L]) :- N rem P =:= 0, !, N1 is N//P, prime_factors(N1,P,L). | |
prime_factors(N,2,X) :- !, prime_factors(N,3,X). | |
prime_factors(N,P,X) :- !, plus(P,2,P1), prime_factors(N,P1,X). |
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:- use_module(library(digits), [i2d/2]). | |
problem4(Answer) :- solve(999,999,0,Answer). | |
solve(99,_,Z,Z) :- !. | |
solve(X,Y,Z,A) :- X*Y =< Z, !, X1 is X-1, solve(X1,X1,Z,A). | |
solve(X,Y,Z,A) :- Y =:= 99, !, X1 is X-1, solve(X1,X1,Z,A). | |
solve(X,Y,_,A) :- Z is X*Y, palindrome(Z), !, X1 is X-1, solve(X1,X1,Z,A). | |
solve(X,Y,Z,A) :- Y1 is Y-1, solve(X,Y1,Z,A). | |
palindrome(N) :- i2d(N,L), reverse(L,L). |
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problem5(Answer) :- solve(20,Answer). | |
solve(1,1) :- !. | |
solve(N,X) :- N1 is N-1, solve(N1,X1), X is N*X1//gcd(N,X1). |
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problem6(Answer) :- | |
numlist(1,100,L), | |
sumlist(L,X), square(X,X1), | |
maplist(square,L,Y), sumlist(Y,Y1), | |
Answer is X1-Y1. | |
square(N,N*N). |
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isPrime(N,P) :- N < P*P, !. | |
isPrime(N,P) :- N rem P =:= 0, !, false. | |
isPrime(N,P) :- P1 is P+2, isPrime(N,P1). | |
nextPrime(2,3) :- !. | |
nextPrime(P,X) :- X is P+2, isPrime(X,3), !. | |
nextPrime(P,X) :- P1 is P+2, nextPrime(P1,X). | |
primes(10001,P,P) :- !. | |
primes(N,P,X) :- N1 is N+1, nextPrime(P,P1), primes(N1,P1,X). | |
problem7(X) :- primes(1,2,X). |
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:- use_module(library(digits),[i2d/2]). | |
problem8(Answer) :- aggregate(max(N),solve(N),Answer). | |
solve(X) :- findall(N,num(N),L), append(_,[A,B,C,D,E|_],L), X is A*B*C*D*E. | |
num(N) :- data(Data), member(L,Data), i2d(L,L1), member(N,L1). | |
data([73167176531330624919225119674426574742355349194934, | |
96983520312774506326239578318016984801869478851843, | |
85861560789112949495459501737958331952853208805511, | |
12540698747158523863050715693290963295227443043557, | |
66896648950445244523161731856403098711121722383113, | |
62229893423380308135336276614282806444486645238749, | |
30358907296290491560440772390713810515859307960866, | |
70172427121883998797908792274921901699720888093776, | |
65727333001053367881220235421809751254540594752243, | |
52584907711670556013604839586446706324415722155397, | |
53697817977846174064955149290862569321978468622482, | |
83972241375657056057490261407972968652414535100474, | |
82166370484403199890008895243450658541227588666881, | |
16427171479924442928230863465674813919123162824586, | |
17866458359124566529476545682848912883142607690042, | |
24219022671055626321111109370544217506941658960408, | |
07198403850962455444362981230987879927244284909188, | |
84580156166097919133875499200524063689912560717606, | |
05886116467109405077541002256983155200055935729725, | |
71636269561882670428252483600823257530420752963450]). |
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problem9(Answer) :- | |
between(1,333,A), | |
Bmin is A+1, Bmax is (1000-A)//2, | |
between(Bmin,Bmax,B), | |
C is 1000-A-B, | |
A*A + B*B =:= C*C, | |
Answer is A*B*C, !. | |
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