Merge branch 'erlang'

erlang/e001.erl

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+% Add all the natural numbers below one thousand that are multiples of 3 or 5.
+
+% If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
+% Find the sum of all the multiples of 3 or 5 below 1000.
+
+-module(e001).
+-export([
+    main/1
+    ]).
+
+sum(3) ->
+    0;
+sum(Max) ->
+    N = Max - 1,
+    if
+        N rem 3 == 0 ->
+            A = N;
+        N rem 5 == 0 ->
+            A = N;
+        true ->
+            A = 0
+    end,
+    sum(N) + A.
+
+main(_) ->
+    io:format("Sum of <   10: ~w~n", [sum(10)]),
+    io:format("Sum of < 1000: ~w~n", [sum(1000)]).

erlang/e002.erl

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+% Find the sum of all the even-valued terms in the Fibonacci sequence which do not exceed four million.
+
+% Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:
+% 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
+% Find the sum of all the even-valued terms in the sequence which do not exceed four million.
+
+-module(e002).
+-export([
+        main/1,
+        fibonacci_max/1
+    ]).
+
+fibonacci_max(Max) ->
+    fibonacci_max_([], Max).
+
+fibonacci_max_([], Max) ->
+    if
+        Max < 1 ->
+            [];
+        true ->
+            fibonacci_max_([1], Max)
+    end;
+fibonacci_max_([N], Max) ->
+    Next = N + N,
+    if
+        Max < Next ->
+            [N];
+        true ->
+            fibonacci_max_([Next, N], Max)
+    end;
+fibonacci_max_([N1, N2 | Seq], Max) ->
+    Next = N1 + N2,
+    if
+        Max < Next ->
+            [N1, N2 | Seq];
+        true ->
+            fibonacci_max_([Next, N1, N2 | Seq], Max)
+    end.
+
+sum_if_even([]) ->
+    0;
+sum_if_even([N | Seq]) ->
+    if
+        N rem 2 == 0 ->
+            N + sum_if_even(Seq);
+        true ->
+            sum_if_even(Seq)
+    end.
+
+main(_) ->
+    Max = 4000000,
+    io:format("Sum for fibonacci <= ~w: ~w~n", [Max, sum_if_even(fibonacci_max(Max))]).

erlang/e003.erl

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+% Find the largest prime factor of a composite number.
+
+% The prime factors of 13195 are 5, 7, 13 and 29.
+% What is the largest prime factor of the number 600851475143 ?
+
+-module(e003).
+-export([
+    main/1,
+    pfactor/1
+]).
+
+pfactor(N) ->
+    pfactor_(N, []).
+pfactor_(N, F) ->
+    Next = pfactor_next(N, 2),
+    if
+        Next == N ->
+            [N | F];
+        true ->
+            pfactor_(trunc(N / Next), [Next | F])
+    end.
+
+pfactor_next(N, Factor) ->
+    if
+        Factor == N ->
+            Factor;
+        N rem Factor == 0 ->
+            Factor;
+        true ->
+            pfactor_next(N, Factor + 1)
+    end.
+
+
+main(_) ->
+    io:format("Prime Factors of 13195: ~w~n", [pfactor(13195)]),
+    io:format("Prime Factors of 600851475143: ~w~n", [pfactor(600851475143)]).

erlang/e004.erl

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+% Find the largest palindrome made from the product of two 3-digit numbers.
+
+% A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91  99.
+% Find the largest palindrome made from the product of two 3-digit numbers.
+
+-module(e004).
+-export([
+    main/1
+]).
+
+product(Min, Max) ->
+    product(Min, Max, Max, Max, 0).
+product(Min, _, N1, _, Product) when N1 < Min ->
+    Product;
+product(Min, Max, N1, N2, Product) when N2 < Min ->
+    product(Min, Max, N1 - 1, Max, Product);
+product(Min, Max, N1, N2, Product) ->
+    P = trunc(N1 * N2),
+    S = integer_to_list(trunc(N1 * N2)),
+    R = lists:reverse(S),
+    if
+        S == R, P > Product ->
+            product(Min, Max, N1, N2 - 1, P);
+        true ->
+            product(Min, Max, N1, N2 - 1, Product)
+    end.
+
+main(_) ->
+    io:format("Largest palindrome product of 2-digit numbers: ~w~n", [product(10, 99)]),
+    io:format("Largest palindrome product of 3-digit numbers: ~w~n", [product(100, 999)]).

erlang/e005.erl

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+% What is the smallest number divisible by each of the numbers 1 to 20?
+
+% 2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
+% What is the smallest number that is evenly divisible by all of the numbers from 1 to 20?
+
+-module(e005).
+-export([
+    main/1
+]).
+
+divisible(N) ->
+    divisible(N, N, 1).
+divisible(_, C, X) when C == 1 ->
+    X;
+divisible(N, C, X) ->
+    if
+        X rem C == 0 ->
+            divisible(N, C - 1, X);
+        true ->
+            divisible(N, N, X + 1)
+    end.
+
+main(_) ->
+    io:format("Smallest number divisible by 1 to 10: ~w~n", [divisible(10)]),
+    io:format("Smallest number divisible by 1 to 10: ~w~n", [divisible(20)]).