From 852c77d428c86e55f71e9734fede6ac684320096 Mon Sep 17 00:00:00 2001
From: ikselven <ikselven@users.noreply.github.com>
Date: Tue, 25 Apr 2017 22:57:51 +0200
Subject: [PATCH] erlang and simple R implementation of project euler problem
 87

---
 2017-04-11/ikselven_euler87.R | 22 +++++++++++++++++++++
 2017-04-11/joe_euler87.erl    | 36 +++++++++++++++++++++++++++++++++++
 2 files changed, 58 insertions(+)
 create mode 100644 2017-04-11/ikselven_euler87.R
 create mode 100644 2017-04-11/joe_euler87.erl

diff --git a/2017-04-11/ikselven_euler87.R b/2017-04-11/ikselven_euler87.R
new file mode 100644
index 0000000..3408ff8
--- /dev/null
+++ b/2017-04-11/ikselven_euler87.R
@@ -0,0 +1,22 @@
+library(numbers)
+MAX <- 5e7
+primes <- Primes(1, ceiling(sqrt(MAX)))
+
+potfilter <- function(numbers, filter)
+    numbers[numbers < filter]
+
+sums <- sapply(
+    potfilter(primes^4, MAX),
+    function(x) { 
+        sapply(
+            potfilter(primes^3, MAX),
+            function(y) { 
+                sapply(primes^2, function(z) {
+                    x+y+z
+                })
+            }
+        )
+    }
+)
+
+length(unique(sums[sums<MAX]))
diff --git a/2017-04-11/joe_euler87.erl b/2017-04-11/joe_euler87.erl
new file mode 100644
index 0000000..6c3450c
--- /dev/null
+++ b/2017-04-11/joe_euler87.erl
@@ -0,0 +1,36 @@
+-module(joe_euler87).
+-export([go/0]).
+
+go() ->
+    Max = 50000000,
+    Primes = sieve(Max),
+    Sums = find_pow234(Max, Primes),
+    length(Sums).
+
+%%% find all solutions for X^2+Y^3+Z^4 smaller Max
+find_pow234(Max, Primes) ->
+    XPrimes = lists:takewhile(fun(P) -> pow2(P) < Max end, Primes),
+    YPrimes = lists:takewhile(fun(P) -> pow3(P) < Max end, Primes),
+    ZPrimes = lists:takewhile(fun(P) -> pow4(P) < Max end, Primes),
+    lists:usort(lists:filter(
+                  fun(Num) -> Num < Max end,
+                  [powsum234(A, B, C) || A<-XPrimes, B<-YPrimes, C<-ZPrimes])).
+
+%%% generate a list of all primes smaller Max
+sieve(Max) ->
+    Until = trunc(math:sqrt(Max)),
+    sieve([], 2, 3, Until).
+
+sieve(Primes, LastPrime, N, Until) when (N > Until) ->
+    lists:append(Primes, [LastPrime]);
+sieve(Primes, LastPrime, N, Until) ->
+    case lists:all(fun(P) -> (N rem P)=/=0 end, Primes) of
+        true  -> sieve(lists:append(Primes, [LastPrime]), N, N+2, Until);
+        false -> sieve(Primes, LastPrime, N+2, Until)
+    end.
+
+%%% helper functions
+powsum234(X, Y, Z) -> pow2(X) + pow3(Y) + pow4(Z).
+pow2(X) -> X*X.
+pow3(X) -> X*X*X.
+pow4(X) -> X*X*X*X.