problem 1 2 in scheme

3 files changed, 75 insertions, 0 deletions

diff --git a/scheme/001-multiples_of_3_or_5.scm b/scheme/001-multiples_of_3_or_5.scm
new file mode 100644
index 0000000..c329de9
--- /dev/null
+++ b/scheme/001-multiples_of_3_or_5.scm
@@ -0,0 +1,20 @@
+;;;;
+;; Multiples of 3 or 5
+;; Problem 1
+;;
+;; 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.
+;;;;
+
+(load "utils.scm")
+
+(define +top+ 1000)
+
+(define result
+  (sum
+    (filter
+      (lambda (x) (or (= 0 (modulo x 3)) (= 0 (modulo x 5))))
+      (range 1 +top+ 1))))
+
+(display result)
diff --git a/scheme/002-even_fibonacci_numbers.scm b/scheme/002-even_fibonacci_numbers.scm
new file mode 100644
index 0000000..65b567d
--- /dev/null
+++ b/scheme/002-even_fibonacci_numbers.scm
@@ -0,0 +1,33 @@
+;;;;
+;; Even Fibonacci numbers
+;; Problem 2
+;;
+;; 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, ...
+;; By considering the terms in the Fibonacci sequence whose values do not exceed four
+;; million, find the sum of the even-valued terms.
+;;;;
+
+(load "utils.scm")
+
+(define +top+ 4000000)
+
+(define fib
+  (lambda (n)
+    (case n
+      ((0) 1)
+      ((1) 1)
+      (else (+ (fib (- n 1))
+               (fib (- n 2)))))))
+
+(define result
+  (sum
+    (filter (lambda (x) (= 0 (modulo x 2)))
+            (do ((x 1 (+ x 1))
+                 (f 1 (fib x))
+                 (fs '()))
+              ((>= f +top+) fs)
+              (set! fs (cons f fs))))))
+
+(display result)
diff --git a/scheme/utils.scm b/scheme/utils.scm
new file mode 100644
index 0000000..6ba98cd
--- /dev/null
+++ b/scheme/utils.scm
@@ -0,0 +1,22 @@
+(define fold
+  (lambda (f acc xs)
+    (if (null? xs)
+      acc
+      (fold f (f acc (car xs)) (cdr xs)))))
+
+(define sum
+  (lambda (xs) (fold + 0 xs)))
+
+(define range
+  (lambda (start stop step)
+    (if (>= start stop)
+      '()
+      (cons start (range (+ start step) stop step)))))
+
+(define filter
+  (lambda (predicate xs)
+    (if (null? xs)
+      '()
+      (let* ((x (car xs))
+             (filtered (filter predicate (cdr xs))))
+        (if (predicate x) (cons x filtered) filtered)))))