initial commit

sum-of-squares.rkt

@@ -0,0 +1,30 @@
+#lang racket
+
+;; Gets the square of a number x
+(define (square x)
+  (* x x))
+; (* 2 2 2)
+
+; O(n)
+(define (sum-of-squares-helper cur upper)
+  (if (> cur upper)
+      0
+      (+ (square cur) (sum-of-squares-helper (+ 1 cur) upper))))
+
+;; Gets the sum of the square of every natural number below and including `upper-bound`
+(define (sum-of-squares upper-bound)
+  (sum-of-squares-helper 0 upper-bound))
+
+(sum-of-squares 1000000000000)
+
+; O(n)
+(define (sum-of-squares-tail-helper cur upper sum)
+  (if (> cur upper)
+      sum
+      (sum-of-squares-tail-helper (+ 1 cur) upper (+ sum (square cur)))))
+
+;; Gets the sum of the square of every natural number below and including `upper-bound`
+(define (sum-of-squares-tail upper-bound)
+  (sum-of-squares-tail-helper 0 upper-bound 0))
+
+; (sum-of-squares-tail 2)

sum-of-squares.scm

@@ -0,0 +1,13 @@
+(define (square x)
+  (* x x))
+;(* 2 2 2)
+
+(define (sum-of-squares-helper cur upper)
+  (if (> cur upper)
+      0
+      (+ (square cur) (sum-of-squares-helper (+ 1 cur) upper))))
+
+(define (sum-of-squares upper-bound)
+  (sum-of-squares-helper 0 upper-bound))
+
+(sum-of-squares 5)