fixup

1 files changed, 90 insertions, 0 deletions

diff --git a/coding-exercises/2/11.rkt b/coding-exercises/2/11.rkt
new file mode 100644
index 0000000..d81d33a
--- /dev/null
+++ b/coding-exercises/2/11.rkt
@@ -0,0 +1,90 @@
+#lang racket
+(require "../../shared/intervals.rkt")
+
+;; Could be written to use less comparisons with nested cond, but this is more readable.
+(define (pos? x)
+  (> x 0))
+(define (neg? x)
+  (< x 0))
+(define (mul-interval x y)
+  (cond
+    ;; 1. all positive
+    ((and
+       (pos? (lower-bound x))
+       (pos? (lower-bound y))
+       (pos? (upper-bound x))
+       (pos? (upper-bound y)))
+     (make-interval (* (lower-bound x) (lower-bound y))
+                    (* (upper-bound x) (upper-bound y))))
+    ;; 2. one lower-bound neg
+    ((and
+       (neg? (lower-bound x))
+       (pos? (lower-bound y))
+       (pos? (upper-bound x))
+       (pos? (upper-bound y)))
+     (make-interval (* (lower-bound x) (upper-bound y))
+                    (* (upper-bound x) (upper-bound y))))
+    ;; 3. one lower-bound neg
+    ((and
+       (pos? (lower-bound x))
+       (neg? (lower-bound y))
+       (pos? (upper-bound x))
+       (pos? (upper-bound y)))
+     (make-interval (* (upper-bound x) (lower-bound y))
+                    (* (upper-bound x) (upper-bound y))))
+    ;; 4. one interval neg
+    ((and
+       (neg? (lower-bound x))
+       (pos? (lower-bound y))
+       (neg? (upper-bound x))
+       (pos? (upper-bound y)))
+     (make-interval (* (upper-bound x) (upper-bound y))
+                    (* (lower-bound x) (lower-bound y))))
+    ;; 5. one interval neg
+    ((and
+       (pos? (lower-bound x))
+       (neg? (lower-bound y))
+       (pos? (upper-bound x))
+       (neg? (upper-bound y)))
+     (make-interval (* (upper-bound x) (upper-bound y))
+                    (* (lower-bound x) (lower-bound y))))
+    ;; 6. one interval neg, one interval crossing zero
+    ((and
+       (neg? (lower-bound x))
+       (neg? (lower-bound y))
+       (neg? (upper-bound x))
+       (pos? (upper-bound y)))
+     (make-interval (* (upper-bound x) (upper-bound y))
+                    (* (upper-bound x) (lower-bound y))))
+    ;; 7. one interval neg, one interval crossing zero
+    ((and
+       (neg? (lower-bound x))
+       (neg? (lower-bound y))
+       (pos? (upper-bound x))
+       (neg? (upper-bound y)))
+     (make-interval (* (upper-bound x) (upper-bound y))
+                    (* (upper-bound x) (lower-bound y))))
+    ;; 8. all neg
+    ((and
+       (neg? (lower-bound x))
+       (neg? (lower-bound y))
+       (neg? (upper-bound x))
+       (neg? (upper-bound y)))
+     (make-interval (* (lower-bound x) (lower-bound y))
+                    (* (upper-bound x) (upper-bound y))))
+    ;; 9. both crossing zero
+    ((and
+       (neg? (lower-bound x))
+       (neg? (lower-bound y))
+       (pos? (upper-bound x))
+       (pos? (upper-bound y)))
+     (make-interval ((lambda (a b) (if (< a b) a b))
+                     (* (lower-bound x) (upper-bound y))
+                     (* (upper-bound x) (lower-bound y)))
+                    ((lambda (a b) (if (> a b) a b))
+                     (* (upper-bound x) (upper-bound y))
+                     (* (lower-bound x) (lower-bound y)))))))
+
+(mul-interval
+  (make-interval -3 3)
+  (make-interval -4 4))