recursion upto ex.27

src/recursion.clj

@@ -1,91 +1,300 @@
 (ns recursion)
-
 (defn product [coll]
-  :-)
+  (if 
+      (empty? coll)
+    1
+    (* 
+     (first coll)
+     (product (rest coll)))))
 
 (defn singleton? [coll]
-  :-)
+  (if 
+      (empty? coll) 
+    false
+    (empty? (rest coll))))
 
 (defn my-last [coll]
-  :-)
+  (if 
+      (empty? (rest coll))
+    (first coll)
+    (my-last (rest coll))))
 
 (defn max-element [a-seq]
-  :-)
+  (if (or (singleton? a-seq) 
+          (empty? a-seq))
 
-(defn seq-max [seq-1 seq-2]
-  [:-])
+    (my-last a-seq)
+    (max (first a-seq)
+         (max-element (rest a-seq)))))
 
-(defn longest-sequence [a-seq]
-  [:-])
-
-(defn my-filter [pred? a-seq]
-  [:-])
+(defn seq-max [seq-1 seq-2]
+  (let 
+      [count-1 (count seq-1)
+       count-2 (count seq-2)]
+    (if 
+        (> 
+         count-1 
+         count-2)
+      seq-1
+      seq-2)))
 
-(defn sequence-contains? [elem a-seq]
-  :-)
 
-(defn my-take-while [pred? a-seq]
-  [:-])
+(defn seq= [a-seq b-seq]
+  (cond
+   (not= 
+    (count a-seq) 
+    (count b-seq))
+   false
+
+   (and
+    (empty? a-seq)
+    (empty? b-seq)) 
+   true
 
-(defn my-drop-while [pred? a-seq]
-  [:-])
+   (= 
+    (first a-seq) 
+    (first b-seq))
+   (seq= 
+    (rest a-seq) 
+    (rest b-seq))
 
-(defn seq= [a-seq b-seq]
-  :-)
+   :else false))
 
 (defn my-map [f seq-1 seq-2]
-  [:-])
+  (if 
+      (or 
+       (empty? seq-1) 
+       (empty? seq-2))
+    '()
+    (cons 
+     (f 
+      (first seq-1) 
+      (first seq-2))
+     (my-map 
+      f 
+      (rest seq-1) 
+      (rest seq-2)))))
 
 (defn power [n k]
-  :-)
+  (if (zero? k)
+    1
+    (* n (power n (dec k)))))
 
 (defn fib [n]
-  :-)
+  (cond
+   (zero? n) 0
+   (= n 1) 1
+   :else
+   (+ (fib (- n 1))
+      (fib (- n 2)))))
 
 (defn my-repeat [how-many-times what-to-repeat]
-  [:-])
+  (if (or 
+       (zero? how-many-times)
+       (neg? how-many-times))
+    '()
+    (cons
+     what-to-repeat
+     (my-repeat
+      (dec how-many-times)
+      what-to-repeat))))
+
+(defn longest-sequence [a-seq]
+  (if (empty? a-seq)
+    nil
+    (seq-max (first a-seq)
+             (longest-sequence (rest a-seq)))))
+
+(defn my-filter [pred? a-seq]
+  (if (empty? a-seq)
+    '()                          ;; limiting condition
+    (if (= 
+         (pred? (first a-seq))   ;; if pred returns true, put it in list
+         true)
+      (cons (first a-seq)
+            (my-filter pred? 
+                       (rest a-seq)))
+      (my-filter pred?           ;; else skip to next element
+                 (rest a-seq)))))
+
+(defn sequence-contains? [elem a-seq]
+  (cond
+   (empty? a-seq) 
+   false
+
+   (not= 
+    elem 
+    (first a-seq))
+   (sequence-contains? 
+    elem 
+    (rest a-seq))
+
+   :else
+   true))
+
+(defn my-take-while [pred? a-seq]
+  (cond
+   (empty? a-seq)
+   '()
+
+   (= (pred? (first a-seq)) 
+      true)
+   (cons 
+    (first a-seq) 
+    (my-take-while 
+     pred? 
+     (rest a-seq)))
+
+   :else
+   '()))
+
+(defn my-drop-while [pred? a-seq]
+  (cond
+   (empty? a-seq)
+   '()
+
+   (= 
+    (pred? (first a-seq)) 
+    true)
+   (my-drop-while 
+    odd? 
+    (rest a-seq))
+
+   :else
+   a-seq))
 
 (defn my-range [up-to]
-  [:-])
+  (if (= up-to 0)
+    '()
+    (cons (dec up-to)
+          (my-range (dec up-to)))))
 
 (defn tails [a-seq]
-  [:-])
+  (if (empty? a-seq)
+    '(())
+    (cons a-seq
+          (tails (rest a-seq)))))
 
 (defn inits [a-seq]
-  [:-])
+  (reverse (map reverse
+                (tails 
+                 (reverse a-seq)))))
 
-(defn rotations [a-seq]
-  [:-])
+(defn rotations
+  ([a-seq] 
+   (rotations a-seq 
+              (count a-seq)))
+
+  ([a-seq count] 
+   (let [new-seq 
+         (concat (rest a-seq) 
+                 (cons 
+                  (first a-seq) 
+                  '()))]
+     (cond 
+      (empty? a-seq) '(())
+      (= count 0) ()
+      :else
+      (cons new-seq
+            (rotations new-seq (dec count)))))))
 
 (defn my-frequencies-helper [freqs a-seq]
-  [:-])
+  (if (empty? a-seq)
+    freqs
+    (let [key (first a-seq)
+          new-freq (if (contains? freqs key)
+                     (assoc freqs 
+                       key 
+                       (inc (get freqs key)))
+
+                     (assoc freqs key 1))]
+      (my-frequencies-helper new-freq (rest a-seq)))))
 
 (defn my-frequencies [a-seq]
-  [:-])
+  (my-frequencies-helper {} a-seq))
 
 (defn un-frequencies [a-map]
-  [:-])
+  (if (empty? a-map)
+    ()
+    (let [key (first (first a-map))
+          value (second (first a-map))] 
+        (concat (repeat value key) 
+                (un-frequencies (rest a-map))))))
 
 (defn my-take [n coll]
-  [:-])
+  (if (or (empty? coll) (= n 0))
+    ()
+    (cons (first coll)
+          (my-take (dec n) (rest coll)))))
 
 (defn my-drop [n coll]
-  [:-])
+  (if (or (empty? coll) (= n 0))
+    coll
+    (my-drop (dec n) (rest coll))))
 
 (defn halve [a-seq]
-  [:-])
+  (let [size (count a-seq)
+        middle (int (/ size 2))]
+    (if (= size 0)
+      []
+      (conj [] 
+            (my-take middle a-seq) 
+            (my-drop middle a-seq)))))
+
+(defn seq-merge-helper [final-seq a-seq b-seq]
+  (cond
+   (empty? a-seq) (concat final-seq b-seq)
+   (empty? b-seq) (concat final-seq a-seq)
+
+   (< (first a-seq) (first b-seq))
+   (concat
+    final-seq
+    (cons (first a-seq) '())
+    (seq-merge-helper final-seq 
+                      (rest a-seq) 
+                      b-seq))
+
+   :else (concat
+          final-seq
+          (cons (first b-seq) '())
+          (seq-merge-helper final-seq
+                            a-seq
+                            (rest b-seq)))))
 
 (defn seq-merge [a-seq b-seq]
-  [:-])
+  (seq-merge-helper [] a-seq b-seq))
 
 (defn merge-sort [a-seq]
-  [:-])
+  (if (or (empty? a-seq) (singleton? a-seq))
+    a-seq
+    (seq-merge (merge-sort 
+                (first (halve a-seq)))
+               (merge-sort 
+                (second (halve a-seq))))))
 
 (defn split-into-monotonics [a-seq]
-  [:-])
+  (let [asc-pred (fn [seq] (apply < seq))
+        desc-pred (fn [seq] (apply > seq))
+        split-seq (drop 2 (inits a-seq))  ; drop empty () and singleton (x)
+        last-asc (last (take-while asc-pred split-seq))
+        count-asc (count last-asc)
+        last-desc (last (take-while desc-pred split-seq))
+        count-desc (count last-desc)]
+    (cond
+     (empty? a-seq) '()
+
+     (not (empty? last-asc))              ; make sure last-asc is not empty 
+     (cons last-asc 
+           (split-into-monotonics (drop count-asc a-seq)))
+
+     :else
+     (cons last-desc 
+           (split-into-monotonics (drop count-desc a-seq))))))
 
 (defn permutations [a-set]
-  [:-])
+  (if (singleton? a-set)
+    (first a-set)
+    ))
 
 (defn powerset [a-set]
   [:-])