pascal-triangle.clj

;; take a vector v and index i
;; index n  + index n-1
(defn add [v i] 
   (+ 
    ;; 0 is default when return value is nil
       (get v i 0) 
       (get v (- i 1) 0)))

; calculates the next row of a given row
(defn new-row [v]
  ; cnt is the number of times the loop runs  with initial value 0
  ; nv is 'new vector' with initial value [] 
   (loop [cnt 0
          nv []]
     ; run as long as cnt is less or equal the lenght/size of the vector
     (if (<= cnt (count v))
       ; each run do:
       ; increase cnt by 1
       ; use add function with vector and cnt & add it into nv ('new vector')
       (recur (inc cnt) (conj nv (add v cnt)))
       ; else retun new vector
       nv)))

; the actual function that puts everything together
; takes a number that represents the row in the pascal triangle
(defn the-function [number]
  ; we need only the last vector in our vector of results...
  (last 
    ; cnt is the number of times the loop runs  with initial value 1
    ; nv is 'new vector' with initial value [[1]] because first row is always [1] 
   (loop [cnt 1
              nv [[1]]]
          ; run as long as cnt is less the provided number 'number'
         (if (< cnt number)
          ; each run do:
          ; increase cnt by 1
          ; use new-row function with the last vector in 'new-vector' & add it into nv ('new vector')
           (recur (inc cnt) 
                  (conj nv (new-row (last nv))))
           ; else return 'new vector' nv
           nv))))

; same function as above just with cool macro (-->) usage! 
(defn the-function-cool [number]
  (last
   (loop [cnt 1
              nv [[1]]]
         (if (< cnt number )
           (recur (inc cnt) 
                  (->>
                   nv last new-row (conj nv)))
           nv))))

;; 4clojure #97

(= (the-function-cool 1) [1])

(= (map the-function-cool (range 1 6))
   [     [1]
        [1 1]
       [1 2 1]
      [1 3 3 1]
     [1 4 6 4 1]])

(= (the-function-cool 11)
   [1 10 45 120 210 252 210 120 45 10 1])

;; last until intager overflow
(the-function-cool 66)