pythonrecursioncommon-lispcoin-change

# Converting a recursion problem code from Python to Common Lisp

I'm trying to convert a recursion problem written in Python (the 4th problem here see its repo page for details) into (Common) Lisp

Here is the Python code which I've edited slightly for readability:

``````def coin(target,coins,res):
# Default output to target
min_coins = target
# Base Case
if target in coins:
res[target] = 1
return 1
# Return a known result if it happens to be greater than 1
elif res[target] > 0:
return res[target]
else:
# for every coin value that is <= than target
for i in [c for c in coins if c <= target]:
num_coins = 1 + coin(target-i,coins,res)
# Reset Minimum if we have a new minimum
if num_coins < min_coins:
min_coins = num_coins
res[target] = min_coins
return min_coins

target = 14
coins = [1,3,5]
res = [0]*(target+1)
print(coin(target,coins,res))
# => returns 4  ( 1 x 1, 1 x 3, 2 x 5)
``````

Here is the Lisp code I've written:

``````(defun coin (target coins res)
(let ((min_coins target))
(if (some (lambda (x) (= target x)) coins)
(progn
(setf (aref res target) 1)
1)
(if (> (aref res target) 0)
(aref res target)
(dolist (i (remove-if-not (lambda (x) (<= x target)) coins))
(let ((num_coins (1+ (coin (- target i) coins res))))
(when (< num_coins min_coins)
(setf min_coins num_coins)
(setf (aref res target) min_coins))
min_coins))))))

(coin 14 '(1 3 5) (make-array 15 :initial-element 0) )
``````

When it's executed it stops with this error:

``````The value
NIL
is not of type
NUMBER
``````

How to arrange it so that it runs correctly?

## Update:

After `(trace coin)` here is the output:

``````CL-USER> (coin 14 '(1 3 5) (make-array 15 :initial-element 0) )
0: (COIN 14 (1 3 5) #(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0))
1: (COIN 13 (1 3 5) #(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0))
2: (COIN 12 (1 3 5) #(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0))
3: (COIN 11 (1 3 5) #(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0))
4: (COIN 10 (1 3 5) #(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0))
5: (COIN 9 (1 3 5) #(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0))
6: (COIN 8 (1 3 5) #(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0))
7: (COIN 7 (1 3 5) #(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0))
8: (COIN 6 (1 3 5) #(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0))
9: (COIN 5 (1 3 5) #(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0))
9: COIN returned 1
9: (COIN 3 (1 3 5) #(0 0 0 0 0 1 2 0 0 0 0 0 0 0 0))
9: COIN returned 1
9: (COIN 1 (1 3 5) #(0 0 0 1 0 1 2 0 0 0 0 0 0 0 0))
9: COIN returned 1
8: COIN returned NIL
; Evaluation aborted on #<TYPE-ERROR expected-type: NUMBER datum: NIL>.
``````

Solution

• # Correctness

Your code fails because your `dolist` returns `nil`.

You need to replace

``````(dolist (i (remove-if-not (lambda (x) (<= x target)) coins)) ...)
``````

with

``````(dolist (i (remove-if-not (lambda (x) (<= x target)) coins) min_coins) ...)
``````

# Efficiency

You are creating gratuitous lists in Python by using `[]` in `for` loop and in Lisp by using `remove-if-not` in `dolist`. A proverbial "sufficiently smart compiler" should be able to eliminate it, but Python 3 is not smart enough and neither is SBCL.

# Style

Code readability matters. I suggest modifying your code:

``````def coin(target,coins,res):
# Default output to target
# Base Case
if target in coins:
res[target] = 1
return 1
# Return a known result if it happens to be greater than 1
if res[target] > 0:
return res[target]
# for every coin value that is <= than target
min_coins = target
for i in target:
if i <= target:
num_coins = 1 + coin(target-i,coins,res)
# Reset Minimum if we have a new minimum
if num_coins < min_coins:
min_coins = num_coins
res[target] = min_coins
return min_coins
``````

and

``````(defun coin (target coins res)
(cond ((find target coins)
(setf (aref res target) 1))
((plusp (aref res target))
(aref res target))
(t
(let ((min-coins target))
(dolist (i coins min-coins)
(when (<= i target)
(let ((num-coins (1+ (coin (- target i) coins res))))
(when (< num-coins min-coins)
(setf min-coins num-coins)
(setf (aref res target) min-coins)))))))))
``````