pwc245_task2 - add comments and minor modification to apply the modulas propert:"If a + b = c , then a ( mod N ) + b ( mod N ) ≡ c ( mod N )"

2 files changed, 21 insertions, 9 deletions

diff --git a/challenge-245/pokgopun/go/ch-2.go b/challenge-245/pokgopun/go/ch-2.go
index b707bf3662..fafc8e1a09 100644
--- a/challenge-245/pokgopun/go/ch-2.go
+++ b/challenge-245/pokgopun/go/ch-2.go
@@ -67,6 +67,14 @@ func main() {
 
 type ints []int
 
+func (d ints) sum() int {
+	s := 0
+	for _, v := range d {
+		s += v
+	}
+	return s
+}
+
 func (d ints) concat() int {
 	r := d[0]
 	var n, t int
@@ -87,8 +95,8 @@ func (d ints) lot() int {
 	for i := l; i > 0; i-- {
 		res, closer := d.permute(i)
 		for v := range res {
-			r := v.concat()
-			if r%3 == 0 {
+			if v.sum()%3 == 0 { // If a + b = c , then a ( mod N ) + b ( mod N ) ≡ c ( mod N ), we can filter lots of them out before concat
+				r := v.concat()
 				if r > max {
 					max = r
 				}
diff --git a/challenge-245/pokgopun/python/ch-2.py b/challenge-245/pokgopun/python/ch-2.py
index 8256bbcfa6..362cb4b6d9 100644
--- a/challenge-245/pokgopun/python/ch-2.py
+++ b/challenge-245/pokgopun/python/ch-2.py
@@ -40,22 +40,26 @@ SO WHAT DO YOU THINK ?
 
 from itertools import permutations, chain
 
+### this function looks a bit messy as it tries to operate on iterators alone to saving memory resources, avoiding storing any of them to intermediate list/tuple 
 def lot(tup: tuple):
-    return max(
+    return max(   ### max() can avoid an error from null permute iterator as it operates on chain.from_iterables that include default (-1,)
             chain.from_iterable(
                 (
                     ( i for i in
                         (
-                            int("".join(x)) for x in
+                            int("".join(j)) for j in   ### concat and convert int strings to an int
                             (
-                                (str(e) for e in y) for y in
-                                chain.from_iterable(
-                                    permutations(tup, n) for n in range(1,len(tup)+1)
+                                ( str(z) for z in y) for y in   ### int-to-string conversion for ints so we can further concat and convert them to an int
+                                (
+                                    x for x in
+                                    chain.from_iterable(   ### need permutations(tup,n) loop instead of permutations(tup) alone to avoid a bug in itertools/permutations
+                                        permutations(tup, n) for n in range(1,len(tup)+1)
+                                        ) if sum(x) % 3 == 0   ### If a + b = c , then a ( mod N ) + b ( mod N ) ≡ c ( mod N )
                                     )
                                 )
-                            ) if i % 3 == 0
+                            )
                         ),
-                    (-1,),
+                    (-1,),   ### add (-1,) to chain.from_iterable to avoid max() error from null iterator from permutations (i.e. when nothing qualifies sum % 3 == 0
                     )
                 )
             )