Solutions to challenge 65 task 1 and 2 in Raku by Noud

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diff --git a/challenge-065/noud/raku/ch-1.p6 b/challenge-065/noud/raku/ch-1.p6
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+# You are given two positive numbers $N and $S.
+#
+# Write a script to list all positive numbers having exactly $N digits where
+# sum of all digits equals to $S.
+#
+# Example
+#
+# Input:
+#     $N = 2
+#     $S = 4
+#
+# Output:
+#     13, 22, 31, 40
+
+sub digits-sum($N, $S) {
+    ([X] ((1..9), |(^9 xx ^($N-1)))).grep({ ([+] $_) eq $S; }).map({ [~] $_ });
+}
+
+digits-sum(2, 4).say;
diff --git a/challenge-065/noud/raku/ch-2.p6 b/challenge-065/noud/raku/ch-2.p6
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+# You are given a string $S. Write a script print all possible partitions that
+# gives Palindrome. Return -1 if none found.
+#
+# Please make sure, partition should not overlap. For example, for given string
+# “abaab”, the partition “aba” and “baab” would not be valid, since they
+# overlap.
+#
+# Example 1
+#
+# Input: $S = 'aabaab'
+# Ouput:
+#  There are 3 possible solutions.
+#  a) 'aabaa'
+#  b) 'aa', 'baab'
+#  c) 'aba'
+#
+# Example 2
+#
+# Input: $S = 'abbaba'
+# Output:
+#  There are 3 possible solutions.
+#  a) 'abba'
+#  b) 'bb', 'aba'
+#  c) 'bab'
+
+
+# I don't understand the task. In my oppinion a single character is a
+# palindrome as well. Also I don't agree that 'aba' of string 'aabaab' is a
+# palindrome, because the rest of the string 'a' and 'ab' are not taken into
+# account. Even if you add the extra restriction that every palindrome should
+# have at least 2 characters, the string 'aabaab' also has to solution 'aa' and
+# 'aa'.
+#
+# I created two other solutions instead:
+# 1. weak-palindromes, where non-used parts are allowed.
+# 2. strong-palindromes, where the whole string has to be used.
+
+sub all-partitions-weak($S) {
+    if ($S.chars == 1) {
+        return [[$S],];
+    }
+
+    my @ret = [[$S],];
+    for 1..($S.chars - 1) -> $i {
+        for $i..($S.chars - 1) -> $j {
+            my $s1 = $S.substr(0, $i);
+            my $s2 = $S.substr($j, $S.chars);
+            for all-partitions-weak($s2) -> $r {
+                @ret.push([$s1, |($r)]);
+            }
+            @ret.push([$s1]);
+            @ret.push([$s2]);
+        }
+    }
+
+    return @ret;
+}
+
+sub all-partitions-strong($S) {
+    if ($S.chars == 1) {
+        return [[$S],];
+    }
+
+    my @ret = [[$S],];
+    for 1..($S.chars - 1) -> $i {
+        my $s1 = $S.substr(0, $i);
+        my $s2 = $S.substr($i, $S.chars);
+        for all-partitions-strong($s2) -> $r {
+            @ret.push([$s1, |($r)]);
+        }
+    }
+
+    return @ret;
+}
+
+sub all-palindrome(@A) {
+    for @A -> $a {
+        if (not $a.flip eq $a) {
+            return False;
+        }
+    }
+    return True;
+}
+
+say 'Weak palindromes:';
+all-partitions-weak('aabaab').grep({ all-palindrome($_ ); }).say;
+all-partitions-weak('abbaba').grep({ all-palindrome($_ ); }).say;
+
+say 'Strong palindromes:';
+all-partitions-strong('aabaab').grep({ all-palindrome($_ ); }).say;
+all-partitions-strong('abbaba').grep({ all-palindrome($_ ); }).say;
+
+# With the extra restriction of at least two characters for a palindrome.
+
+sub at-least-two(@A) {
+    for @A -> $a {
+        if ($a.chars < 2) {
+            return False;
+        }
+    }
+    return True;
+}
+
+say 'Weak palindromes (len > 1):';
+all-partitions-weak('aabaab').grep({
+    all-palindrome($_ ) and at-least-two($_);
+}).say;
+all-partitions-weak('abbaba').grep({
+    all-palindrome($_ ) and at-least-two($_);
+}).say;
+
+say 'Strong palindromes (len > 1):';
+all-partitions-strong('aabaab').grep({
+    all-palindrome($_ ) and at-least-two($_);
+}).say;
+all-partitions-strong('abbaba').grep({
+    all-palindrome($_ ) and at-least-two($_);
+}).say;