Count the coins/0-1: Difference between revisions
→{{header|Raku}}: Add a Raku example
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Number of ways: 464
</pre>
=={{header|Raku}}==
This is pretty much duplicating other tasks, in process if not wording. First part is combinations filtered on a certain property. Second part (extra credit) is permutations of those combinations. Even though I am adding a solution, my vote would be for deletion as it doesn't really add anything to the other tasks. [[Combinations]], [[Subset sum problem]] and to a large extent [[4-rings or 4-squares puzzle]].
<lang perl6>sub which (*@items, :$sum-to) { ^@items .combinations.grep: { @items[$_].sum == $sum-to } }
for <1 2 3 4 5>, 6
,<1 1 2 3 3 4 5>, 6
,<1 2 3 4 5 5 5 5 15 15 10 10 10 10 25 100>, 40
-> @items, $sum {
put "\n\nHow many combinations of [{ @items.join: ', ' }] sum to $sum?";
given @items.&which: :sum-to( $sum ) {
put "\nOrder unimportant:\nCount: { +$_ }\nIndices" ~ ( +$_ > 10 ?? ' (10 random examples):' !! ':' );
put .pick(10).sort».join(', ').join: "\n";
}
given @items.&which( :sum-to( $sum ) ).map: { Slip(.permutations) } {
put "\nOrder important:\nCount: { +$_ }\nIndices" ~ ( +$_ > 10 ?? ' (10 random examples):' !! ':' );
put .pick(10).sort».join(', ').join: "\n";
}
}</lang>
{{out}}
<pre>How many combinations of [1, 2, 3, 4, 5] sum to 6?
Order unimportant:
Count: 3
Indices:
0, 1, 2
0, 4
1, 3
Order important:
Count: 10
Indices:
0, 1, 2
0, 2, 1
0, 4
1, 0, 2
1, 2, 0
1, 3
2, 0, 1
2, 1, 0
3, 1
4, 0
How many combinations of [1, 1, 2, 3, 3, 4, 5] sum to 6?
Order unimportant:
Count: 9
Indices:
0, 1, 5
0, 2, 3
0, 2, 4
0, 6
1, 2, 3
1, 2, 4
1, 6
2, 5
3, 4
Order important:
Count: 38
Indices (10 random examples):
0, 4, 2
1, 2, 3
1, 2, 4
1, 5, 0
1, 6
2, 1, 3
2, 1, 4
2, 4, 0
3, 2, 0
6, 0
How many combinations of [1, 2, 3, 4, 5, 5, 5, 5, 15, 15, 10, 10, 10, 10, 25, 100] sum to 40?
Order unimportant:
Count: 464
Indices (10 random examples):
0, 1, 2, 3, 5, 7, 10, 11
0, 1, 2, 3, 5, 8, 12
0, 1, 2, 3, 6, 7, 11, 13
0, 3, 5, 7, 9, 13
0, 3, 9, 10, 11
1, 2, 5, 7, 9, 13
4, 5, 10, 12, 13
5, 6, 7, 9, 10
5, 6, 10, 11, 12
5, 8, 10, 12
Order important:
Count: 3782932
Indices (10 random examples):
0, 11, 3, 4, 7, 5, 6, 1, 2
1, 10, 5, 4, 6, 2, 0, 3, 7
2, 7, 13, 4, 1, 3, 5, 6, 0
2, 12, 4, 13, 10, 1
3, 0, 5, 4, 7, 13, 6, 2, 1
5, 7, 9, 4, 0, 1, 2, 3
6, 2, 7, 11, 0, 3, 5, 1, 4
10, 0, 12, 6, 5, 3, 4
13, 0, 1, 5, 7, 3, 2, 12
13, 6, 10, 1, 4, 3, 2, 0</pre>
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