This is not algorithm problem, it is homework problem do it yourself.
I see there one problem, and it is how large is N
I suggest you to represent sets as pairs(cardID,repeat number )
that means for each card you remember number of how much you have of that
card, and when there is zero, it means you desire to have it.
But this approach assumes that you will keep at least one card, and will not
want ot have card twice.
The interesting would be problem to exchange cards in way to maximize
desired cards received by all players. But this would need one player to
have card that he does not desire.
2009/2/17 Luciano Pinheiro <luciano....@gmail.com>
>
> I have several collections of cards (baseball league, championship
> bascketball, etc..), Where each collection C (i) is numbered from 1 to N, 1
> <=
> i <= |C|, where |C| = total number of collections that I have. I heve too
> many
> friends, F, that I can make exchange my recurring cards with their
> derised cards.
>
> For each collection C (i) have a repeated set (R(i)) of cards to share with
> my
> friends. Repeated this set of cards, I have cards with the same number, or
> only a single card repeated. And I also have relations of the cards I need
> (desired items D(i)) to fill my collection C(i).
>
> For example:
> I have follow card's collections:
> 2000 Baseball Cards - numbers (1, 2, 3, 4, 5, 6, 10, 23, 45)
> recurring items (1, 1, 2, 5, 5, 6, 23, 23)
> items desired (7, 8, 9, 11, 12, 13, 14, 15, 16,
> 17, 18, 19, 20, 21, 22, 23,
> 24,
> 25, .. , 44)
>
> 2000 Bascketball Cards - numbers (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15,
> 17,
> 18, 20, 23, 30, 33, 36,
> 47)
> recurring items (1, 2, 2, 4, 4, 5, 10, 12, 23,
> 23)
> items desired (11, 13, 14, 16, 19, 21, 22,
> 24,
> 25, .. , 29, 31,
> 32, 34, 35, 37, .. , 46)
>
> I have two friends (John and Mary) whom I exchange the cards I need. Each
> of
> these friends also have collections of cards and collection of cards for
> each
> of them, they repeated a set of cards and a list of cards you want.
>
> My friend Mary's card's collections is:
> 1999 Baseball Cards - numbers (1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16,
> 18,
> 20, 21, 22, 23, 24,
> 25, 27, 29, 30, 33, 36,
> 38, 39, 40, 41, 42, 43,
> 44, 45)
> recurring items (1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14,
> 16,
> 18, 23, 42, 43)
> items desired (9, 11, 13, 15, 17, 19, 26, 28, 31, 32,
> 34, 35, 37)
>
> 2000 Baseball Cards - numbers (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
> 14, 15, 16, 17, 18,
> 19, 20, 21, 22, 23, 24,
> 25, 27, 29, 30, 31, 32,
> 33, 34, 35, 36, 37,
> 38, 39, 40, 41, 42, 43,
> 44, 45)
> recurring items (1, 1, 1, 2, 3, 4, 5, 5, 6, 6, 12, 13,
> 14, 18, 19, 19, 19, 22, 22, 23,
> 24,
> 27, 27, 29, 30, 31, 32,
> 35, 35, 36,
> 39, 40, 44, 45)
> items desired (26, 28)
>
> Mary's friend John's card's collections is:
> 2000 Baseball Cards - numbers (1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 18,
> 20, 21, 22, 23, 24,
> 25, 27, 29, 30, 33, 36,
> 38, 39, 40, 41, 42, 43, 44,
> 45)
> recurring items (1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14,
> 16,
> 18, 23, 42, 43)
> items desired (9, 11, 13, 15, 17, 19, 26, 28, 31, 32,
> 34, 35, 37)
>
> 2000 Bascketball Cards - numbers (1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14,
> 15,
> 16, 17, 18, 19,
> 20, 21, 22, 23, 24, 25,
> 27, 29, 30, 31,
> 32, 33, 34, 38, 39, 40,
> 41, 42, 43, 44, 45)
> recurring items (1, 1, 1, 2, 3, 4, 5, 5, 6, 6, 12,
> 13, 14, 18, 19, 19, 19,
> 22, 24, 27, 27, 29,
> 30, 31, 32, 35, 39, 40, 44,
> 45)
> items desired (7, 8, 9, 26, 28, 35, 36, 37)
>
> Let C collections set:
> C = {2000 Baseball Cards, 2000 Bascketball Cards, 1999 Baseball Cards)
>
> Let F people set that will exchange cards is:
> F = {Me, John, Mary}
>
> have this collections
> Where : Me = P[1] = {2000 Baseball Cards, 2000 Bascketball Cards}
> John = P[2] = {2000 Baseball Cards, 1999 Baseball Cards}
> Mary = P[3] = {2000 Baseball Cards, 2000 Bascketball Cards}
>
> My "2000 Baseball Cards" collection have bellow sets:
> numbers that I have N[1] = (1, 2, 3, 4, 5, 6, 10, 23, 45)
> recurring items R[1] = (1, 1, 2, 5, 5, 6, 23, 23)
> items desired D[1] = (7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18,
> 19,
> 20, 21, 22, 23, 24, 25, .. , 44)
>
> I need the follow John's recurring cards: (12, 13, 14, 18, 19, 22, 23, 24,
> 27,
> 29, 30, 31,
> 32, 35, 36, 39, 40, 44)
> And I need too the follow Mary's recurring cards: (15, 17, 26, 28, 34, 43)
>
> Then, after these exchanges, my new desired set is : (7, 8, 9, 11, 16, 20,
> 21,
>
> 25, 33, 37, 38, 41, 42)
>
> Whereas this example we have only three people involved, and only three
> collections of cards for each one, asking for that:
>
> 1. Create an abstract method to handle | F | people involved in
> relationships
> of exchange with | C | collections of cards for each one;
>
> 2. Develop a data structure that facilitates the search for desired items;
>
> 3. Make routines at run time at most O (n. m), where n = | C | and m = | F
> |.
>
> >
>
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