I have modified some part of the above post below to avoid confusion
regarding the generation of all subsets:
Say, we need to find all the subsets which led to A[N, K] = 1, to do
this we will take the following steps :
a) If ( i == 0 ) print the subset and return.
b) if A[N -1 , K] = 1,
b1) then W[N] doesn't belong to the subset , continue
recursively ( goto step a).
b2) goto step c.
else goto step c.
c) if A[N -1 , K - W[N] ] = 1, then W[N] belongs to the subset ,
continue recursively ( goto step a) .
else return.
On Dec 7, 6:29 pm, Lucifer <sourabhd2...@gmail.com> wrote:
> I have an idea, i think it can be done in O(N * Wmax).
>
> Let the weight array be W[N].
>
> Take an array A[N][Wmax] , where N is the no. of weights provided and
> Wmax is the max weight.
>
> Initialize the array with the following values,
> 1) A[0, j] = 0 for 1 <= j <= Wmax
> 2) A[i, 0] = 1 for 0 <= i <= Wmax
>
> Now, if an A[i , j] = 1, that means using the first "i" weights it is
> possible pick a subset whose sum is "j",
> else if A[i , j] = 0, then it not possible to have subset of first
> "i" weights whose sum would sum up to "j".
>
> Now, to solve the above problem we can use the following equation,
>
> A[i , j] = A[i-1, j] or A[ i-1 , j - W[i] ]
>
> Using the above equation calculate all values A[i, j] where 1 <= i <=
> N and 1 <= j <= Wmax.
>
> Now,
> Scan A[N, j] from right to left ( Wmax >= j >= 0 ) till you get a
> value of 1, let the found column index be "K".
> A[N, K] = 1, basically signifies the maximum sum that you can make
> which is "K".
>
> Now that you have the maximum sum <= Wmax which can be made i.e "K",
> the next problem will be 2 figure all the subsets.
> To find all the subsets backtrack based on the equation given above
> and record the weights for which A[i, j] = 1,
> i.e.
> Say, we need to find all the subsets which led to A[N, K] = 1, to do
> this we will check for,
> a) if A[N -1 , K] = 1, then W[N] doesn't belong to the subset ,
> continue recursively.
> b) if A[N -1 , K - W[N] ] = 1, then W[N] belongs to the subset ,
> continue recursively.
>
> Hence,
> To find the max value it will take O( N * Wmax) + O( Wmax)
> To find all the subsets, it will take O( X * Y) where, x is the no. of
> subsets and y is the average no. of elements in it.
>
> On Dec 5, 5:09 pm, Shashank Narayan <shashank7andr...@gmail.com>
> wrote:
>
>
>
>
>
>
>
> > @piyuesh 3-Sum is not exponential ? its quadratic , check wiki for refrence
> > ?
>
> > On Mon, Dec 5, 2011 at 5:36 PM, Piyush Grover
> > <piyush4u.iit...@gmail.com>wrote:
>
> > > As I mentioned earlier solution with exponential time-complexity is the
> > > obvious one. Is there any way to solve this problem by greedy/Dynamic
> > > algo?
>
> > > On Mon, Dec 5, 2011 at 5:24 PM, WgpShashank
> > > <shashank7andr...@gmail.com>wrote:
>
> > >> @piyuesh , Saurabh isn't 3-Sum Suffics Here ?
>
> > >> Another thought problem can also be thought by generating power set of
> > >> given set e.g. if set has n elemnts its power set has 2^n elements ,
> > >> then
> > >> finds the set that has sum up yo given weight isn't it ? hope you know
> > >> how
> > >> to find power set efficiently ?
>
> > >> correct if is missed anything ?
>
> > >> Thanks
> > >> Shashank
> > >> Computer Science
> > >> BIT Mesra
> > >>http://www.facebook.com/wgpshashank
> > >>http://shashank7s.blogspot.com/
>
> > >> --
> > >> You received this message because you are subscribed to the Google Groups
> > >> "Algorithm Geeks" group.
> > >> To view this discussion on the web visit
> > >>https://groups.google.com/d/msg/algogeeks/-/a9F-gPQkjm0J.
>
> > >> To post to this group, send email to algogeeks@googlegroups.com.
> > >> To unsubscribe from this group, send email to
> > >> algogeeks+unsubscr...@googlegroups.com.
> > >> For more options, visit this group at
> > >>http://groups.google.com/group/algogeeks?hl=en.
>
> > > --
> > > You received this message because you are subscribed to the Google Groups
> > > "Algorithm Geeks" group.
> > > To post to this group, send email to algogeeks@googlegroups.com.
> > > To unsubscribe from this group, send email to
> > > algogeeks+unsubscr...@googlegroups.com.
> > > For more options, visit this group at
> > >http://groups.google.com/group/algogeeks?hl=en.
>
> > *
> > **
> > *
--
You received this message because you are subscribed to the Google Groups
"Algorithm Geeks" group.
To post to this group, send email to algogeeks@googlegroups.com.
To unsubscribe from this group, send email to
algogeeks+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/algogeeks?hl=en.
