11026  A Grouping Problem
Moderator: Board moderators
11026  A Grouping Problem
Can anyone describe the idea to solve this problem.
Thanks in advance.
Thanks in advance.
Ami ekhono shopno dekhi...
HomePage
HomePage
I've used O(n^2) dynamic programming. The recurrence is very similar to binomial's formula.
(spoiler:)
If C[m][k] denotes the sum of products of elements of all subsets of size k chosen from first m elements,
then we have: C[m][k] = C[m1][k] + C[m1][k1] * A[m], (where A[m] is mth number in input.)
(spoiler:)
If C[m][k] denotes the sum of products of elements of all subsets of size k chosen from first m elements,
then we have: C[m][k] = C[m1][k] + C[m1][k1] * A[m], (where A[m] is mth number in input.)
Thanks Timo and mf for your beautiful explanations.
I have got the idea.
Thanks again.
I have got the idea.
Thanks again.
Ami ekhono shopno dekhi...
HomePage
HomePage
I don't know if what i did is the same that you're talking.
Let a=1, b=2, c=3
(x1)*(x2)*(x3) = x^36x^2+11x6
a + b + c =6
ab+ac+bc= 11
abc=6
so we can multiply (xx1)*(xx2).....(xxn) store the coeficients in an array and look for the coeficient with highest value mod m
it got ac in 1.2 seconds during contest
Time complexity O(n^2)
Space Complexity O(n)
Let a=1, b=2, c=3
(x1)*(x2)*(x3) = x^36x^2+11x6
a + b + c =6
ab+ac+bc= 11
abc=6
so we can multiply (xx1)*(xx2).....(xxn) store the coeficients in an array and look for the coeficient with highest value mod m
it got ac in 1.2 seconds during contest
Time complexity O(n^2)
Space Complexity O(n)
I don't understand this problem at all..
I think this problem wants us to compute maxfitness from all Kcombination out of N elements ( 1 <= K <= N ), but I don't see any relation between this idea and the problem's Sample I/O.
eg. on 2nd sample i/o :
4 100
1 2 3 4
if K = 0 > 0...
if K = 1 > 1 + 2 + 3 + 4 > 10
if K = 2 > 1.2 + 1.3 + 1.4 + 2.3 + 2.4 + 3.4  > 35
if K = 3 > 1.2.3 + 1.2.4 + 2.3.4 > 38
if K = 4 > 1.2.3.4 > 24
if K > 4 > don't tell me this one is possibe..
how can the maximum fitness be 50 ?
I think this problem wants us to compute maxfitness from all Kcombination out of N elements ( 1 <= K <= N ), but I don't see any relation between this idea and the problem's Sample I/O.
eg. on 2nd sample i/o :
4 100
1 2 3 4
if K = 0 > 0...
if K = 1 > 1 + 2 + 3 + 4 > 10
if K = 2 > 1.2 + 1.3 + 1.4 + 2.3 + 2.4 + 3.4  > 35
if K = 3 > 1.2.3 + 1.2.4 + 2.3.4 > 38
if K = 4 > 1.2.3.4 > 24
if K > 4 > don't tell me this one is possibe..
how can the maximum fitness be 50 ?
Suhendry Effendy
ups.. too late. someone has replied my question. yeah. it's a very stupid mistake I've just figured this out. How can ( 4! / 3! ) be 3...
shouldn't fall into this again..
btw, my friend also participate in this contest and i asked the same question to him. but he also forgot 1.3.4 how can both of us fell into the same mistake..
anyway, thanks ferng1021. it's time to code..
shouldn't fall into this again..
btw, my friend also participate in this contest and i asked the same question to him. but he also forgot 1.3.4 how can both of us fell into the same mistake..
anyway, thanks ferng1021. it's time to code..
Suhendry Effendy

 Experienced poster
 Posts: 122
 Joined: Sun Nov 13, 2005 10:25 am
 Location: Taiwan
My accepted program prints 1 for your second test case.
Here are some tests:
Here are some tests:
Code: Select all
10 2147483647
1000 999 998 997 996 995 994 993 992 991
10 2147483647
997 997 997 997 997 997 997 997 997 997
13 2147483647
997 991 983 977 971 967 953 947 941 937 929 919 911
2 1
1 1
0 0
Code: Select all
2111939040
1668905003
1828513970
0
Luckily there was no similar case in the judge data.
Even though (K=0) isn't mentioned in the problem statement, but one gets the feeling that it shouldn't be considered, just by reading the problem statement.
But this is of course my opinion.
Even though (K=0) isn't mentioned in the problem statement, but one gets the feeling that it shouldn't be considered, just by reading the problem statement.
But this is of course my opinion.
Last edited by sohel on Tue May 30, 2006 11:07 am, edited 1 time in total.