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This problem is not a homework, it's from SPOJ. I don't know what you mention, k must be an integer (for this problem) and I think temper_3243 can easily solve this if k is not (without anything called Lagrange multipliers...). What he needs is that someone can help him to solve the problem.

This is my program which got WA in spoj, please help me...
http://www.spoj.pl/problems/DISUBSTR/

const
lowc=char(ord(32));
highc=char(ord(127));
maxs=1000;
type
trie=^trienode;
trienode=array[lowc..highc] of trie;
var
s:array[1..maxs] of char;
k,i,j,ss:integer;
a:trie;
res:longint ...

Please tell me how to do this in O(n^2)
I think inserting a substring costs O(n). With n^2 substrings we need O(n^3) to complete constructing trie, right?

I want to find an efficient algorithm to count the number of maximum bipartite matching, anyone could help me?...

Harry Potter has n mixtures in front of him, arranged in a row. Each mixture has one of 100 different colors (colors have numbers from 0 to 99).

He wants to mix all these mixtures together. At each step, he is going to take two mixtures that stand next to each other and mix them together, and put ...

Let's come to this problem:
there's a set A={x1,x2,...,xn}. Our goal is dividing the set into 2 groups in order to the difference between sum of all the elements in group 1 and sum of all elements in group 2 is smallest

this is a typical problem using DP, the array's size for DP is |max{x1,x2,..,xn ...