xuanquang1999's blog

By xuanquang1999, history, 2 years ago, In English,

One of my friend recently asked me the following problem:

"Given an array a1, a2, ..., an and a number K (n ≤ 105, ai ≤ 109). Is there a way split the array into K disjoint sub-arrays (don't have to be contiguous) such that sum of each sub-array is equal to each other (and equal to )?"

My teacher came up with the following greedy solution: for each sub-array, keep choosing the maximum number such that sum of sub-array with that number is still smaller or equal to S. When it's impossible to add more number from a to this sub-array, check if the current sum is equal to S.

However, both my teacher and me are unable to neither prove the correctness of the solution nor find a counter-example for it. Is this greedy solution always optimal? How to prove (or disprove) it? Thanks in advance.

 
 
 
 
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2 years ago, # |
Rev. 2   Vote: I like it +17 Vote: I do not like it

That greedy is wrong — same reason why you can't do knapsack greedily

n = 6, k = 2 sum = 48

2 2 4 5 17 18

you will find 18 5 and terminate.

I guess that problem is np complete.