[algogeeks] Re: Proving Waring hypothesis...

Tue, 31 Oct 2006 14:57:53 -0800

The range for a,b,c would be 0 to sqrt(n). Iterating over all values would give complexity O(n^(3/2)).
Using bitmaps, we can determine which numbers within 0..n are not in the list of a^2 + b^2 + c^2.
I guess, here we need to assume that we have O(n) space atleast.
 
For making computationally efficient, use ranges for a, b, c as  [0..sqrt(n)], [a .. sqrt(n)], [b..sqrt(n)].
 
~Vishal
 
On 10/31/06, Dhyanesh (ધયાનેશ) <[EMAIL PROTECTED]> wrote:
I have a slight improvement O ( n^2 log (n )  )

Say you have a^2 + b^2 + c^2 = d.

Keep a sorted list of all possible a^2 + b ^ 2 ... this would take n^2 time to generate and n^2 log n to sort. Now loop over all possible 'd' and 'c' and compute  d - c ^ 2. Use binary search to  determine whether that number is in the list ... if it is then 'd' is a number which CAN be represented otherwise try for the next 'c'.

There might be a better solution ... still thinking

-Dhyanesh
On 10/31/06, Karthik Rathinavelu < [EMAIL PROTECTED]> wrote:
Question: Given n, find the numbers in the range of 0...n which CAN'T be represented in the form of sum of squares of 3 non-negative numbers.

If anyone could possibly give a solution better than O(n^3), it will be good.

Thanks,
R.Karthik



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