Thursday, July 7, 2011

Double Square Problem

A double-square number is an integer X which can be expressed as the sum of two perfect squares. For example, 10 is a double-square because 10 = 32 + 12. Your task in this problem is, given X, determine the number of ways in which it can be written as the sum of two squares. For example, 10 can only be written as 32 + 12 (we don’t count 12 + 32 as being different). On the other hand, 25 can be written as 52 + 02 or as 42 + 32.

Input
You should first read an integer N, the number of test cases. The next N lines will contain N values of X.

Constraints
0 ≤ X ≤ 2147483647
1 ≤ N ≤ 100

Output
For each value of X, you should output the number of ways to write X as the sum of two squares.

3 comments :

Karthick said...

Hi, I am Karthick. A question in careercup website goes like this
"Find two nodes in a BST such that their keys' sum equals K."

Time: O(n)
Space: O(1)

There, you had referred to this blog and said that you have provided a solution. But when I followed that link, it says "Webpage not found".
Can you give me the correct link or can you explain me on how the problem must be solved?

Regards-

Unknown said...

@karthick you can find here , you have to replace "dot" with . there i have given the link as career cup doesn't allow href :) anyways see here

http://shashank7s.blogspot.com/2011/06/wap-to-find-two-nodes-into-binary.html

do notify me if anything wrong :)

Shashank

Karthick said...

Thanks for you superfast reply :).

But since the algorithm uses recurstion, would not it imply an internal stack which goes against the O(1) constraint?