AE00 - Rectangles

Byteman has a collection of N squares with side 1. How many different rectangles can he form using these squares?

Two rectangles are considered different if none of them can be rotated and moved to obtain the second one. During rectangle construction, Byteman can neither deform the squares nor put any squares upon any other ones.


The first and only line of the standard input contains one integer N (1 <= N <= 10000).


The first and only line of the standard output should contain a single integer equal to the number of different rectangles that Byteman can form using his squares.


For the input data:


the correct result is:


Task author: Jakub Radoszewski.

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sina_ss: 2017-03-08 11:30:46

:| badihie

Last edit: 2017-03-08 11:31:02
tuandayhehe: 2017-02-14 08:29:38

AC in 1 GO with 5 lines :">

dgfreak: 2017-01-24 17:15:45

Using some elementary summing formulas, you can get it down to a formula that's calculated in O(sqrt(n)) time.

vetox: 2017-01-03 12:57:10

Calculating the number of possible rectangles for each squares takes O( sqrt(n) ) time. To do that for n numbers 1, 2, 3, 4.....n, takes O( n * sqrt(n) ) operations. So that makes it O(n ^ 1.5) complexity.

Correct me if I'm wrong.

ignacio: 2016-12-27 07:31:46

Nice problem

shantanu_sarin: 2016-12-06 23:17:12

Just try to judge the pattern .......for n=2,3,4.......15 and your job is done...

tawhidkuet04: 2016-12-04 19:00:35

AC in one go !!!!!!!! :D

soodan: 2016-12-04 15:31:02

AC IN ONE GO!!!!!!!!!

anurag200698: 2016-11-17 17:26:54

very simple got AC in first go:)

mohitgupta07: 2016-11-16 08:09:50

O(n) not O(sqrt(n)). Since n>sqrt(n) . Well this question is good enough to make your basic concepts more clear also these type of adhoc question generally come up in competitions

Added by:Race with time
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:Algorithmic Engagements 2009