Find sum of odd numbers

Question

Write a program to find the sum of all odd numbers between a given range [a,b]. Input consists of a single line containing two integers a and b separated by a space. 0 ≤ a,b ≤ 1,000,000,000,000. Your program should not take more than 10 secs.

Sample Inputs
1 5
4 8
1 8
0 5

Sample Outputs
9
12
16
9

Answer 1

Funciton

Not a language particularly suitable for golfing, but I gave it my best shot to cram everything together in best code-golf tradition. Near the end I was making rearrangements that gave net savings of a single character until I could find no more ways to improve it :)

This is 398 characters (or 786 bytes in UTF-16). I challenge anyone to find a way to make it smaller :)

 ┌───┐    ┌──────────┐
╔╧╗┌─┴╖┌─╖│╔═╗┌──╖┌─╖│
║ ║│>>╟┤_╟┘║1╟┤>>╟┤♯╟┘
╚═╝╘╤═╝╘═╝ ╚═╝╘═╤╝╘═╝
    └┐ ┌─┐ ╔══╗┌┴───┐
╔══╗┌┴╖│┌┴╖║32║│ ┌─╖│
║21╟┤×╟┘│♯║╚╤═╝└─┤×╟┘
╚══╝╘═╝ ╘╤╝┌┘ ┌─┐╘╤╝
┌──────┬─┘┌┘ ┌┴╖└─┘
│╔═╗  ┌┴╖┌┘  │−╟┐┌───────╖
│║0║ ┌┤ʘ╟┘┌─┐╘╤╝└┤int→str╟
│╚╤╝ │╘═╝┌┴╖└─┘  ╘═══════╝
│┌┴╖╔╧╗┌─┤×╟┐
└┤ʃ╟╢ ║│ ╘═╝│
 ╘╤╝╚═╝└┬───┘
  │┌─╖┌─┴╖╔═╗╓─╖┌───────╖
  └┤_╟┤>>╟╢1║║_╟┤str→int╟
   ╘═╝╘══╝╚═╝╙─╜╘═══════╝

Answer 2

Ruby, 43 characters

p eval"-(%d/2)**2+((%d+1)/2)**2"%gets.split

Example for largest input:

$ time echo "1 10000000000000000" | ruby oddsum.rb
25000000000000000000000000000000

real    0m0.006s
user    0m0.000s
sys     0m0.000s

Answer 3

Windows PowerShell, 84 61 55

$a,$b=-split"$input+1"|iex|%{($_-band-2)/2}
$b*$b-$a*$a

O(1) runtime.

Answer 4

Golfscript - 12 chars

~)2/2?\2/2?-

can be done in 11 chars if the order of the inputs is reversed

~)]{2/2?}/-

Answer 5

Python, 32 bytes

As unnamed lambda function:

lambda a,b:((b+1)/2)**2-(a/2)**2

Did some math to get a direct formula. Proof will follow.

Answer 6

Vyxal s, 7 bytes

›"2ḭ²Ḃ¯

Try it Online!

STACK = [4,8]
›               Increment, [5, 8]
"               Pair  [[5, 8]]
2              Push 2 [[5, 8], 2]
ḭ               Integer Division [[2, 4]]
²               Square [[4, 16]]
Ḃ              Reverse [[16, 4]]
¯               Deltas    [[12]]
                 Implicit Sum [12]