LEGO - Lego

It's Christmas morning, and you've got what you wanted: a box of Lego™! (Okay, maybe not, but better than nothing)

Lego is pretty fun to tinker with, and you've decided to build some sort of shape.
(For the sake of this problem, let's say your shape is basically 2-dimensional - it'll be a slab)

But once you pick it up, you discover that you didn't plan it properly, and your wonderful shape just falls apart.
Now, you're planning to build something big, and so you're going to use the computer to help you.
Write a program, that given the layout of a Lego design, outputs the number of pieces it would break into if picked up.
(Assume that the bricks bind together perfectly)

The Legos will be built on a x-y coordinate plane, with (0,0) being the bottom left corner.
The blocks are flat on your carpet, so a block will never 'fall down'.
(If you haven't seen a Lego brick before: A Lego brick has grooves on its top that match with notches on the bottom.
If a groove and a notch bind, the bricks will stay together. See the diagram.
A brick will bind with another brick securely even if just a single notch touches another groove.


The first line contains N (the number of Lego pieces), 1 ≤ N ≤ 100000.
N lines follow, each with 4 integers x1, y1, x2, y2 (0 ≤ x1 < x2 ≤ 2×109, 0 ≤ y1 < y2 ≤ 2×109)

This means that there is a brick with bottom left corner (x1,y1) and top right corner (x2,y2). x denotes the horizontal coordinate and y the vertical coordinate. Two bricks will bind if one's bottom y-coordinate coincides with the other's top y-coordinate and the intersection of the two intervals (the bottom of one and the top of the other) has nonzero length.
No bricks will overlap.


A single line containing the number of separate pieces that these blocks form.

Sample Input:

0 0 2 2
1 2 3 4
2 0 4 2
4 0 6 2

Sample Output:



Blocks #1,2,3 are joined securely.
However, #4 is just hanging around.

hide comments
Sajal Sarkar: 2016-12-28 11:02:23

Did someone solve this question via counting connected component?

Last edit: 2016-12-28 11:02:51
SANYAM JAIN: 2016-08-03 19:01:48

Finally solved it, took so many wa and tle.

lalitesh: 2016-08-02 20:55:23

After WA n TLE , got AC ;)

Liquid_Science: 2016-08-01 09:54:30

AC in a go , but took me a lot of time though! :/

Shubham Sinha: 2016-05-28 22:38:29

dsu rocks !!

shikhar0037: 2016-05-26 03:40:31

Nice problem . AC in 1 GO :)

Last edit: 2016-05-26 14:54:26
birdie: 2015-02-20 10:53:27

i am getting wa.. any tricky testcase ?

shakaal: 2015-01-20 06:12:09

please explain test case it snot clear

Christoph Dürr: 2015-01-20 06:12:09

The time limit seems too small for python.

Sigma Kappa: 2015-01-20 06:12:09

"the union of the two intervals (the bottom of one and the top of the other) has nonzero length"
I'd rather say "intersection", not union.

Added by:Brian Bi
Time limit:0.118s-0.356s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Resource:Hanson Wang