STICKS - Editorial

cook71
editorial
greedy
simple
sticks

#1

PROBLEM LINK:

Practice
Contest

Author: Hasan Jaddouh
Tester: Misha Chorniy
Editorialist: Pushkar Mishra

DIFFICULTY:

Simple

PREREQUISITES:

Greedy

PROBLEM:

Given an array of A of N integers which represent stick lengths, we have to report the maximal area over all the rectangles that we can form with the given sticks without breaking any.

EXPLANATION:

The problem is a simple one based on a very basic property of all rectangles: the opposite sides of a rectangle are parallel, and hence, equal in length. The area of a rectangle is given by base B multiplied by height H. Now, to maximise the area, we simply need to maximise the length of sticks we choose as our B and H. This is pretty intuitive but we can also invoke the exchange argument method (page 3 of link) to give a more formal argument as proof of why this works (left to reader as a simple learning exercise).

Now we come to the implementation detail of the above mentioned algorithm. Note that N and A_{max} both range between 1 and 10^3. So, one way is that we simply keep an array Count of length 10^3 wherein Count* is the number of sticks of length i that we have. Once we have populated this structure, we can simply scan from 10^3 down to 1. If while scanning, we can find one field which has more than 3 sticks, then that i can be our height and base both; at this point we terminate our scan. If we find a field that has more than 1 stick, we can make it either our height or base and continue our scan to find a value for the other one. If at the end of scan we don’t find at least two i for which the count is more than 1, then we output -1 since no rectangle can be formed.

The other implementation can be by using a map instead of an array. In that case, if the N is much smaller than A_{max}, we can get a better performance. Both of the implementations easily pass for the given constraints.

Please see editorialist’s/setter’s program for implementation details.

COMPLEXITY:

\mathcal{O}(N\log N) or \mathcal{O}(A_{max}) per test case.

SAMPLE SOLUTIONS:

Author
Tester
Editorialist


#2

whats wrong with my implementation ? link-
https://www.codechef.com/viewsolution/10624567


#3

I implemented in c++ and java. In c++ I am getting run-time error when I am running the code in the code-compile-run here. And in Java it’s wrong answer.

Java Implementation:

http://pastebin.com/gAFVG2Fs

C++ Implementation:

http://pastebin.com/nf4zuNSM

If possible please tell me what is wrong with these two codes.


#4

A different implementation of the above logic.

https://www.codechef.com/viewsolution/10616757

First enter all the length of the sticks in an array, sort it in O(nlogn) and then traverse the array from the right end, checking for multiple instances of any stick. This also covers the special case of a square.


#5

hey,can anyone just help me to find error in my code…
https://www.codechef.com/viewsolution/10623972


#6

A different approach,which has O(N*logN) time complexity but uses Only One Array is as follows:

After storing the array containing the lengths of sticks, sort it.
We must note that the same lengths will automatically come together after sorting.
For example,

the array 5 2 8 3 1 2 4 3 5

becomes 1 2 2 3 3 4 5 5 8

Then if we traverse the array from backwards picking up the first two occurrences of a pair of same numbers(for e.g (5,5) would be the first occurrence and (3,3) would be the second in this case.Don’t forget to break the loop here. :stuck_out_tongue: )
the answer would be 5*3=15.If we are unable to find two occurrences we print -1.

The JAVA solution of the problem using this method is:

https://www.codechef.com/viewsolution/10620032.


#7

@code_blooded_ I did same in C++.
https://www.codechef.com/viewsolution/10622129


#8

https://www.codechef.com/viewsolution/10618548 Please let me know what is wrong with this solution.


#9

@sreedishps if N<3 , then you are not reading sticks length


#10

https://www.codechef.com/viewsolution/10627623 Hey, Can anybody tell why I am getting WA ? I used the algorithm mentioned in editorial.


#11

https://www.codechef.com/viewsolution/10621785 Can somebody please look into it,I am getting a WA.


#12

Can anybody tell why I am getting WA ? link-https://www.codechef.com/viewsolution/10630873


#13

Hi,

This is my code
https://www.codechef.com/viewsolution/10630891

Can anyone please help me to tell why is this WA ?

Thanks


#14

y am i getting WA in this solution? https://www.codechef.com/viewsolution/10632476


#15

https://www.codechef.com/viewsolution/10633288

can someone help me with my code…? its coming as “time limit exceeded”…


#16

Can anyone help with the code. I have included the square case too. But I don’t know why my solution is not getting accepted. https://www.codechef.com/viewsolution/10624628


#17

@pada1211
Your code fails for
1 4 1 2 3 3


#18

https://www.codechef.com/viewsolution/10621220 I cant seem to figure out whats wrong with my solution. It passes most of the test cases I can come up with.
Please help out. Thanks in advance :slight_smile:
PS: I looked through some solutions… They use the size of count array as 10000 whereas the mentioned size is 10^3 = 1000. Why is that so?
I tried both ways by the way. Still wrong answer.


#19

@sreedishps
This case gives Runtime error with your code :
1
7
4 4 3 3 3 3 1


#20

@sebastinsanty,

check the case

1

7

2 3 1 1 2 1 1

answer should be 2