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# STICKS - Editorial

Tester: Misha Chorniy
Editorialist: Pushkar Mishra

Simple

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 $Count[i]$ 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:

This question is marked "community wiki".

1.3k156381
accept rate: 4%

18.3k347492525

 2 @code_blooded_ I did same in C++. https://www.codechef.com/viewsolution/10622129 answered 27 Jun '16, 10:08 2★easy_ 128●6 accept rate: 0%
 0 whats wrong with my implementation ? link- https://www.codechef.com/viewsolution/10624567 answered 27 Jun '16, 00:15 21●3 accept rate: 0% Try this test: 1 4 1 2 3 3 Your solution output 0, but must be -1 BTW, change for(i=0;i<10002;i++) to for(i=0;i<10001;i++), your arrays size only 10001 (27 Jun '16, 01:33) mgch6★
 0 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. answered 27 Jun '16, 00:28 1 accept rate: 0% You forget about square: 1 4 1 1 1 1 Your solution output -1, but must be 1. (27 Jun '16, 01:35) mgch6★
 0 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. answered 27 Jun '16, 00:32 774●9 accept rate: 11%
 0 hey,can anyone just help me to find error in my code.. https://www.codechef.com/viewsolution/10623972 answered 27 Jun '16, 00:58 3★nanhe 41●3 accept rate: 0% You forget about square case too (27 Jun '16, 01:37) mgch6★ can u elaborate more ,which case i have omitted (27 Jun '16, 01:53) nanhe3★ 1 4 1 1 1 1 (27 Jun '16, 01:57) mgch6★ ok,I got it ..thank U (27 Jun '16, 02:00) nanhe3★
 0 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. :P ) 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. answered 27 Jun '16, 02:50 21●1 accept rate: 0%
 0 https://www.codechef.com/viewsolution/10618548 Please let me know what is wrong with this solution. answered 27 Jun '16, 10:46 1 accept rate: 0%
 0 @sreedishps if N<3 , then you are not reading sticks length answered 27 Jun '16, 11:41 9●2 accept rate: 0%
 0 https://www.codechef.com/viewsolution/10627623 Hey, Can anybody tell why I am getting WA ? I used the algorithm mentioned in editorial. answered 27 Jun '16, 12:13 2★chandan5 1●1 accept rate: 0% 1 8 1 1 2 2 2 2 3 3 Answer is 6 = 2 * 3, but your output will be 2 * 2 = 4 (27 Jun '16, 12:26) mgch6★ @mgch Thanks :) (27 Jun '16, 14:50) chandan52★
 0 https://www.codechef.com/viewsolution/10621785 Can somebody please look into it,I am getting a WA. answered 27 Jun '16, 15:59 3★pada1211 1 accept rate: 0%
 0 Can anybody tell why I am getting WA ? link-https://www.codechef.com/viewsolution/10630873 answered 27 Jun '16, 20:20 1 accept rate: 0%
 0 Hi, This is my code https://www.codechef.com/viewsolution/10630891 Can anyone please help me to tell why is this WA ? Thanks answered 27 Jun '16, 20:23 0★nits24 1 accept rate: 0%
 0 y am i getting WA in this solution? https://www.codechef.com/viewsolution/10632476 answered 28 Jun '16, 00:45 1 accept rate: 0%
 0 can someone help me with my code..? its coming as "time limit exceeded".. answered 28 Jun '16, 09:21 1 accept rate: 0%
 0 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 answered 28 Jun '16, 11:18 1 accept rate: 0%
 0 @pada1211 Your code fails for 1 4 1 2 3 3 answered 28 Jun '16, 19:17 2★rc1c2 45●5 accept rate: 22%
 0 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 :) 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. answered 29 Jun '16, 03:28 2★apheleia 1 accept rate: 0%
 0 @sreedishps This case gives Runtime error with your code : 1 7 4 4 3 3 3 3 1 answered 29 Jun '16, 17:16 2★yashkant 1 accept rate: 0%
 0 check the case 1 7 2 3 1 1 2 1 1 answer should be 2 answered 30 Jun '16, 13:22 21●1 accept rate: 0%
 0 https://www.codechef.com/viewsolution/10644839 Can someone explain why am i getting WA answered 30 Jun '16, 16:08 1 accept rate: 0%
 0 Can somebody please tell me at what test i got wrong answer https://www.codechef.com/viewsolution/10647330 answered 01 Jul '16, 00:29 1 accept rate: 0%
 0 Please can anyone point out the error in my code- https://www.codechef.com/viewsolution/10793814 answered 11 Jul '16, 20:01 2★newbie20 1 accept rate: 0%
 0 https://www.codechef.com/viewsolution/10864425 I am getting the required output, but its saying wrong answer :( answered 21 Jul '16, 13:04 1 accept rate: 0%
 0 https://www.codechef.com/viewsolution/10867659 Java Code: I am getting wrong answer for this, while its running perfectly on local compiler. Yes i have taken some extra boolean flags ..:P answered 22 Jul '16, 00:06 1 accept rate: 0%
 0 https://www.codechef.com/viewsolution/10867659 Java code: I am getting WA, but its running perfectly on my system. ye I have taken few extra boolean flags :P answered 22 Jul '16, 00:08 1 accept rate: 0%
 0 As usual,although I have passed the given test cases,I cant seem to find the reason why my code is getting a WA! Here's the link to the code:- http://pastebin.com/NbKdECcb answered 27 Jul '16, 00:18 1★arpanm96 1 accept rate: 0%
 0 Please somebody help me, I am getting WA https://www.codechef.com/viewsolution/10935149 answered 29 Jul '16, 10:59 3★ssgg2 1 accept rate: 0%
 0 Can anyone help me with my code https://www.codechef.com/viewsolution/11238582 . Getting wrong answer answered 24 Aug '16, 00:34 11●1 accept rate: 0%
 0 can anyone say me what is wrong with my output?? or which case did i miss https://www.codechef.com/viewsolution/13211673 answered 06 Apr '17, 17:32 0★mahiyuvi 1 accept rate: 0%
 0 C code Can any one say me what is wrong with the code.. its working fine in code blocks..but am getting wrong answer warning while submitting. could anyone please explain?? here is the link https://www.codechef.com/submit/complete/13211715 answered 06 Apr '17, 17:46 0★mahiyuvi 1 accept rate: 0%
 0 C code Can any one say me what is wrong with the code.. its working fine in code blocks..but am getting wrong answer warning while submitting. could anyone please explain?? here is the link https://www.codechef.com/submit/complete/13211715 answered 06 Apr '17, 17:46 0★mahiyuvi 1 accept rate: 0%
 0 Iam getting WA.But it is working fine in code blocks https://www.codechef.com/viewsolution/13211715 could anyone explain pls answered 06 Apr '17, 17:48 0★mahiyuvi 1 accept rate: 0%
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question asked: 25 Jun '16, 12:31

question was seen: 6,299 times

last updated: 25 Jun '17, 21:09