SKYLINE - Skyline

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The director of a new movie needs to create a scaled set for the movie. In the set there will be N skyscrapers, with distinct integer heights from 1 to N meters. The skyline will be determined by the sequence of the heights of the skyscrapers from left to right. It will be a permutation of the integers from 1 to N.

The director is extremely meticulous, so she wants to avoid a certain sloping pattern. She doesn’t want for there to be ANY three buildings in positions i, j and k, i < j < k, where the height of building i is smaller than that of building j, and building j’s height is smaller than building k’s height.

Your task is to tell the director, for a given number of buildings, how many distinct orderings for the skyline avoid the sloping pattern she doesn't like.


There will be several test cases in the input. Each test case will consist of a single line containing a single integer N (3 ≤ N ≤ 1,000), which represents the number of skyscrapers. The heights of the skyscrapers are assumed to be 1, 2, 3, ..., N. The input will end with a line with a single 0.


For each test case, output a single integer, representing the number of good skylines - those avoid the sloping pattern that the director dislikes - modulo 1,000,000. Print each integer on its own line with no spaces. Do not print any blank lines between answers.




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nikhil1234hnd: 2023-12-13 15:04:09

i came to known that catalan numbers will help here but i am not able to relate catalan number concept to this question can anybody help me. how i can know i should use catalan numbers here

hori_josu2002: 2023-11-05 03:35:50

Can someone Help me with this :CC

yasser1110: 2021-05-14 13:47:01

Such a poor question. If you know x, you will easily be able to solve, otherwise keep struggling. search for x.

codephilic: 2020-10-04 13:52:06

See the modulo carefully !!

linkret: 2020-09-06 20:57:31

preach brother

nadstratosfer: 2018-04-18 14:37:08

You know the problem is from an american contest when the movie director is a "she". Because, if we only repeat feminist slogans often and aggresively enough, the she's will stop uploading selfies or calling everything rape, and flood us with Godfather's and other Taxi Driver's. In the meantime, the most recent US team ICPC triumph was 20 years ago. And look at these horribly not diverse countries they keep losing to... Technology > ideology.

vivace: 2016-12-15 19:16:49

discrete mathematics :D

MishThi: 2015-10-25 19:31:17

@Ankit Kumar : Plz dont post solutions!

MishThi: 2015-10-23 09:02:20

Great problem. Learnt a few new concepts.

Although the same solution is accepted for C and C++ but it shows TLE for Python 2.7 and Python 3.4.

Re: Finally solved in Python as well. Learnt new tricks for code optimization in python. :D

Last edit: 2015-10-25 19:30:41
Aayush: 2015-01-07 11:25:18

Getting "internal error" with python 3.4..

Edit : Same code. Got AC with python 2.7

Last edit: 2015-01-07 11:28:26

Added by:Iqram Mahmud
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:ACM ICPC Southeast USA Regional 2010