CITY2 - A Famous City

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After Mr. B arrived in Warsaw, he was shocked by the skyscrapers and took several photos. But now when he looks at these photos, he finds in surprise that he isn't even able to point out the number of buildings in it. So he decides to work it out as follows:

- divide the photo into n vertical pieces from left to right. The buildings in the photo can be treated as rectangles, the lower edge of which is the horizon. One building may span several consecutive pieces, but each piece can only contain one visible building, or no buildings at all.

- measure the height of each building in that piece.

- write a program to calculate the minimum number of buildings.

Mr. B has finished the first two steps, the remaining comes to you.


Each test case starts with a line containing an integer n (1 <= n <= 100,000). Following this is a line containing n integers - the height of building in each piece respectively. Note that zero height means there are no buildings in this piece at all. All the input numbers will be nonnegative and less than 1,000,000,000.


For each test case, display a single line containing the case number and the minimum possible number of buildings in the photo.


1 2 3
1 2 1

Case 1: 3
Case 2: 2


The possible configurations of the samples are illustrated below:

hide comments
phoemur: 2018-11-23 23:15:35

In the case
1 2 1

The building with height 1 is considered only one building, behind the building with height 2, which is at the front.

I got no difference in Runtime using Segment Tree vs Sparse Table for RMQ despite the difference in asymptotic complexity

Abhimanyu: 2015-12-25 16:17:41

most vague problem description ever.

Utkarsh Rastogi: 2015-01-11 09:56:19

Good problem....testcases are really helpful.. :)

Hasil Sharma: 2014-06-22 15:18:33

Nice Problem :)

abdou_93: 2013-04-29 19:11:55

Take care of:-
3 4 3 4 3 4 3

Last edit: 2013-04-29 19:15:24
abdelkarim: 2013-04-29 12:01:12

nice one !

Vikas Kushwaha: 2012-12-28 09:40:10

easy but good one. :)

kamalesh: 2012-12-26 14:36:51

thanks Runtime Error!!!!

Swapnil R.Mehta: 2012-12-22 18:18:29

Take care of:-
0 1 0 1 0

nikoo28: 2012-12-15 18:15:09

the test cases by @Runtime Error helped me... :)

Added by:Fudan University Problem Setters
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:FDU Local Contest 2012