## VM7WC '15 #2 Gold - Uniting the Earth Empire

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Points: 12
Time limit: 1.0s
Memory limit: 64M

Author:
Problem type

After the Earth Queen fell, the Earth Kingdom fell into anarchy and was overrun by bandits. Luckily for the citizens of the Earth Kingdom, Kuvira the Great Uniter has brought security to the new Earth Empire and wishes to reconnect the nation by building bridges. She thinks that bridges symbolize power and wealth and will be necessary in rebuilding Republic City.

The Earth Empire consists of hills in a straight line, with the hill having a height of . Kuvira can build a bridge between hill and hill if and only if both hill and hill are greater or equal in height to all other hills in between them.

After losing her smartest engineer and nuking her second smartest engineer, Kuvira has been left engineer-less (and fiance-less). Seeing the opportunity for a big time promotion, you decide to help her count the number of different bridges that she can build between hills!

Use a stack!

#### Hint 2

Note that each bridge that can be made has a left and a right hill. Consider a right hill . Then you must count all left hills with such that you can build a bridge between hills and . However, observe that you do not need to consider all the hills between . Consider hills and with such that the height of is greater than the height of . Hill will never be able to act as a left hill for hill because hill is "blocking" it. Thus, we will never have to consider hill as a left hill for all right hills from onward.

#### Input Specification

The first line will contain the integer .

The next lines will each contain a single integer, .

The heights of the hills will be given in order.

#### Output Specification

Print a single integer, the number of distinct bridges that can be built between hills.

#### Sample Input

5
2
10
5
7
10

#### Sample Output

6

• commented on Aug. 4, 2018, 2:16 a.m.

there should be an explanation for the sample input for more clarity tbh

• commented on Sept. 13, 2017, 1:25 a.m.

Any hints on how to improve my solution? Is my idea even correct in the first place?

• commented on Sept. 13, 2017, 9:46 p.m. edited

I'd also try "A Classic problem".

edit: oops you solved it a second few i posted this comment

• commented on Sept. 13, 2017, 2:38 a.m. edited

I don't think your solution would work even if you optimize. (Time complexity is similar to )

Try using a stack instead for an time complexity.

Here is a similar problem that might help you solve this one: https://dmoj.ca/problem/mwc15c2p2

• commented on Jan. 16, 2015, 11:58 p.m. edited

• commented on Jan. 17, 2015, 1:58 p.m. edited

2-->10

10-->5 10-->7 10-->10

5-->7

7-->10

• commented on Jan. 17, 2015, 10:59 p.m. edited

BMP do you get it? Basically if all the stuff in the middle of the outer ones are less than or equal to both the outer ones, you can build a bridge.

• commented on Jan. 16, 2015, 12:39 a.m. edited

It would be really cool if we could also have other themed contests as time goes on, like a Doctor Who or Sherlock (none of that Elementary crap) contest!

:3

• commented on Jan. 18, 2015, 7:27 p.m. edited

Unfortunately, those of us who make the contest are losers and have not watched any of those :(

• commented on Jan. 18, 2015, 7:37 p.m. edited

It's okay, my contests are almost guaranteed to be full of spoilers about ongoing anime.