**PROBLEM 4 - WATER TANKS**

There are n identical large cylindrical tanks for storing water. The tanks are arranged

in a circle on level ground. Each tank is connected with its two neighbours by means

of pipes situated at its base. There is a valve between each adjacent pair of tanks

(tank n is next to tank 1). All valves are initially closed. All the outlets and the pipes

are at the same level and are always full of water, even if all the tanks are deemed to

be “empty”.

The volume in any tank is measured by the height of the surface of the water above

the level of the top of the outlets. If all valves (or all valves but one) are opened so

that water can flow between the tanks, then the levels will eventually equalise.

Conversely, if all tanks are initially at the same level, no valves need be opened to

equalise the levels. Thus it may be necessary to only open some of the valves to

achieve this result.

For example, consider n=4 tanks each 5 metres high. Assume that the water level in

these tanks is at 4, 4, 3, and 3 meters respectively. Their water level will equalise if

we open the valves between tanks #2 and #3 and between #4 and #1, as suggested

by the following diagram. Thus for this set we need to open only two valves:

Given a set of initial heights, determine the minimum number of valves to open so

that the final water levels in all tanks is equal.

closed open closed open

to #4 to #1

#1 #2 #3 #4

P4 - ACM SPPC 2 of 2 Saturday, 20/09/2003

INPUT FORMAT 1

The input will consist of one or more scenarios, each scenario consisting of two lines.

The first line contains a descriptive title, which is a string of letters or spaces no more

than 200 characters long, containing at least 1 letter.

The second line starts with the number of basins n (3 £ n £ 200), a space, and then n

integers in the range 0 to 99, separated by single spaces, representing the water

levels in the tanks.

The scenarios sequence is terminated by a single ‘#’ character on a line by itself.**SAMPLE INPUT:**

High four dude basins

4 4 4 3 3

The Australasian eight

8 2 1 1 2 2 1 1 6

#**OUTPUT FORMAT**

Output one line for each input scenario. The line consists of the first letter of each

word in the descriptive title in upper case, followed by a colon (‘:’), a space, and then

the minimum number of valves that need to be open to achieve equal heights in all

tanks.

SAMPLE OUTPUT:

HFDB: 2

TAE: 5

i dont understand how the output is generated..

please help if anyone understand this....