CCC '21 S1 - Crazy Fencing - Olympiads Online Judge

CCC '21 S1 - Crazy Fencing

Points: 5 (partial)

Time limit: 1.0s

Memory limit: 1G

Problem type

Canadian Computing Competition: 2021 Stage 1, Senior #1

You need to paint a wooden fence between your house and your neighbour's house. You want to determine the area of the fence, in order to determine how much paint you will use. However, the fence is made out of $N$ ~N~ non-uniform pieces of wood, and your neighbour believes that they have an artistic flair. In particular, the pieces of wood may be of various widths. The bottom of each piece of wood will be horizontal, both sides will be vertical, but its top may be cut on an angle. Two such pieces of wood are shown below:

$\text{[math]}$

Thankfully, the fence has been constructed so that adjacent pieces of wood have the same height on the sides where they touch, which makes the fence more visually appealing.

Input Specification

The first line of the input will be a positive integer $N$ ~N~, where $N \le 10\,000$ ~N \le 10\,000~.

The second line of input will contain $N+1$ ~N+1~ space-separated integers $h_1, \dots, h_{N+1}$ ~h_1, \dots, h_{N+1}~ $(1 \le h_i \le 100, 1 \le i \le N+1)$ ~(1 \le h_i \le 100, 1 \le i \le N+1)~ describing the left and right heights of each piece of wood. Specifically, the left height of the $i^\text{th}$ ~i^\text{th}~ piece of wood is $h_i$ ~h_i~ and the right height of the $i^\text{th}$ ~i^\text{th}~ piece of wood is $h_{i+1}$ ~h_{i+1}~.

The third line of input will contain $N$ ~N~ space-separated integers $w_i$ ~w_i~ $(1 \le w_i \le 100, 1 \le i \le N)$ ~(1 \le w_i \le 100, 1 \le i \le N)~ describing the width of the $i^\text{th}$ ~i^\text{th}~ piece of wood.

Output Specification

Output the total area of the fence. If the correct answer is $C$ ~C~, the grader will view $A$ ~A~ correct if $|A-C| \le 10^{-6}$ ~|A-C| \le 10^{-6}~.

Sample Input 1

3
2 3 6 2
4 1 1

Output for Sample Input 1

18.5

Explanation of Output for Sample Input 1

The fence looks like the following:

$\text{[math]}$

When looking from left to right, the individual areas of the pieces of wood are $10 = 4 \cdot (2+3)/2$ ~10 = 4 \cdot (2+3)/2~, $4.5 = 1 \cdot (3+6)/2$ ~4.5 = 1 \cdot (3+6)/2~, and $4 = 1 \cdot (6+2)/2$ ~4 = 1 \cdot (6+2)/2~, for a total area of $18.5$ ~18.5~.

Sample Input 2

4
6 4 9 7 3
5 2 4 1

Output for Sample Input 2

Explanation of Output for Sample Input 2

The fence looks like the following:

$\text{[math]}$

When looking from left to right, the individual areas of the pieces of wood are $25$ ~25~, $13$ ~13~, $32$ ~32~, and $5$ ~5~, for a total area of $75$ ~75~.

Comments

0

PHo3NIX commented on Oct. 27, 2024, 7:18 p.m.

You don't need to worry about using Python and the answer is an integer with .0 (such as 75.0) is still correct, so just use /2. On the contrary, if you use //2, the printed answer will be wrong.

1

Joel_M commented on Jan. 22, 2024, 4:21 a.m.

Not Including the inputs, this can be done in 1 line in python

0

Joel_M commented on Jan. 22, 2024, 4:26 a.m.

U can get away with not using the first input

1

darek commented on Feb. 21, 2022, 12:15 p.m. ← edit 4 →

I have run the 'best' Python 3 solution (ID: 4226630, Jan. 20, 2022) for sample 2 and the output is 75.0 (float), not the int (75) as shown in the sample 2 output...How come?

5

henrybaolol9 commented on Feb. 21, 2022, 4:33 p.m.

an int output is not required

1

darek commented on Feb. 21, 2022, 4:56 p.m.

Apparently the tests do not validate that then.

41
HOPE commented on May 25, 2021, 5:31 p.m. ← edited →
I actually found the solution and anyone who will code this in c++ will probably also need it.

Instead of printing the answer like this:

cout << area;

do this...

cout << fixed << area;

The fixed function will keep it from turning into scientific notation: 5.789E13

2

kopichiki commented on Aug. 12, 2022, 6:05 p.m. ← edited →

Also, setprecision in C++ allows you to choose how many decimal places you want in the float/double output.

8

theOldSheep commented on July 22, 2021, 10:57 p.m. ← edited →

I think printf("%.1f", area); also works :)

1

antboi commented on June 27, 2021, 10:25 p.m.

Saved me from hours of malding o7

2

JustinFan591 commented on May 30, 2021, 5:59 p.m.

Dude this really helped out a lot!!

6

EpicChadGamer commented on May 25, 2021, 8:25 p.m.

ORRRZZZZZ HOPE