##### Canadian Computing Competition: 2005 Stage 1, Senior #5

Pinball is an arcade game in which an individual player controls a silver ball by means of flippers, with the objective of accumulating as many points as possible. At the end of each game, the player's score and rank are displayed. The score, an integer between and , is that achieved by the player in the game just ended. The rank is displayed as " of ". is the total number of games ever played on the machine, and is the position of the score for the just-ended game within this set.

*More precisely, is one greater than the number of games whose score exceeds that of the game just ended.*

#### Input Specification

You are to implement the pinball machine's ranking algorithm. The first line of input contains a positive integer, , the total number of games played in the lifetime of the machine. lines follow, given the scores of these games, in chronological order.

#### Output Specification

You are to output the average of the ranks up to an absolute error of that would be displayed on the board.

At least one test case will have . All test cases will have .

#### Sample Input

```
5
100
200
150
170
50
```

#### Sample Output

`2.20`

#### Explanation for Sample Output

The pinball screen would display (in turn):

```
1 of 1
1 of 2
2 of 3
2 of 4
5 of 5
```

The average rank is .

## Comments

Since the data were not language friendly, the specificity for the answer has been updated (refer to the problem statement), and all submissions were rejudged.

If you find that you're WA on only test case 4, it's likely an issue with your rounding.

The test data was generated with an implementation of round which rounds towards even, thus

round(4.5) -> 4, but round(5.5) -> 6.Change your round function accordingly. In C/C++, you can just use

`rint()`

instead of`std::round()`

.In case you wanted to see what life was like before C++11: http://man7.org/linux/man-pages/man3/lrint.3.html

It appears that the statement

`rounded to two digits after the decimal`

is slightly misleading and should actually say`truncated to two digits after the decimal`

. Most of the accepted solutions and the official CCC data incorrectly rounded in the 4th test case due to double precision issues.(For longer version, see comment edit history)

You're correct -- the test data is actually incorrect with respect to the problem statement: but it's not supposed to be truncation either.

Before C++11 introduced std::round(), people had to implement their own round functions, or use

`rint`

/`lrint`

, which reads your system state for the "rounding mode". The default rounding mode for IEEE 754 floating point operations is Banker's Rounding, which rounds halfway numbers to even integers. I believe this is the rounding used to generate the test case, which rounded 24794.5 to 24794.Note that this is not the behavior of std::round.

EDIT: Looking at many of the other user submissions, many people are just using

`printf("%.2f", ans);`

. This just rounds the answer to two decimal places using`rint`

as the backend I think.Can we assume no two input are the same?

If they are the same, what should I output?

Inputs are not necessarily distinct

I implemented BST and still got TLE? Is there something faster?

Read this for more info.

According to DMOJ my code is too slow, but I run the test-files from CCC's website and it finishes all of them instantly. Is my approach wrong? I feel like the 1sec time limit is too close to my solution or something.

Your solution is $(O(N^2\ log N)$ because insertion into an ArrayList at an arbitrary position is $O(N)$ time

Really? Okay thanks a lot!

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