Educational DP Contest AtCoder J - Sushi - Olympiads Online Judge

Educational DP Contest AtCoder J - Sushi

View as PDF

Submit solution

All submissions

Best submissions

Points: 12

Time limit: 1.0s

Memory limit: 1G

Problem types

There are $N$ ~N~ dishes, numbered $1, 2, \dots, N$ ~1, 2, \dots, N~. Initially, for each $i$ ~i~ $(1 \le i \le N)$ ~(1 \le i \le N)~, Dish $i$ ~i~ has $a_i$ ~a_i~ $(1 \le a_i \le 3)$ ~(1 \le a_i \le 3)~ pieces of sushi on it.

Taro will perform the following operation repeatedly until all the pieces of sushi are eaten:

Roll a die that shows the numbers $1, 2, \dots, N$ ~1, 2, \dots, N~ with equal probabilities, and let $i$ ~i~ be the outcome. If there are some pieces of sushi on Dish $i$ ~i~, eat one of them; if there is none, do nothing.

Find the expected number of times the operation is performed before all the pieces of sushi are eaten.

Constraints

All values in input are integers.
$1 \le N \le 300$ ~1 \le N \le 300~
$1 \le a_i \le 3$ ~1 \le a_i \le 3~

Input Specification

The first line will contain the integer $N$ ~N~.

The next line will contain $N$ ~N~ integers, $a_1, a_2, \dots, a_N$ ~a_1, a_2, \dots, a_N~.

Output Specification

Print the expected number of times the operation is performed before all the pieces of sushi are eaten. The output is considered correct when the relative difference is not greater than $10^{-9}$ ~10^{-9}~.

Sample Input 1

3
1 1 1

Sample Output 1

5.5

Explanation For Sample 1

The expected number of operations before the first piece of sushi is eaten, is $1$ ~1~. After that, the expected number of operations before the second sushi is eaten, is $1.5$ ~1.5~. After that, the expected number of operations before the third sushi is eaten, is $3$ ~3~. Thus, the expected total number of operations is $1+1.5+3=5.5$ ~1+1.5+3=5.5~.

Sample Input 2

1
3

Sample Output 2

Explanation For Sample 2

Outputs such as 3.00, 3.000000003 and 2.999999997 will also be accepted.

Sample Input 3

2
1 2

Sample Output 3

4.5

Sample Input 4

10
1 3 2 3 3 2 3 2 1 3

Sample Output 4

54.48064457488221

Comments

0
TUSA commented on Feb. 25, 2026, 8:54 p.m.
Not sure why Time Limit is 1.0s here when AtCoder J gives 2.0s.

My favorite part in implementing this in Python was when the algorithmic flow and pruning logic was spot on, but TLE'd on DMOJ while not on AtCoder

Was found to be attributed simply due to the initial allocation step being too hefty

Honorable mention to cpp for entirely circumventing the need to even care about this

0.178s at most compared to >1.0s TLE in Python equivilent code

Honorable mention also during debugging process when Python3 timed out on AtCoder while PyPy3 worked with the same exact submission

-1

do_ur_homwork commented on Feb. 25, 2026, 8:58 p.m.

I believe the DMOJ judge is faster that the AtCoder one. Also pypy is usually faster that python but uses more memory. (noter that i havent tried this problem yet)

0

dchoo333 commented on Feb. 26, 2026, 1:56 a.m.

I believe this could be relevant