Hello everyone. I have noticed the absence of round 273's editorial, so I decided to write one. This is the first time I write an editorial, so hope everyone like this!

I didn't know how to solve C and E yet, so it would be appreciated if someone help me with these problems.

Also, how to use LaTex in codeforces? I want to use this so my editorial would be more clear to read.

UDP: Actually, there's a (well-hidden) tutorial for this round, but it's written in Russian. If you can read Russian, click here.

# A — Initial Bet

Since the coin only pass from this player to other player, the coins sum of all player won’t change in the game. That mean, we’ll have `5*b = c1+c2+c3+c4+c5`

. We’ll put `sum = c1+c2+c3+c4+c5`

. So, if `sum is divisible by b`

, the answer will be `sum/b`

. Otherwise, the answer doesn’t exist.

Be careful with the case `0 0 0 0 0`

too, since `b > 0`

, answer doesn’t exist in this case.

**My solution:** 11607374

**Complexity: O(1)**

# B — Random Teams

If a team have `a`

participants, there will be `a*(a-1)/2`

pairs of friends formed.

For the minimum case, the participants should be unionly – distributed in all the team. More precisely, each team should not have more than one contestant compared to other team. Suppose we’ve already had `n div m`

contestant in each team, we’ll have `n mod m`

contestant left, we now should give each contestant left in first `n mod m`

teams.

For example, with the test `8 3`

, we’ll first give all team 8 div 3 = 2 contestants, the result now is `2 2 2`

. We’ll have 8 mod 3 = 2 contestants left, we should each contestant in the first and the second team, so the final result is: `3 3 2`

.

The maximum case is more simple, we should give only give one contestant in first `m-1`

teams, and give the last team all the contestant left. For example with above test, the result is `1 1 6`

.

Since number of the contestant in one team can be 10^9, the maximum numbers of pairs formed can be 10^18, so we should use `int64`

(`long long`

in c++) to avoid overflow.

**My solution:** 11607784

**Complexity: O(1)**

# C — Table Decorations

Unfinished...

# D — Red-Green Towers

For more convenient, we’ll call a function `trinum(x) = (x*(x+1))/ 2`

. First, we’ll find h, the maximum height possible of the tower. We know that `h <= trinum(l+r)`

. Since `(l+r) <= 2*10^5`

, `h <= 631`

, so we can just use a brute-force to fill this value.

Now, the main part of this problem, which can be solved by using dynamic programming. We’ll `f[ih, ir]`

the number of towers that have height `ih`

, can be built from `ir`

red block and `trinum(ih)-ir`

green blocks.

For each `f[ih, ir]`

, there’s two way to reach it:

Add

`ih`

red block. This can only be done if`ih <= ir <= min(r, trinum(ih))`

. In this case,`f[ih, ir] = f[ih, ir] + f[ih-1, ir-ih]`

.Add

`ih`

green block. This can only be done if`max(0, trinum(ih)-g) <= ir <= min(r, trinum(ih-1))`

. In this case,`f[ih, ir] = f[ih, ir] + f[ih-1, ir-ih]`

.

The answer to this problem is sum of all `f[h, ir]`

with `0 <= ir <= r`

.

We will probably get MLE now...

**MLE solution:** 11600887

How to improve the memory used? We'll see that all `f[ih]`

can only be affected by `f[ih-1]`

, so we'll used two one-dimension arrays to store the result instead of a two-dimension array. The solution should get accepted now.

**Accepted solution:** 11600930

**Complexity: O(r*sqrt(l+r))**

# E — Wavy numbers

Unfinished...