I usually like to wait for chrome or someone else to remind all you good folk about an upcoming SRM but it seems like they have forgotten. So here goes.

Hi there!

Tomorrow at 6:30 IST will be held Topcoder SRM 661.

Let's discuss problems after contest!

GL && HF.

Anyone knows about the

goodies, rankwise or random?Will you be able to wake up in time? :P

real question is, how you are still awake? :P

(source: prequeladventure.com, go read it)

Reminder for anyone who is awake but not registered. 5 minutes left till end of registration.

Congratulations to Swistakk on finally getting into top5 :)

BTW, can someone please explain where does that magic formula for div1 450 come from?

if you mean i(k — 1) + 1 then i can explain : we either take no edges for the i'th node then we can color it with k colors else we can take either of the (i-1) edges and since this nodes color can't be the same as the node where the edge is pointing we can color it with k — 1 colors thus it's (k-1)(i-1) + k = i(k-1) + 1

Thanks... Now after your explanation it sounds so obvious and easy)

And I had to write a brute force to get the formula :(

you're welcome xD it took a time for me to get it that's why i couldn't complete it :((

Yeah, similar situation here too. I came to a formula thas was wrong, coded it, forgot to add a couple of lines and it magically worked (yeah, coding it wrong fixed the formula). I was really lucky there.

Daaaamn. Just noticed that we had to pick only one edge. I was making a formula thinking if at the ith node I have degree 0, or degree 1, or degree 2.... to get a recurrence with binomial coefficients in it.

Is my misread version of the problem solvable?

sounds pretty damn hard

i noticed it just after seeing your comment :(

to Sumeet.Varma and akulsareen:

it's always better if you check that you completely understand the samples before you start thinking of the problem, even if you think your self that you understand the problem completely

I learnt that lesson after one of my previous contest I participated

Can somebody tell me what is the problem with this code for Div1 450? Thanks in advance!

Plot twist: Petr forget to cover today's SRM

Whats your handle on TC?

How to solve Div2 500?

Since constraint is only 11, we can simply iterate over all possible combinations of bridges to build and then run a Floyd-Warshall on each of them to find the diameter. (By finding max of distance between 2 nodes)

Thank you! minimario we were in one room. my handle is leon_kg on topcoder

Hey, can you explain the recurrence for div2 1000?

it's easy DP

You have to choose k elements out of n elements(k <= n);

So iterate from 0 to (1 << n), if number of set bits is equal to k , use all pair shortest path(floyd-warshall).

My implementation of Floyd was wrong which made me nervous and I could not complete in Time.

950 < 500 < 250

Div-2 contestants will understand -_-

Well, I did solve only 1000 in div1 :D (why did I have to misread 250...)

Positions of guys who have solved 1000 — 1, 2, 3, 4 and 63 xD

How to solve div2 1000? Was there some

magicformula there?Imagine that you are constructing the same graphs but in a different way: for each i between 1 and N, inclusive, you:

Now I think I should have spent a little more time on the 1000(in today's case 950) rather than the 500. :(

Okay, so for some i<=n, shouldn't the correct relation be

`ans = ans * (k + (k-1)*(i-1)*k)`

?Where the second term means : Colour the current value in k ways, and have i-1 possible edges leading to k-1 different colours?

no the recurrence is something like

f(1) = K, as we can choose one node with colour 1, 2, ..., K

f(n) = K*f(n-1) + (n-1)*(K-1)*f(n-1)

the first term is translation to: put the n-th node on the right side of the f(n-1) old graphs choosing its colour to be 1, 2, ..., K

and about the (k-1)*f(n-1) it is about: for some i in the range 1<= i <=n-1 (so there is (n-1) such i) put the n-th node and connect it with an edge to this i-th node we can do that only if n-th colour is different from i-th colour which allows to choose (K-1) colour

Yes, but regarding the second term, Shouldn't you select the current element's colour in K ways, and the for each of these colours, an edge which leads to the n-1 elements each with k-1 colours?

yes I understand what you mean, the approach written above is about another approach from what you are thinking. In my opinion it is simpler. However if you want to solve it considering the idea you have, you have to change the definition of f(n), for the approach above f(n) = the number of graphs that can be constructed in the way mentioned in the problem statement (and have n nodes) using all K colours. Maybe for your approach you have to define something like f(n, m) = the number of graphs that can be constructed in the way mentioned in the problem statement (and have n nodes) using m colours or something else.

Approach to solve Div1 250 plaease?

Since

LCM(N+ 1..M)|LCM(1..M) (think why) and LCM is the product of maximum prime powers dividing some number in the respective ranges, you only needMlarge enough for anyp^{k}that divides some number ≤N(i.e. anyp^{k}≤N, but you don't need this) to divide also some numberxbetweenN+ 1 andM(the smallest suchx), soMis the maximum of thesex. Therefore, you just need to factorise all numbers up toNby the sieve of Erathostenes.Btw, Can you prove that in fact we only need to consider

p^{k}- > 2p^{k}and that all casesxp^{k}- > (x+ 1)p^{k}are not needed? It is sufficient to prove that there is any power in an interval and that is in fact true even for just primes (maybe for sufficiently large n's), but it's some freaking hard math xd.Hmm idk, but I can finally prove that a non-constant polynomial has at least one root :D. Complex calculus is weird in many ways.