Anybody would like to share some ideas? Thanks.

Anybody would like to share some ideas? Thanks.

Re: Anybody would like to share some ideas? Thanks.

Greedy algorithm.

For every bus you can comptute "Critical time"=p[i]+t[i]-i.

If 1st Bus from "Small Vasyuki" will pass the road after critical time of *i*th bus from "Small Vasyuki" then *i*th bus will be late. If *j*th bus from "Small Vasyuki" will pass the road after (critical time + j-1) then *i*th bus will be late.

If k1-1 buses from "Small Vasyuki" passed and k2-1 buses from "Big Vasyuki" passed then buses from direction with lower *critcaltime(of some bus)+k (k1 or k2)* are prefered.

*Edited by author 17.10.2010 14:17*

Re: Anybody would like to share some ideas? Thanks.

Get it.

Thank you.

Re: Anybody would like to share some ideas? Thanks.

Let 'l' and 'r' be the waiting buses on each direction.

Let l[i].f be l[i].t + l[i].p

I define the priority between buses as follows:

1. If l[i].t < r[j].t then l[i] should pass first.

2. If l[i].t > r[j].t then r[j] should pass first.

ELSE (l[i].t==r[j].t)

3. If l[i].f < r[j].f then l[i] should pass first.

4. If l[i].f > r[j].f then r[i] should pass first.

ELSE (l[i].f==r[j].f)

5. If l[i+1] should pass before r[j+1] then l[i] should pass first, else r[j]

Can anyone provide a counterexample for this approach?

Thanks in advance.

---

Nevermind, I was terribly wrong.

*Edited by author 18.10.2010 22:10*

Re: Anybody would like to share some ideas? Thanks.

Posted by

svr 19 Oct 2010 15:41

You said about greedy criterion as it is your discovery.

More rightly to note math theorem, name of schedulling

problem, article in wiki.

We have two decks of cards. On each step we dicide from which of them to take one card. For decision we must compare two new states acording two way of choice. You formula is criterion of compairing. But prove is unknown and criterion may be very deep but not absolute greedy.

*Edited by author 19.10.2010 16:01*

Re: Anybody would like to share some ideas? Thanks.

Consider the following algorithm:

current_time = 0

While there are buses, select a bus i according to Avriskin's priority.

If current_time + 1 > ti + pi then answer "NO" else current_time = max(current_time, ti) + 1 and erase the bus.

Does anyone see something wrong?

Re: Anybody would like to share some ideas? Thanks.

Posted by

RR 16 Jan 2011 21:36

I used simple dynamic programming :)