Interesting problem with DAG

tom's blog

By tom, 11 years ago, In English

Problem for you for today's evening:

You are given DAG with N < = 1000 vertexes and M < = 10000 edges. Vertex 0 is starting vertex and vertex 1 is goal vertex. Set weights to edges from {1, 2} in that way that all paths from start to goal will have the same distance or print "NO" if it's not possible.

dag, distance

tom
11 years ago
5

Comments (5)

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StarCuriosity

11 years ago, hide # |

← Rev. 2 →

Can I submit this problem or download tests somewhere? I have an idea, but I can't prove it.

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Reyna

11 years ago, hide # ^ |

+21

it's problem 241E

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adelnobel

11 years ago, hide # ^ |

← Rev. 3 →

A similar problem also appeared in a previous world finals where you could increase the weights on edges and you had to find the minimal increase required.

Fare and balanced — Stockholm 2009

https://icpcarchive.ecs.baylor.edu/index.php?option=com_onlinejudge&Itemid=8&category=43&page=show_problem&problem=2450

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tom

11 years ago, hide # ^ |

Thanks, I didn't know that.

I found pretty code from gawry — 2616676
I don't understand one thing.

How do we know which value (d[a[i]] or d[b[i]]) we should change? I understand constraints and I know it works (he got Accepted :)), but it seems to me unclear. Can anybody help me?

Lines:

if(d[a[i]]+2<d[b[i]])change=true,d[b[i]]=d[a[i]]+2;
if(d[b[i]]-1<d[a[i]])change=true,d[a[i]]=d[b[i]]-1;

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ed1d1a8d

11 years ago, hide # ^ |

We change whichever value is on the right side of the inequality. The code is essentially running Bellman-Ford, so the change can be thought of as an edge relaxation.

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