can anyone help in solving the following question.

consider a weighted undirected graph. There is a source S and destination D and a value K. Find the length of the shortest path such that you can make at most K edges 0.

# | User | Rating |
---|---|---|

1 | Benq | 3539 |

2 | tourist | 3532 |

3 | wxhtxdy | 3425 |

4 | Radewoosh | 3316 |

5 | ecnerwala | 3297 |

6 | mnbvmar | 3280 |

7 | LHiC | 3276 |

8 | Um_nik | 3260 |

9 | yutaka1999 | 3190 |

10 | TLE | 3145 |

# | User | Contrib. |
---|---|---|

1 | Errichto | 192 |

2 | Radewoosh | 179 |

3 | tourist | 172 |

4 | Vovuh | 167 |

4 | antontrygubO_o | 167 |

6 | PikMike | 166 |

7 | rng_58 | 160 |

8 | majk | 157 |

9 | Um_nik | 154 |

9 | 300iq | 154 |

can anyone help in solving the following question.

consider a weighted undirected graph. There is a source S and destination D and a value K. Find the length of the shortest path such that you can make at most K edges 0.

↑

↓

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Nov/14/2019 05:29:27 (h3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|

We can create a graph with $$$k$$$ layers — lets call it $$$G[n][k]$$$. For each edge $$$(v,u,w)$$$ we add two types of edges to our graph:

$$$G[v][i]$$$ — $$$G[u][i]$$$ with weight $$$w$$$ (standard edge, needs to be in each layer)

$$$G[v][i]$$$ — $$$G[u][i+1]$$$ with weight $$$0$$$ ("skipping" edge, also in each layer)

Now if we calculate minimum distances to each vertex in the whole graph, distance to $$$G[v][l]$$$ will mean minimum distance to vertex $$$v$$$ if we made exactly $$$l$$$ edges to be equal 0.

If the weights are positive we can use Dijkstra's algorithm to calculate minimum distances giving us $$$O(nk*log(nk))$$$ complexity.

If weights can be negative we use Bellman–Ford algorithm giving us $$$O(n^2k^2)$$$ comlpexity.

Note that we need to take minimum distance to $$$d$$$ in all layers in order to find the answer (we "skip"

at most$$$k$$$ edges)greg19 thanks for the solution. Can you please elaborate the process of adding an edge in the graph. And is it possible to have a dp solution??