We have a tree with n(n < 1e5) nodes and we have a constant k(k < 1e5) can we store the k'th ancestor of all nodes in an array or there is no way to do that??? Thank you for helping :)

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

1 | tourist | 4009 |

2 | jiangly | 3823 |

3 | Benq | 3738 |

4 | Radewoosh | 3633 |

5 | jqdai0815 | 3620 |

6 | orzdevinwang | 3529 |

7 | ecnerwala | 3446 |

8 | Um_nik | 3396 |

9 | ksun48 | 3390 |

10 | gamegame | 3386 |

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

1 | cry | 164 |

1 | maomao90 | 164 |

3 | Um_nik | 163 |

4 | atcoder_official | 160 |

5 | adamant | 158 |

5 | -is-this-fft- | 158 |

7 | awoo | 157 |

8 | TheScrasse | 154 |

8 | Dominater069 | 154 |

8 | nor | 154 |

We have a tree with n(n < 1e5) nodes and we have a constant k(k < 1e5) can we store the k'th ancestor of all nodes in an array or there is no way to do that??? Thank you for helping :)

↑

↓

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Nov/13/2024 17:15:24 (l2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|

easiest way is binary lifting to kth parent using sparse table (similar to lca).

space complexity:O(nlogn)

Complexity:O(nlogn)

Hi teja349 how can I do the binary search in O(logn)? I already know it in O(logn*logn) because I know the kth parent in O(logn) plus the binary search

let's say that

khas the following binary representation: 0011010This means that you need to climb up (2

^{1}= 2 nodes) + (2^{3}= 8 nodes) + (2^{4}= 16 nodes), the order doesn't matterTo do this you can loop over the bits of

kand if thei^{th}bit set, go up 2^{i}nodesSince we have

O(log_{2}(n)) bits, we go up by a power of two and we doO(1) work on the sparse table, the overall complexity isO(log_{2}(n))You can solve in O(N) by maintaining an explicit dfs stack in a vector as you dfs from the root. From each node you then look at the kth last thing in the vector if it exists.

I think this is actually much easier than using a sparse stable (although sparse tables can be easily extended to non constant k-th ancestor queries)