| № | Пользователь | Рейтинг |
|---|---|---|
| 1 | tourist | 3845 |
| 2 | jiangly | 3707 |
| 3 | Benq | 3630 |
| 4 | orzdevinwang | 3573 |
| 5 | Geothermal | 3569 |
| 5 | cnnfls_csy | 3569 |
| 7 | jqdai0815 | 3532 |
| 8 | ecnerwala | 3501 |
| 9 | gyh20 | 3447 |
| 10 | Rebelz | 3409 |
| Страны | Города | Организации | Всё → |
| № | Пользователь | Вклад |
|---|---|---|
| 1 | maomao90 | 171 |
| 2 | adamant | 163 |
| 3 | awoo | 161 |
| 4 | nor | 152 |
| 5 | maroonrk | 151 |
| 5 | -is-this-fft- | 151 |
| 7 | TheScrasse | 148 |
| 8 | atcoder_official | 146 |
| 9 | Petr | 145 |
| 10 | pajenegod | 144 |
How to solve this simple problem?
You are given a tree of N vertices, and an integer K. How many ways are there to colour the tree with K colours such that no edge is adjacent to vertices of the same colour.
Since the answer may be large, output the answer modulo 1,000,000,007.
Please explain how did u arrive at the result?
Answer is
Fix the color of vertex 1 in K ways. For every other vertex, you have K-1 choices.
how did you ensure the condition??
no edge is adjacent to vertices of the same colour.
root has k choices.. Then take the nodes at level 1 : they have k-1 choices as it is a tree and there are no cycles Similarly for nodes in level 2 as there can be only one parent, each of them has k-1 choices(excluding the color of its parent node) So root has k choices while the rest of the nodes have k-1 choices and hence you arrive at k*(k-1)^(n-1)