Splatter Painting

AtCoder

IDagc012_b

Time2000ms

Memory256MB

Difficulty—

Squid loves painting vertices in graphs. There is a simple undirected graph consisting of $N$ vertices numbered $1$ through $N$, and $M$ edges. Initially, all the vertices are painted in color $0$. The $i$\-th edge bidirectionally connects two vertices $a_i$ and $b_i$. The length of every edge is $1$. Squid performed $Q$ operations on this graph. In the $i$\-th operation, he repaints all the vertices within a distance of $d_i$ from vertex $v_i$, in color $c_i$. Find the color of each vertex after the $Q$ operations. ## Constraints * $1 ≤ N,M,Q ≤ 10^5$ * $1 ≤ a_i,b_i,v_i ≤ N$ * $a_i ≠ b_i$ * $0 ≤ d_i ≤ 10$ * $1 ≤ c_i ≤10^5$ * $d_i$ and $c_i$ are all integers. * There are no self-loops or multiple edges in the given graph. ## Input Input is given from Standard Input in the following format: $N$ $M$ $a_1$ $b_1$ $:$ $a_{M}$ $b_{M}$ $Q$ $v_1$ $d_1$ $c_1$ $:$ $v_{Q}$ $d_{Q}$ $c_{Q}$ ## Partial Score * $200$ points will be awarded for passing the testset satisfying $1 ≤ N,M,Q ≤ 2{,}000$. [samples]

Samples

Input #1

Output #1

2
2
2
2
2
1
0

Initially, each vertex is painted in color $0$. In the first operation, vertices $5$ and $6$ are repainted in color $1$. In the second operation, vertices $1$, $2$, $3$, $4$ and $5$ are repainted in color $2$.

![image](https://atcoder.jp/img/agc012/2ab7e180230b159d42d35ea7e555b3b0.png)

Input #2

Output #2

1
0
3
1
5
5
3
3
6
1
3
4
5
3

The given graph may not be connected.

API Response (JSON)

{
  "problem": {
    "name": "Splatter Painting",
    "description": {
      "content": "Squid loves painting vertices in graphs. There is a simple undirected graph consisting of $N$ vertices numbered $1$ through $N$, and $M$ edges. Initially, all the vertices are painted in color $0$. Th",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc012_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Squid loves painting vertices in graphs.\nThere is a simple undirected graph consisting of $N$ vertices numbered $1$ through $N$, and $M$ edges. Initially, all the vertices are painted in color $0$. Th...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments