Red and Blue Spanning Tree

AtCoder

IDagc064_b

Time2000ms

Memory256MB

Difficulty—

You are given a connected undirected graph $G$ with $N$ vertices and $M$ edges. For each $i=1,2,\ldots,M$, the $i$\-th edge connects vertices $a_i$ and $b_i$, and is colored red if $c_i=$ `R` and blue if $c_i=$ `B`. Determine if there is a spanning tree of $G$ that satisfies the following condition, and if so, display such a tree. * For every $i=1,2,\ldots,N$, * if $s_i = $ `R`, at least one red edge has vertex $i$ as its endpoint; * if $s_i = $ `B`, at least one blue edge has vertex $i$ as its endpoint. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $N-1 \leq M \leq 2 \times 10^5$ * $1 \leq a_i \lt b_i \leq N$ * $c_i$ is `R` or `B`. * $(a_i,b_i,c_i) \neq (a_j,b_j,c_j)$ if $i \neq j$. * The given graph is connected. * $s_i$ is `R` or `B`. * $N,M,a_i,b_i$ are integers. ## Input The input is given from Standard Input in the following format: $N$ $M$ $a_1$ $b_1$ $c_1$ $\vdots$ $a_M$ $b_M$ $c_M$ $s_1 s_2 \ldots s_N$ [samples]

Samples

Input #1

3 3
1 2 R
1 3 B
2 3 B
RRB

Output #1

Yes
2 1

Here we show that the spanning tree formed by the first and second edges of $G$ satisfies the condition.

*   $s_1 = $ `R`, so for $i=1$, at least one red edge must have vertex $1$ as its endpoint. The first edge of $G$ is such an edge.
*   $s_2 = $ `R`, so for $i=2$, at least one red edge must have vertex $2$ as its endpoint. The first edge of $G$ is such an edge.
*   $s_3 = $ `B`, so for $i=3$, at least one blue edge must have vertex $3$ as its endpoint. The second edge of $G$ is such an edge.

Input #2

3 4
1 2 R
1 2 B
1 3 B
2 3 B
RRR

Output #2

No

Input #3

8 16
5 7 B
2 7 R
1 6 R
1 4 R
6 7 R
4 6 B
4 8 R
2 3 R
3 5 R
6 7 B
2 6 B
5 6 R
1 3 B
4 5 B
2 7 B
1 8 B
BRBRRBRB

Output #3

Yes
1 2 4 9 11 13 16

Input #4

8 10
1 7 R
1 3 B
2 5 B
2 8 R
1 5 R
3 6 R
2 6 B
3 4 B
2 8 B
4 6 B
RRRBBBRB

Output #4

No

API Response (JSON)

{
  "problem": {
    "name": "Red and Blue Spanning Tree",
    "description": {
      "content": "You are given a connected undirected graph $G$ with $N$ vertices and $M$ edges. For each $i=1,2,\\ldots,M$, the $i$\\-th edge connects vertices $a_i$ and $b_i$, and is colored red if $c_i=$ `R` and blue",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc064_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a connected undirected graph $G$ with $N$ vertices and $M$ edges. For each $i=1,2,\\ldots,M$, the $i$\\-th edge connects vertices $a_i$ and $b_i$, and is colored red if $c_i=$ `R` and blue...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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