Builder Takahashi

AtCoder

IDabc239_g

Time2000ms

Memory256MB

Difficulty—

We have a simple connected undirected graph with $N$ vertices and $M$ edges. The vertices are numbered as Vertex $1$, Vertex $2$, $\dots$, Vertex $N$. The edges are numbered as Edge $1$, Edge $2$, $\dots$, Edge $M$. Edge $i$ connects Vertex $a_i$ and Vertex $b_i$ bidirectionally. There is no edge that directly connects Vertex $1$ and Vertex $N$. Each vertex is either empty or occupied by a wall. Initially, every vertex is empty. Aoki is going to travel from Vertex $1$ to Vertex $N$ along the edges on the graph. However, Aoki is not allowed to move to a vertex occupied by a wall. Takahashi has decided to choose some of the vertices to build walls on, so that Aoki cannot travel to Vertex $N$ no matter which route he takes. Building a wall on Vertex $i$ costs Takahashi $c_i$ yen (the currency of Japan). **He cannot build a wall on Vertex $1$ and Vertex $N$**. How many yens is required for Takahashi to build walls so that the conditions is satisfied? Also, print the way of building walls to achieve the minimum cost. ## Constraints * $3 \leq N \leq 100$ * $N - 1 \leq M \leq \frac{N(N-1)}{2} - 1$ * $1 \leq a_i \lt b_i \leq N$ $(1 \leq i \leq M)$ * $(a_i, b_i) \neq (1, N)$ * The given graph is simple and connected. * $1 \leq c_{i} \leq 10^9$ $(2 \leq i \leq N-1)$ * $c_1 = c_N = 0$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $a_1$ $b_1$ $a_2$ $b_2$ $\vdots$ $a_M$ $b_M$ $c_1$ $c_2$ $\dots$ $c_N$ [samples]

Samples

Input #1

Output #1

7
2
3 4

If Takahashi builds walls on Vertex $3$ and Vertex $4$, paying $3 + 4 = 7$ yen, Aoki is unable to travel from Vertex $1$ to Vertex $5$.  
There is no way to satisfy the condition with less cost, so $7$ yen is the answer.

Input #2

Output #2

1
1
2

Input #3

5 9
1 2
1 3
1 4
2 3
2 4
2 5
3 4
3 5
4 5
0 1000000000 1000000000 1000000000 0

Output #3

3000000000
3
2 3 4

API Response (JSON)

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  "problem": {
    "name": "Builder Takahashi",
    "description": {
      "content": "We have a simple connected undirected graph with $N$ vertices and $M$ edges.   The vertices are numbered as Vertex $1$, Vertex $2$, $\\dots$, Vertex $N$.   The edges are numbered as Edge $1$, Edge $2$,",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc239_g"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a simple connected undirected graph with $N$ vertices and $M$ edges.  \nThe vertices are numbered as Vertex $1$, Vertex $2$, $\\dots$, Vertex $N$.  \nThe edges are numbered as Edge $1$, Edge $2$,...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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