Erasing Vertices 2

AtCoder

IDabc267_e

Time4000ms

Memory256MB

Difficulty—

You are given a simple undirected graph with $N$ vertices and $M$ edges. The $i$\-th edge connects Vertices $U_i$ and $V_i$. Vertex $i$ has a positive integer $A_i$ written on it. You will repeat the following operation $N$ times. * Choose a Vertex $x$ that is not removed yet, and remove Vertex $x$ and all edges incident to Vertex $x$. The cost of this operation is the sum of the integers written on the vertices directly connected by an edge with Vertex $x$ that are not removed yet. We define the cost of the entire $N$ operations as the maximum of the costs of the individual operations. Find the minimum possible cost of the entire operations. ## Constraints * $1 \le N \le 2 \times 10^5$ * $0 \le M \le 2 \times 10^5$ * $1 \le A_i \le 10^9$ * $1 \le U_i,V_i \le N$ * The given graph is simple. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $A_2$ $\dots$ $A_N$ $U_1$ $V_1$ $U_2$ $V_2$ $\vdots$ $U_M$ $V_M$ [samples]

Samples

Input #1

Output #1

3

By performing the operations as follows, the maximum of the costs of the $N$ operations can be $3$.

*   Choose Vertex $3$. The cost is $A_1=3$.
*   Choose Vertex $1$. The cost is $A_2+A_4=3$.
*   Choose Vertex $2$. The cost is $0$.
*   Choose Vertex $4$. The cost is $0$.

The maximum of the costs of the $N$ operations cannot be $2$ or less, so the solution is $3$.

Input #2

7 13
464 661 847 514 74 200 188
5 1
7 1
5 7
4 1
4 5
2 4
5 2
1 3
1 6
3 5
1 2
4 6
2 7

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Erasing Vertices 2",
    "description": {
      "content": "You are given a simple undirected graph with $N$ vertices and $M$ edges. The $i$\\-th edge connects Vertices $U_i$ and $V_i$. Vertex $i$ has a positive integer $A_i$ written on it. You will repeat the ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc267_e"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a simple undirected graph with $N$ vertices and $M$ edges. The $i$\\-th edge connects Vertices $U_i$ and $V_i$. Vertex $i$ has a positive integer $A_i$ written on it.\nYou will repeat the ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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