Destruction

AtCoder

IDabc218_e

Time2000ms

Memory256MB

Difficulty—

We have a connected undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1$ through $N$, and the edges are numbered $1$ through $M$. Edge $i$ connects Vertices $A_i$ and $B_i$. Takahashi is going to remove zero or more edges from this graph. When removing Edge $i$, a reward of $C_i$ is given if $C_i \geq 0$, and a fine of $|C_i|$ is incurred if $C_i<0$. Find the maximum total reward that Takahashi can get when the graph must be connected after removing edges. ## Constraints * $2 \leq N \leq 2\times 10^5$ * $N-1 \leq M \leq 2\times 10^5$ * $1 \leq A_i,B_i \leq N$ * $-10^9 \leq C_i \leq 10^9$ * The given graph is connected. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $B_1$ $C_1$ $A_2$ $B_2$ $C_2$ $\vdots$ $A_M$ $B_M$ $C_M$ [samples]

Samples

Input #1

Output #1

4

Removing Edges $4$ and $5$ yields a total reward of $4$. You cannot get any more, so the answer is $4$.

Input #2

Output #2

1

There may be edges that give a negative reward when removed.

Input #3

Output #3

5

There may be multi-edges and self-loops.

API Response (JSON)

{
  "problem": {
    "name": "Destruction",
    "description": {
      "content": "We have a connected undirected graph with $N$ vertices and $M$ edges.   The vertices are numbered $1$ through $N$, and the edges are numbered $1$ through $M$. Edge $i$ connects Vertices $A_i$ and $B_i",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc218_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a connected undirected graph with $N$ vertices and $M$ edges.  \nThe vertices are numbered $1$ through $N$, and the edges are numbered $1$ through $M$. Edge $i$ connects Vertices $A_i$ and $B_i...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments