Road Reduction

AtCoder

IDabc252_e

Time2000ms

Memory256MB

Difficulty—

The Kingdom of AtCoder has $N$ cities called City $1,2,\ldots,N$ and $M$ roads called Road $1,2,\ldots,M$. Road $i$ connects Cities $A_i$ and $B_i$ bidirectionally and has a length of $C_i$. One can travel between any two cities using some roads. Under financial difficulties, the kingdom has decided to maintain only $N-1$ roads so that one can still travel between any two cities using those roads and abandon the rest. Let $d_i$ be the total length of the roads one must use when going from City $1$ to City $i$ using only maintained roads. Print a choice of roads to maintain that minimizes $d_2+d_3+\ldots+d_N$. ## Constraints * $2 \leq N \leq 2\times 10^5$ * $N-1 \leq M \leq 2\times 10^5$ * $1 \leq A_i < B_i \leq N$ * $(A_i,B_i)\neq(A_j,B_j)$ if $i\neq j$. * $1\leq C_i \leq 10^9$ * One can travel between any two cities using some roads. * 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

1 2

Here are the possible choices of roads to maintain and the corresponding values of $d_i$.

*   Maintain Road $1$ and $2$: $d_2=1$, $d_3=3$.
*   Maintain Road $1$ and $3$: $d_2=1$, $d_3=10$.
*   Maintain Road $2$ and $3$: $d_2=12$, $d_3=10$.

Thus, maintaining Road $1$ and $2$ minimizes $d_2+d_3$.

Input #2

Output #2

3 1 2

API Response (JSON)

{
  "problem": {
    "name": "Road Reduction",
    "description": {
      "content": "The Kingdom of AtCoder has $N$ cities called City $1,2,\\ldots,N$ and $M$ roads called Road $1,2,\\ldots,M$.   Road $i$ connects Cities $A_i$ and $B_i$ bidirectionally and has a length of $C_i$.   One c",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc252_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "The Kingdom of AtCoder has $N$ cities called City $1,2,\\ldots,N$ and $M$ roads called Road $1,2,\\ldots,M$.  \nRoad $i$ connects Cities $A_i$ and $B_i$ bidirectionally and has a length of $C_i$.  \nOne c...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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