Tree and Hamilton Path 2

AtCoder

IDabc361_e

Time2000ms

Memory256MB

Difficulty—

In the nation of AtCoder, there are $N$ cities numbered $1$ to $N$ and $N-1$ roads numbered $1$ to $N-1$. Road $i$ connects cities $A_i$ and $B_i$ bidirectionally, and its length is $C_i$. Any pair of cities can be reached from each other by traveling through some roads. Find the minimum travel distance required to start from a city and visit all cities at least once using the roads. ## Constraints * $2 \leq N \leq 2\times 10^5$ * $1 \leq A_i, B_i \leq N$ * $1 \leq C_i \leq 10^9$ * All input values are integers. * Any pair of cities can be reached from each other by traveling through some roads. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $B_1$ $C_1$ $\vdots$ $A_{N-1}$ $B_{N-1}$ $C_{N-1}$ [samples]

Samples

Input #1

Output #1

11

If you travel as $4 \to 1 \to 2 \to 1 \to 3$, the total travel distance is $11$, which is the minimum.
Note that you do not need to return to the starting city.

Input #2

10
10 9 1000000000
9 8 1000000000
8 7 1000000000
7 6 1000000000
6 5 1000000000
5 4 1000000000
4 3 1000000000
3 2 1000000000
2 1 1000000000

Output #2

9000000000

Beware overflow.

API Response (JSON)

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  "problem": {
    "name": "Tree and Hamilton Path 2",
    "description": {
      "content": "In the nation of AtCoder, there are $N$ cities numbered $1$ to $N$ and $N-1$ roads numbered $1$ to $N-1$. Road $i$ connects cities $A_i$ and $B_i$ bidirectionally, and its length is $C_i$. Any pair of",
      "description_type": "Markdown"
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      "memory_limit": 262144
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "In the nation of AtCoder, there are $N$ cities numbered $1$ to $N$ and $N-1$ roads numbered $1$ to $N-1$.\nRoad $i$ connects cities $A_i$ and $B_i$ bidirectionally, and its length is $C_i$. Any pair of...",
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}

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