Subsequence Path

AtCoder

IDabc271_e

Time2000ms

Memory256MB

Difficulty—

There are $N$ towns numbered $1, \dots, N$, and $M$ roads numbered $1, \dots, M$. Every road is directed; road $i$ $(1 \leq i \leq M)$ leads you from Town $A_i$ to Town $B_i$. The length of road $i$ is $C_i$. You are given a sequence $E = (E_1, \dots, E_K)$ of length $K$ consisting of integers between $1$ and $M$. A way of traveling from town $1$ to town $N$ using roads is called a **good path** if: * the sequence of the roads' numbers arranged in the order used in the path is a subsequence of $E$. Note that a subsequence of a sequence is a sequence obtained by removing $0$ or more elements from the original sequence and concatenating the remaining elements without changing the order. Find the minimum sum of the lengths of the roads used in a good path. If there is no good path, report that fact. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $1 \leq M, K \leq 2 \times 10^5$ * $1 \leq A_i, B_i \leq N, A_i \neq B_i \, (1 \leq i \leq M)$ * $1 \leq C_i \leq 10^9 \, (1 \leq i \leq M)$ * $1 \leq E_i \leq M \, (1 \leq i \leq K)$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $M$ $K$ $A_1$ $B_1$ $C_1$ $\vdots$ $A_M$ $B_M$ $C_M$ $E_1$ $\ldots$ $E_K$ [samples]

Samples

Input #1

Output #1

4

There are two possible good paths as follows:

*   Using road $4$. In this case, the sum of the length of the used road is $5$.
*   Using road $1$ and $2$ in this order. In this case, the sum of the lengths of the used roads is $2 + 2 = 4$.

Therefore, the desired minimum value is $4$.

Input #2

Output #2

\-1

There is no good path.

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Subsequence Path",
    "description": {
      "content": "There are $N$ towns numbered $1, \\dots, N$, and $M$ roads numbered $1, \\dots, M$.   Every road is directed; road $i$ $(1 \\leq i \\leq M)$ leads you from Town $A_i$ to Town $B_i$. The length of road $i$",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc271_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ towns numbered $1, \\dots, N$, and $M$ roads numbered $1, \\dots, M$.  \nEvery road is directed; road $i$ $(1 \\leq i \\leq M)$ leads you from Town $A_i$ to Town $B_i$. The length of road $i$...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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