Shortest Path on a Line

AtCoder

IDnikkei2019_2_qual_d

Time2000ms

Memory256MB

Difficulty—

We have $N$ points numbered $1$ to $N$ arranged in a line in this order. Takahashi decides to make an undirected graph, using these points as the vertices. In the beginning, the graph has no edge. Takahashi will do $M$ operations to add edges in this graph. The $i$\-th operation is as follows: * The operation uses integers $L_i$ and $R_i$ between $1$ and $N$ (inclusive), and a positive integer $C_i$. For every pair of integers $(s, t)$ such that $L_i \leq s < t \leq R_i$, add an edge of length $C_i$ between Vertex $s$ and Vertex $t$. The integers $L_1, ..., L_M$, $R_1, ..., R_M$, $C_1, ..., C_M$ are all given as input. Takahashi wants to solve the shortest path problem in the final graph obtained. Find the length of the shortest path from Vertex $1$ to Vertex $N$ in the final graph. ## Constraints * $2 \leq N \leq 10^5$ * $1 \leq M \leq 10^5$ * $1 \leq L_i < R_i \leq N$ * $1 \leq C_i \leq 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $M$ $L_1$ $R_1$ $C_1$ $:$ $L_M$ $R_M$ $C_M$ [samples]

Samples

Input #1

Output #1

5

We have an edge of length $2$ between Vertex $1$ and Vertex $2$, and an edge of length $3$ between Vertex $2$ and Vertex $4$, so there is a path of length $5$ between Vertex $1$ and Vertex $4$.

Input #2

4 2
1 2 1
3 4 2

Output #2

\-1

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Shortest Path on a Line",
    "description": {
      "content": "We have $N$ points numbered $1$ to $N$ arranged in a line in this order. Takahashi decides to make an undirected graph, using these points as the vertices. In the beginning, the graph has no edge. Tak",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "nikkei2019_2_qual_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have $N$ points numbered $1$ to $N$ arranged in a line in this order.\nTakahashi decides to make an undirected graph, using these points as the vertices. In the beginning, the graph has no edge. Tak...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments