Hamiltonish Path

AtCoder

IDagc013_b

Time2000ms

Memory256MB

Difficulty—

You are given a connected undirected simple graph, which has $N$ 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 $B_i$. Your task is to find a path that satisfies the following conditions: * The path traverses two or more vertices. * The path does not traverse the same vertex more than once. * A vertex directly connected to at least one of the endpoints of the path, is always contained in the path. It can be proved that such a path always exists. Also, if there are more than one solution, any of them will be accepted. ## Constraints * $2 \leq N \leq 10^5$ * $1 \leq M \leq 10^5$ * $1 \leq A_i < B_i \leq N$ * The given graph is connected and simple (that is, for every pair of vertices, there is at most one edge that directly connects them). ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $B_1$ $A_2$ $B_2$ $:$ $A_M$ $B_M$ [samples]

Samples

Input #1

Output #1

4
2 3 1 4

There are two vertices directly connected to vertex $2$: vertices $3$ and $4$. There are also two vertices directly connected to vertex $4$: vertices $1$ and $2$. Hence, the path $2$ → $3$ → $1$ → $4$ satisfies the conditions.

Input #2

Output #2

7
1 2 3 4 5 6 7

API Response (JSON)

{
  "problem": {
    "name": "Hamiltonish Path",
    "description": {
      "content": "You are given a connected undirected simple graph, which has $N$ vertices and $M$ edges. The vertices are numbered $1$ through $N$, and the edges are numbered $1$ through $M$. Edge $i$ connects vertic",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc013_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a connected undirected simple graph, which has $N$ vertices and $M$ edges. The vertices are numbered $1$ through $N$, and the edges are numbered $1$ through $M$. Edge $i$ connects vertic...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments