Graph Partition

AtCoder

IDagc039_b

Time2000ms

Memory256MB

Difficulty—

Given is a connected undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$, and the edges are described by a grid of characters $S$. If $S_{i,j}$ is `1`, there is an edge connecting Vertex $i$ and $j$; otherwise, there is no such edge. Determine whether it is possible to divide the vertices into non-empty sets $V_1, \dots, V_k$ such that the following condition is satisfied. If the answer is yes, find the maximum possible number of sets, $k$, in such a division. * Every edge connects two vertices belonging to two "adjacent" sets. More formally, for every edge $(i,j)$, there exists $1\leq t\leq k-1$ such that $i\in V_t,j\in V_{t+1}$ or $i\in V_{t+1},j\in V_t$ holds. ## Constraints * $2 \leq N \leq 200$ * $S_{i,j}$ is `0` or `1`. * $S_{i,i}$ is `0`. * $S_{i,j}=S_{j,i}$ * The given graph is connected. * $N$ is an integer. ## Input Input is given from Standard Input in the following format: $N$ $S_{1,1}...S_{1,N}$ $:$ $S_{N,1}...S_{N,N}$ [samples]

Samples

Input #1

2
01
10

Output #1

2

We can put Vertex $1$ in $V_1$ and Vertex $2$ in $V_2$.

Input #2

Output #2

\-1

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Graph Partition",
    "description": {
      "content": "Given is a connected undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$, and the edges are described by a grid of characters $S$. If $S_{i,j}$ is `1`, there is an e",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc039_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a connected undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$, and the edges are described by a grid of characters $S$. If $S_{i,j}$ is `1`, there is an e...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments