Copy and Paste Graph

AtCoder

IDarc159_a

Time2000ms

Memory256MB

Difficulty—

You are given an $N$\-by-$N$ matrix $A=(a_{i,j})$, where $a_{i,j} \in {0,1}$. We have the following directed graph. * The graph has $NK$ vertices numbered $1,2,\ldots,NK$. * The edges correspond to the $NK$\-by-$NK$ matrix $X=(x_{i,j})$ obtained by arranging $K^2$ copies of $A$ in $K$ rows and $K$ columns (see Sample Input/Output 1 for an example). If $x_{i,j}=1$, there is a directed edge from vertex $i$ to vertex $j$; if $x_{i,j}=0$, that edge does not exist. Answer the following question for $i=1,2,\ldots,Q$. * Find the shortest length (number of edges) of a path from vertex $s_i$ to vertex $t_i$. If there is no such path, print `-1` instead. ## Constraints * $1 \leq N \leq 100$ * $1 \leq K \leq 10^9$ * $a_{i,j} \in {0,1}$ * $1 \leq Q \leq 100$ * $1 \leq s_i,t_i \leq NK$ * $s_i \neq t_i$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $K$ $a_{1,1}$ $\ldots$ $a_{1,N}$ $\vdots$ $a_{N,1}$ $\ldots$ $a_{N,N}$ $Q$ $s_1$ $t_1$ $\vdots$ $s_Q$ $t_Q$ [samples]

Samples

Input #1

Output #1

1
1
1
3

Below is the matrix $X$ representing the edges.

1 1 1 1 1 1
1 1 0 1 1 0
0 1 0 0 1 0
1 1 1 1 1 1
1 1 0 1 1 0
0 1 0 0 1 0

Input #2

4 1000000000
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
1
1 4000000000

Output #2

\-1

There is no edge.

API Response (JSON)

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  "problem": {
    "name": "Copy and Paste Graph",
    "description": {
      "content": "You are given an $N$\\-by-$N$ matrix $A=(a_{i,j})$, where $a_{i,j} \\in {0,1}$. We have the following directed graph. *   The graph has $NK$ vertices numbered $1,2,\\ldots,NK$. *   The edges correspond ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc159_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an $N$\\-by-$N$ matrix $A=(a_{i,j})$, where $a_{i,j} \\in {0,1}$.\nWe have the following directed graph.\n\n*   The graph has $NK$ vertices numbered $1,2,\\ldots,NK$.\n*   The edges correspond ...",
      "is_translate": false,
      "language": "English"
    }
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}

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