Two Faced Edges

AtCoder

IDarc092_d

Time5000ms

Memory256MB

Difficulty—

You are given a directed graph with $N$ vertices and $M$ edges. The vertices are numbered $1, 2, ..., N$, and the edges are numbered $1, 2, ..., M$. Edge $i$ points from Vertex $a_i$ to Vertex $b_i$. For each edge, determine whether the reversion of that edge would change the number of the strongly connected components in the graph. Here, the reversion of Edge $i$ means deleting Edge $i$ and then adding a new edge that points from Vertex $b_i$ to Vertex $a_i$. ## Constraints * $2 \leq N \leq 1000$ * $1 \leq M \leq 200,000$ * $1 \leq a_i, b_i \leq N$ * $a_i \neq b_i$ * If $i \neq j$, then $a_i \neq a_j$ or $b_i \neq b_j$. ## 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

same
diff
same

The number of the strongly connected components is $3$ without reversion of edges, but it will become $1$ if Edge $2$ is reversed.

Input #2

2 2
1 2
2 1

Output #2

diff
diff

Reversion of an edge may result in multiple edges in the graph.

Input #3

Output #3

same
same
same
same
same
diff
diff
diff
diff

API Response (JSON)

{
  "problem": {
    "name": "Two Faced Edges",
    "description": {
      "content": "You are given a directed graph with $N$ vertices and $M$ edges. The vertices are numbered $1, 2, ..., N$, and the edges are numbered $1, 2, ..., M$. Edge $i$ points from Vertex $a_i$ to Vertex $b_i$. ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 5000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc092_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a directed graph with $N$ vertices and $M$ edges. The vertices are numbered $1, 2, ..., N$, and the edges are numbered $1, 2, ..., M$. Edge $i$ points from Vertex $a_i$ to Vertex $b_i$.\n...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments