Longest Path

AtCoder
IDdp_g
Time2000ms
Memory256MB
Difficulty
There is a directed graph $G$ with $N$ vertices and $M$ edges. The vertices are numbered $1, 2, \ldots, N$, and for each $i$ ($1 \leq i \leq M$), the $i$\-th directed edge goes from Vertex $x_i$ to $y_i$. $G$ **does not contain directed cycles**. Find the length of the longest directed path in $G$. Here, the length of a directed path is the number of edges in it. ## Constraints * All values in input are integers. * $2 \leq N \leq 10^5$ * $1 \leq M \leq 10^5$ * $1 \leq x_i, y_i \leq N$ * All pairs $(x_i, y_i)$ are distinct. * $G$ **does not contain directed cycles**. ## Input Input is given from Standard Input in the following format: $N$ $M$ $x_1$ $y_1$ $x_2$ $y_2$ $:$ $x_M$ $y_M$ [samples]
Samples
Input #1
4 5
1 2
1 3
3 2
2 4
3 4
Output #1
3

The red directed path in the following figure is the longest:
![image](https://img.atcoder.jp/dp/longest_0_muffet.png)
Input #2
6 3
2 3
4 5
5 6
Output #2
2

The red directed path in the following figure is the longest:
![image](https://img.atcoder.jp/dp/longest_1_muffet.png)
Input #3
5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3
Output #3
3

The red directed path in the following figure is one of the longest:
![image](https://img.atcoder.jp/dp/longest_2_muffet.png)
API Response (JSON)
{
  "problem": {
    "name": "Longest Path",
    "description": {
      "content": "There is a directed graph $G$ with $N$ vertices and $M$ edges. The vertices are numbered $1, 2, \\ldots, N$, and for each $i$ ($1 \\leq i \\leq M$), the $i$\\-th directed edge goes from Vertex $x_i$ to $y",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "dp_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a directed graph $G$ with $N$ vertices and $M$ edges. The vertices are numbered $1, 2, \\ldots, N$, and for each $i$ ($1 \\leq i \\leq M$), the $i$\\-th directed edge goes from Vertex $x_i$ to $y...",
      "is_translate": false,
      "language": "English"
    }
  ]
}
Full JSON Raw Segments