K-th Largest Connected Components

AtCoder

IDabc372_e

Time2000ms

Memory256MB

Difficulty—

There is an undirected graph with $N$ vertices and $0$ edges. The vertices are numbered $1$ to $N$. You are given $Q$ queries to process in order. Each query is of one of the following two types: * Type $1$: Given in the format `1 u v`. Add an edge between vertices $u$ and $v$. * Type $2$: Given in the format `2 v k`. Print the $k$\-th largest vertex number among the vertices connected to vertex $v$. If there are fewer than $k$ vertices connected to $v$, print `-1`. ## Constraints * $1 \leq N, Q \leq 2 \times 10^5$ * In a Type $1$ query, $1 \leq u < v \leq N$. * In a Type $2$ query, $1 \leq v \leq N$, $1 \leq k \leq 10$. * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $Q$ $\mathrm{query}_1$ $\mathrm{query}_2$ $\vdots$ $\mathrm{query}_Q$ Here, $\mathrm{query}_i$ is the $i$\-th query and is given in one of the following formats: $1$ $u$ $v$ $2$ $v$ $k$ [samples]

Samples

Input #1

Output #1

2
1
-1
4
2
-1

*   In the first query, an edge is added between vertices $1$ and $2$.
*   In the second query, two vertices are connected to vertex $1$: $1$ and $2$. Among them, the $1$\-st largest vertex number is $2$, which should be printed.
*   In the third query, two vertices are connected to vertex $1$: $1$ and $2$. Among them, the $2$\-nd largest vertex number is $1$, which should be printed.
*   In the fourth query, two vertices are connected to vertex $1$: $1$ and $2$, which is fewer than $3$, so print `-1`.
*   In the fifth query, an edge is added between vertices $1$ and $3$.
*   In the sixth query, an edge is added between vertices $2$ and $3$.
*   In the seventh query, an edge is added between vertices $3$ and $4$.
*   In the eighth query, four vertices are connected to vertex $1$: $1,2,3,4$. Among them, the $1$\-st largest vertex number is $4$, which should be printed.
*   In the ninth query, four vertices are connected to vertex $1$: $1,2,3,4$. Among them, the $3$\-rd largest vertex number is $2$, which should be printed.
*   In the tenth query, four vertices are connected to vertex $1$: $1,2,3,4$, which is fewer than $5$, so print `-1`.

Input #2

Output #2

API Response (JSON)

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  "problem": {
    "name": "K-th Largest Connected Components",
    "description": {
      "content": "There is an undirected graph with $N$ vertices and $0$ edges. The vertices are numbered $1$ to $N$. You are given $Q$ queries to process in order. Each query is of one of the following two types: *  ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc372_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is an undirected graph with $N$ vertices and $0$ edges. The vertices are numbered $1$ to $N$.\nYou are given $Q$ queries to process in order. Each query is of one of the following two types:\n\n*  ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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