Game on Tree

AtCoder

IDagc017_d

Time2000ms

Memory256MB

Difficulty—

There is a tree with $N$ vertices numbered $1, 2, ..., N$. The edges of the tree are denoted by $(x_i, y_i)$. On this tree, Alice and Bob play a game against each other. Starting from Alice, they alternately perform the following operation: * Select an existing edge and remove it from the tree, disconnecting it into two separate connected components. Then, remove the component that does not contain Vertex $1$. A player loses the game when he/she is unable to perform the operation. Determine the winner of the game assuming that both players play optimally. ## Constraints * $2 \leq N \leq 100000$ * $1 \leq x_i, y_i \leq N$ * The given graph is a tree. ## Input Input is given from Standard Input in the following format: $N$ $x_1$ $y_1$ $x_2$ $y_2$ : $x_{N-1}$ $y_{N-1}$ [samples]

Samples

Input #1

Output #1

Alice

If Alice first removes the edge connecting Vertices $1$ and $2$, the tree becomes a single vertex tree containing only Vertex $1$. Since there is no edge anymore, Bob cannot perform the operation and Alice wins.

Input #2

Output #2

Bob

Input #3

Output #3

Alice

Input #4

Output #4

Bob

API Response (JSON)

{
  "problem": {
    "name": "Game on Tree",
    "description": {
      "content": "There is a tree with $N$ vertices numbered $1, 2, ..., N$. The edges of the tree are denoted by $(x_i, y_i)$. On this tree, Alice and Bob play a game against each other. Starting from Alice, they alte",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc017_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a tree with $N$ vertices numbered $1, 2, ..., N$. The edges of the tree are denoted by $(x_i, y_i)$.\nOn this tree, Alice and Bob play a game against each other. Starting from Alice, they alte...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments