Tree Degree Subset Sum

AtCoder

IDarc125_f

Time6000ms

Memory256MB

Difficulty—

Given is a tree with $N$ vertices. The vertices are numbered $1$ through $N$, and the $i$\-th edge connects Vertex $A_i$ and Vertex $B_i$. Find the number of pairs of integers $(x,y)$ that satisfy the following conditions. * $0 \leq x \leq N$. * There is a way to choose exactly $x$ vertices from the tree so that the sum of their degrees equals $y$. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $1 \leq A_i < B_i \leq N$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $B_1$ $A_2$ $B_2$ $\vdots$ $A_{N-1}$ $B_{N-1}$ [samples]

Samples

Input #1

3
1 2
2 3

Output #1

6

The following six pairs $(x,y)$ satisfy the conditions.

*   $x=0,y=0$
*   $x=1,y=1$
*   $x=1,y=2$
*   $x=2,y=2$
*   $x=2,y=3$
*   $x=3,y=4$

$x=2,y=3$, for example, satisfies the condition because choosing Vertex $1$ and Vertex $2$ achieves the total degree of $3$.

Input #2

Output #2

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Tree Degree Subset Sum",
    "description": {
      "content": "Given is a tree with $N$ vertices. The vertices are numbered $1$ through $N$, and the $i$\\-th edge connects Vertex $A_i$ and Vertex $B_i$. Find the number of pairs of integers $(x,y)$ that satisfy the",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 6000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc125_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a tree with $N$ vertices. The vertices are numbered $1$ through $N$, and the $i$\\-th edge connects Vertex $A_i$ and Vertex $B_i$.\nFind the number of pairs of integers $(x,y)$ that satisfy the...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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