Friend Suggestions

AtCoder

IDabc157_d

Time2000ms

Memory256MB

Difficulty—

An SNS has $N$ users - User $1$, User $2$, $\cdots$, User $N$. Between these $N$ users, there are some relationships - $M$ _friendships_ and $K$ _blockships_. For each $i = 1, 2, \cdots, M$, there is a bidirectional friendship between User $A_i$ and User $B_i$. For each $i = 1, 2, \cdots, K$, there is a bidirectional blockship between User $C_i$ and User $D_i$. We define User $a$ to be a _friend candidate_ for User $b$ when all of the following four conditions are satisfied: * $a \neq b$. * There is not a friendship between User $a$ and User $b$. * There is not a blockship between User $a$ and User $b$. * There exists a sequence $c_0, c_1, c_2, \cdots, c_L$ consisting of integers between $1$ and $N$ (inclusive) such that $c_0 = a$, $c_L = b$, and there is a friendship between User $c_i$ and $c_{i+1}$ for each $i = 0, 1, \cdots, L - 1$. For each user $i = 1, 2, ... N$, how many friend candidates does it have? ## Constraints * All values in input are integers. * $2 ≤ N ≤ 10^5$ * $0 \leq M \leq 10^5$ * $0 \leq K \leq 10^5$ * $1 \leq A_i, B_i \leq N$ * $A_i \neq B_i$ * $1 \leq C_i, D_i \leq N$ * $C_i \neq D_i$ * $(A_i, B_i) \neq (A_j, B_j) (i \neq j)$ * $(A_i, B_i) \neq (B_j, A_j)$ * $(C_i, D_i) \neq (C_j, D_j) (i \neq j)$ * $(C_i, D_i) \neq (D_j, C_j)$ * $(A_i, B_i) \neq (C_j, D_j)$ * $(A_i, B_i) \neq (D_j, C_j)$ ## Input Input is given from Standard Input in the following format: $N$ $M$ $K$ $A_1$ $B_1$ $\vdots$ $A_M$ $B_M$ $C_1$ $D_1$ $\vdots$ $C_K$ $D_K$ [samples]

Samples

Input #1

Output #1

0 1 0 1

There is a friendship between User $2$ and $3$, and between $3$ and $4$. Also, there is no friendship or blockship between User $2$ and $4$. Thus, User $4$ is a friend candidate for User $2$.
However, neither User $1$ or $3$ is a friend candidate for User $2$, so User $2$ has one friend candidate.

Input #2

Output #2

0 0 0 0 0

Everyone is a friend of everyone else and has no friend candidate.

Input #3

Output #3

1 3 5 4 3 3 3 3 1 0

API Response (JSON)

{
  "problem": {
    "name": "Friend Suggestions",
    "description": {
      "content": "An SNS has $N$ users - User $1$, User $2$, $\\cdots$, User $N$. Between these $N$ users, there are some relationships - $M$ _friendships_ and $K$ _blockships_. For each $i = 1, 2, \\cdots, M$, there is ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc157_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "An SNS has $N$ users - User $1$, User $2$, $\\cdots$, User $N$.\nBetween these $N$ users, there are some relationships - $M$ _friendships_ and $K$ _blockships_.\nFor each $i = 1, 2, \\cdots, M$, there is ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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