Manhattan Christmas Tree 2

AtCoder

IDabc437_f

Time3000ms

Memory256MB

Difficulty—

There are $N$ Christmas trees on a two-dimensional plane. The $i$\-th $(1\le i\le N)$ Christmas tree is located at coordinates $(X_i,Y_i)$. You are given $Q$ queries. Process the queries in order. Each query is one of the following: * Type $1$ : Given in the form `1 i x y`. Change the coordinates of the $i$\-th Christmas tree to $(x,y)$. * Type $2$ : Given in the form `2 L R x y`. Output the Manhattan distance from the coordinates $(x,y)$ to the farthest Christmas tree among the $L,L+1,\ldots,R$\-th Christmas trees. Here, the Manhattan distance between coordinates $(x_1,y_1)$ and coordinates $(x_2,y_2)$ is defined as $|x_1-x_2|+|y_1-y_2|$. ## Constraints * $1\le N,Q\le 2\times 10^5$ * $-10^9\le X_i,Y_i\le 10^9$ * $1\le i\le N$ * $1\le L\le R\le N$ * $-10^9\le x,y\le 10^9$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $Q$ $X_1$ $Y_1$ $X_2$ $Y_2$ $\vdots$ $X_N$ $Y_N$ $\text{query}_1$ $\text{query}_2$ $\vdots$ $\text{query}_Q$ Here, the $i$\-th query $\text{query}_i$ is given in one of the following formats: $1$ $i$ $x$ $y$ $2$ $L$ $R$ $x$ $y$ [samples]

Samples

Input #1

Output #1

3
3
2

Initially, the $1$st, $2$nd, $3$rd Christmas trees are located at coordinates $(-1,-1)$, $(1,2)$, $(-2,1)$, respectively.
Each query is processed as follows:

*   The Manhattan distances from the $1$st and $2$nd Christmas trees to coordinates $(0,0)$ are $2$ and $3$, respectively. Thus, output $3$, which is the maximum value among $2,3$.
*   The Manhattan distances from the $1$st, $2$nd, $3$rd Christmas trees to coordinates $(-1,2)$ are $3$, $2$, $2$, respectively. Thus, output $3$, which is the maximum value among $3,2,2$.
*   Change the coordinates of the $1$st Christmas tree to $(0,1)$. The coordinates of the $1$st, $2$nd, $3$rd Christmas trees become $(0,1),(1,2),(-2,1)$, respectively.
*   The Manhattan distances from the $1$st, $2$nd, $3$rd Christmas trees to coordinates $(-1,2)$ are $2$, $2$, $2$, respectively. Thus, output $2$, which is the maximum value among $2,2,2$.

Input #2

5 7
-9 5
-2 -9
10 -6
9 8
2 9
1 3 -9 -6
2 3 4 2 7
1 4 -2 -10
2 1 2 0 -10
2 3 4 10 -9
2 3 4 8 7
2 5 5 0 2

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Manhattan Christmas Tree 2",
    "description": {
      "content": "There are $N$ Christmas trees on a two-dimensional plane. The $i$\\-th $(1\\le i\\le N)$ Christmas tree is located at coordinates $(X_i,Y_i)$. You are given $Q$ queries. Process the queries in order. Eac",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc437_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ Christmas trees on a two-dimensional plane. The $i$\\-th $(1\\le i\\le N)$ Christmas tree is located at coordinates $(X_i,Y_i)$.\nYou are given $Q$ queries. Process the queries in order. Eac...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments