Operations on a Matrix

AtCoder

IDabc253_f

Time2000ms

Memory256MB

Difficulty—

We have an $N \times M$ matrix, whose elements are initially all $0$. Process $Q$ given queries. Each query is in one of the following formats. * `1 l r x` : Add $x$ to every element in the $l$\-th, $(l+1)$\-th, $\ldots$, and $r$\-th column. * `2 i x`: Replace every element in the $i$\-th row with $x$. * `3 i j`: Print the $(i, j)$\-th element. ## Constraints * $1 \leq N, M, Q \leq 2 \times 10^5$ * Every query is in one of the formats listed in the Problem Statement. * For each query in the format `1 l r x`, $1 \leq l \leq r \leq M$ and $1 \leq x \leq 10^9$. * For each query in the format `2 i x`, $1 \leq i \leq N$ and $1 \leq x \leq 10^9$. * For each query in the format `3 i j`, $1 \leq i \leq N$ and $1 \leq j \leq M$. * At least one query in the format `3 i j` is given. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $Q$ $\mathrm{Query}_1$ $\vdots$ $\mathrm{Query}_Q$ $\mathrm{Query}_i$, which denotes the $i$\-th query, is in one of the following formats: $1$ $l$ $r$ $x$ $2$ $i$ $x$ $3$ $i$ $j$ [samples]

Samples

Input #1

Output #1

1
2
2
5
3
4

The matrix transitions as follows.
$\begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ \end{pmatrix} \rightarrow \begin{pmatrix} 1 & 1 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 0 \\ \end{pmatrix} \rightarrow \begin{pmatrix} 1 & 1 & 0 \\ 1 & 1 & 0 \\ 2 & 2 & 2 \\ \end{pmatrix} \rightarrow \begin{pmatrix} 1 & 4 & 3 \\ 1 & 4 & 3 \\ 2 & 5 & 5 \\ \end{pmatrix}$

Input #2

1 1 10
1 1 1 1000000000
1 1 1 1000000000
1 1 1 1000000000
1 1 1 1000000000
1 1 1 1000000000
1 1 1 1000000000
1 1 1 1000000000
1 1 1 1000000000
1 1 1 1000000000
3 1 1

Output #2

9000000000

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Operations on a Matrix",
    "description": {
      "content": "We have an $N \\times M$ matrix, whose elements are initially all $0$. Process $Q$ given queries. Each query is in one of the following formats. *   `1 l r x` : Add $x$ to every element in the $l$\\-th",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc253_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have an $N \\times M$ matrix, whose elements are initially all $0$.\nProcess $Q$ given queries. Each query is in one of the following formats.\n\n*   `1 l r x` : Add $x$ to every element in the $l$\\-th...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments