D. Rectangles

Codeforces

IDCF10110D

Time5000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

Given an R×C grid with each cell containing an integer, find the number of subrectangles in this grid that contain only one distinct integer; this means every cell in a subrectangle contains the same integer. A subrectangle is defined by two cells: the top left cell (r1, c1), and the bottom-right cell (r2, c2) (1 ≤ r1 ≤ r2 ≤ R) (1 ≤ c1 ≤ c2 ≤ C), assuming that rows are numbered from top to bottom and columns are numbered from left to right. The first line of input contains a single integer T, the number of test cases. The first line of each test case contains two integers R and C (1 ≤ R, C ≤ 1000), the number of rows and the number of columns of the grid, respectively. Each of the next R lines contains C integers between 1 and 109, representing the values in the row. For each test case, print the answer on a single line. ## Input The first line of input contains a single integer T, the number of test cases.The first line of each test case contains two integers R and C (1 ≤ R, C ≤ 1000), the number of rows and the number of columns of the grid, respectively.Each of the next R lines contains C integers between 1 and 109, representing the values in the row. ## Output For each test case, print the answer on a single line. [samples]

**Definitions** Let $ T \in \mathbb{Z} $ be the number of test cases. For each test case $ k \in \{1, \dots, T\} $: - Let $ R_k, C_k \in \mathbb{Z} $ denote the dimensions of the grid, with $ 1 \leq R_k, C_k \leq 1000 $. - Let $ G_k = (g_{i,j})_{1 \leq i \leq R_k, 1 \leq j \leq C_k} $ be a matrix of integers where $ 1 \leq g_{i,j} \leq 10^9 $. **Constraints** 1. $ 1 \leq T \leq \text{unspecified (implied by input)} $ 2. For each test case $ k $: - $ 1 \leq R_k, C_k \leq 1000 $ - $ g_{i,j} \in \mathbb{Z} $, $ 1 \leq g_{i,j} \leq 10^9 $ for all $ i,j $ **Objective** For each test case $ k $, compute the number of subrectangles defined by top-left $ (r_1, c_1) $ and bottom-right $ (r_2, c_2) $ with $ 1 \leq r_1 \leq r_2 \leq R_k $, $ 1 \leq c_1 \leq c_2 \leq C_k $, such that: $$ \forall (i,j), (i',j') \in [r_1, r_2] \times [c_1, c_2], \quad g_{i,j} = g_{i',j'} $$

API Response (JSON)

{
  "problem": {
    "name": "D. Rectangles",
    "description": {
      "content": "Given an R×C grid with each cell containing an integer, find the number of subrectangles in this grid that contain only one distinct integer; this means every cell in a subrectangle contains the same ",
      "description_type": "Markdown"
    },
    "platform": "Codeforces",
    "limit": {
      "time_limit": 5000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "CF10110D"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given an R×C grid with each cell containing an integer, find the number of subrectangles in this grid that contain only one distinct integer; this means every cell in a subrectangle contains the same ...",
      "is_translate": false,
      "language": "English"
    },
    {
      "statement_type": "Markdown",
      "content": "**Definitions**  \nLet $ T \\in \\mathbb{Z} $ be the number of test cases.  \nFor each test case $ k \\in \\{1, \\dots, T\\} $:  \n- Let $ R_k, C_k \\in \\mathbb{Z} $ denote the dimensions of the grid, with $ 1 ...",
      "is_translate": false,
      "language": "Formal"
    }
  ]
}

Full JSON Raw Segments