check-if-grid-can-be-cut-into-sections.json

{
  "id": 3657,
  "name": "check-if-grid-can-be-cut-into-sections",
  "difficulty": "Medium",
  "link": "https://leetcode.com/problems/check-if-grid-can-be-cut-into-sections/",
  "date": "2024-12-07",
  "task_description": "You are given an integer `n` representing the dimensions of an `n x n` grid, with the origin at the bottom-left corner of the grid. You are also given a 2D array of coordinates `rectangles`, where `rectangles[i]` is in the form `[startx, starty, endx, endy]`, representing a rectangle on the grid. Each rectangle is defined as follows: `(startx, starty)`: The bottom-left corner of the rectangle. `(endx, endy)`: The top-right corner of the rectangle. **Note **that the rectangles do not overlap. Your task is to determine if it is possible to make **either two horizontal or two vertical cuts** on the grid such that: Each of the three resulting sections formed by the cuts contains **at least** one rectangle. Every rectangle belongs to **exactly** one section. Return `true` if such cuts can be made; otherwise, return `false`. **Example 1:** **Input:** n = 5, rectangles = [[1,0,5,2],[0,2,2,4],[3,2,5,3],[0,4,4,5]] **Output:** true **Explanation:** The grid is shown in the diagram. We can make horizontal cuts at `y = 2` and `y = 4`. Hence, output is true. **Example 2:** **Input:** n = 4, rectangles = [[0,0,1,1],[2,0,3,4],[0,2,2,3],[3,0,4,3]] **Output:** true **Explanation:** We can make vertical cuts at `x = 2` and `x = 3`. Hence, output is true. **Example 3:** **Input:** n = 4, rectangles = [[0,2,2,4],[1,0,3,2],[2,2,3,4],[3,0,4,2],[3,2,4,4]] **Output:** false **Explanation:** We cannot make two horizontal or two vertical cuts that satisfy the conditions. Hence, output is false. **Constraints:** `3 <= n <= 109` `3 <= rectangles.length <= 105` `0 <= rectangles[i][0] < rectangles[i][2] <= n` `0 <= rectangles[i][1] < rectangles[i][3] <= n` No two rectangles overlap.",
  "test_case": [
    {
      "label": "Example 1",
      "input": "n = 5, rectangles = [[1,0,5,2],[0,2,2,4],[3,2,5,3],[0,4,4,5]]",
      "output": "true "
    },
    {
      "label": "Example 2",
      "input": "n = 4, rectangles = [[0,0,1,1],[2,0,3,4],[0,2,2,3],[3,0,4,3]]",
      "output": "true "
    },
    {
      "label": "Example 3",
      "input": "n = 4, rectangles = [[0,2,2,4],[1,0,3,2],[2,2,3,4],[3,0,4,2],[3,2,4,4]]",
      "output": "false "
    }
  ],
  "constraints": [
    "(startx, starty): The bottom-left corner of the rectangle.",
    "(endx, endy): The top-right corner of the rectangle.",
    "Each of the three resulting sections formed by the cuts contains at least one rectangle.",
    "Every rectangle belongs to exactly one section.",
    "3 <= n <= 109",
    "3 <= rectangles.length <= 105",
    "0 <= rectangles[i][0] < rectangles[i][2] <= n",
    "0 <= rectangles[i][1] < rectangles[i][3] <= n",
    "No two rectangles overlap."
  ],
  "python_template": "class Solution(object):\n    def checkValidCuts(self, n, rectangles):\n        \"\"\"\n        :type n: int\n        :type rectangles: List[List[int]]\n        :rtype: bool\n        \"\"\"\n        ",
  "java_template": "class Solution {\n    public boolean checkValidCuts(int n, int[][] rectangles) {\n        \n    }\n}",
  "metadata": {
    "func_name": "checkValidCuts"
  }
}