Solve matrix groups and recipe inventory

Part 1: Grid Block Minima

Given a 2D integer grid of size M x N and a block size K x K, find the minimum value within every possible K x K subgrid. The output should be a grid of size (M-K+1) x (N-K+1) where result[i][j] is the minimum of the subgrid starting at (i, j).

Constraints: 1 <= K <= M, N <= 1000. Aim for a solution more efficient than O(M * N * K^2).

Part 2: Recipe Dependency Resolution

You are given a list of recipes, where each recipe has a name and a list of required ingredients. Some ingredients are 'base' items, while others are 'derived' recipes that must be prepared first. Return an order in which the recipes should be prepared to satisfy all dependencies, or return an empty list if a circular dependency exists.

Interface:

def get_preparation_order(recipes):
    # recipes is a dictionary: { 'recipe_name': ['ingredient1', 'recipe2', ...] }
    # returns a list of strings representing the preparation order

Example: Input:

{
  "Cake": ["Flour", "Frosting"],
  "Frosting": ["Sugar", "Butter"],
  "Flour": []
}

Output: ["Flour", "Frosting", "Cake"] (or similar valid topological sort)

Edge Cases:

• Empty input.
• Disconnected components (multiple independent recipe trees).
• Cycles (e.g., A needs B, B needs A).