Problem: Property Booking Optimizer

Given:

• A list of properties where each property has (id, neighborhood, capacity)
• A group size (number of people that need accommodation)
• A target neighborhood

Goal:
Find the optimal combination of properties in the given neighborhood that can accommodate the group with these rules:

1. Total capacity must be >= group size
2. Choose the combination with minimum total capacity that exceeds group size
3. If multiple combinations have same capacity, choose the one with fewer properties
4. If no valid combination exists, return empty list

Examples:

Example 1:
Properties:

• (1, "area1", 5)
• (2, "area1", 3)
• (3, "area1", 2)
• (4, "area2", 4)
  GroupSize = 5, neighborhood = "area1"
  Output: [1] // Property 1 alone has capacity 5, which is optimal

Example 2:
Same properties, GroupSize = 6, neighborhood = "area1"
Output: [1, 3] // Properties 1+3 give capacity 7, which is minimal solution

Example 3:
Properties:

• (1, "area1", 5)
• (2, "area1", 3)
  GroupSize = 10, neighborhood = "area1"
  Output: [] // No combination can accommodate 10 people