Design a Recommender System Based on Price and Distance

Problem Statement

Build a recommendation engine that suggests items to a user by considering both price and geographic proximity. An item is eligible only if its price does not exceed the user's budget. Eligible items are then ranked from closest to farthest based on the user's current location.

Input

• A list of items. Each item has:
  • price (numeric)
  • latitude (float)
  • longitude (float)
• The user's current location as latitude and longitude (floats).
• The user's budget (numeric).

Output

Return the items that are within the budget, sorted in ascending order of Euclidean distance from the user's location. The output should include each item's price, location, and computed distance.

Constraints

• The total number of items will not exceed 1000.
• Distance must be calculated using the Euclidean distance formula on the raw latitude and longitude values (treat them as coordinates in a plane).

Examples

Example 1

Input:

• User location: 34.052235, -118.243683
• Budget: 100
• Items:
  • Price: 100, Location: (40.712776, -74.005974)
  • Price: 150, Location: (34.052235, -118.243683)
  • Price: 50, Location: (37.774929, -122.419418)

Output:

• Price: 50, Location: (37.774929, -122.419418), Distance: ~5.59
• Price: 100, Location: (40.712776, -74.005974), Distance: ~44.74

Explanation: The item priced at 150 is excluded because it exceeds the budget of 100. The remaining two items are sorted by distance; the item at (37.77, -122.42) is much closer than the one at (40.71, -74.01).

Example 2

Input:

• User location: 0, 0
• Budget: 50
• Items:
  • Price: 30, Location: (3, 4)
  • Price: 20, Location: (1, 1)
  • Price: 60, Location: (0, 0)

Output:

• Price: 20, Location: (1, 1), Distance: ~1.41
• Price: 30, Location: (3, 4), Distance: 5.00

Explanation: The item at (0,0) costs 60, which is over budget. The other two items are both affordable; the one at (1,1) is nearer than the one at (3,4), so it appears first.

Note

Your solution should include at least two test cases to demonstrate correctness.