Problem
Welcome to the mystical Enchanted Forest, where each tree glows at a unique coordinate on a 2D plane. As a daring adventurer, your mission is to collect a rare fruit from each glowing tree. You begin your journey at the origin point (0, 0). Your task is to devise a route that allows you to visit each tree exactly once, collect the fruits, and return to the origin, while ensuring the total distance traveled is minimized. This problem is a simplified version of the Traveling Salesman Problem, crucial for efficient route planning. To solve this challenge, follow these steps: 1. Identify the coordinates of each glowing tree. 2. Plan a route that visits all the trees, minimizing the distance traveled. 3. Ensure you return to the starting point (0, 0) after collecting all the fruits. Consider this
- Consider using algorithms like nearest neighbor or dynamic programming to find an optimal path.
- Think about how to efficiently calculate distances between points; a hash map might be useful for storing and retrieving these distances quickly.
- Pay attention to edge cases, such as very few or very many trees, and how they might affect your approach.
- For optimization, focus on reducing the computational complexity of your solution, especially as the number of trees increases.
Input format
The first line contains a single integer n (1 <= n <= 100) representing the number of magical trees. Each of the next n lines contains two integers x and y (-1000 <= x, y <= 1000) representing the coordinates of a tree.
Output format
Output a single integer, the shortest possible path that covers all trees, starting at the origin.
Constraints
1 <= n <= 100, -1000 <= x, y <= 1000
Sample input
3 0 2 2 0 1 1
Sample output
4