Solution Explanation: Design Snake Game

This problem involves designing a Snake game. The game takes place on a grid of size height x width. The snake starts at (0, 0) with length 1. Food is provided at various coordinates, and eating food increases the snake's length and score. The game ends if the snake hits a wall or itself.

The solution uses a queue (q) to store the snake's body coordinates and a set (vis) to track visited coordinates. The head of the queue represents the snake's head, and the tail represents its tail. The food array provides the coordinates of food items to be consumed sequentially.

Approach:

1. Initialization (__init__ or constructor): The constructor initializes the game parameters: height, width, food coordinates, score, food index (idx), and the snake's initial position in the queue and visited set.

2. Movement (move): The move function simulates a single move of the snake in the given direction. It determines the next head position based on the direction.

3. Collision Detection: The function first checks for collisions with the walls. If the next position is out of bounds, it returns -1 (game over). Then, it checks for self-collision by verifying if the next position is already in the vis set. If a self-collision is detected, it returns -1.

4. Food Consumption: If the next position matches a food item's coordinates (checked using idx to track the current food item), the snake eats the food. The score and length increment, and idx advances to the next food item.

5. Snake Body Update: If the snake did not eat food, the tail is removed from the queue and vis (because it is no longer occupied).

6. Updating State: The new head position is added to the front of the queue and vis set. The updated score is returned.

Time and Space Complexity Analysis:

• Time Complexity:

  • __init__ (or constructor): O(1) - Constant time initialization.
  • move: O(1) on average. While the queue operations are O(1) in amortized time, removing the tail in the worst case might take O(N) if the snake is very long, where N is the length of the snake. However, the length of the snake is bounded by the number of food items which is at most 50 in this problem, making it effectively O(1).

• Space Complexity:

  • O(M*N) in the worst case to store the visited positions in vis, where M and N are the dimensions of the grid. However, in practice, it will be O(L), where L is the snake's length because only the snake's body positions are stored in vis. L is bounded by the number of food items, so this becomes effectively O(1) given the constraints of the problem. The queue q also stores at most L elements.

The different code implementations (Python, Java, C++, Go, TypeScript) all follow the same underlying algorithm and have the same time and space complexity characteristics as described above. Note that the use of a deque (double-ended queue) in Python and similar data structures in other languages is crucial for efficient O(1) time complexity for both adding and removing from the ends of the snake.