353. Design Snake Game

353. Design Snake Game
Design a Snake game that is played on a device with screen size = width x height. Play the game online if you are not familiar with the game.
The snake is initially positioned at the top left corner (0,0) with length = 1 unit.
You are given a list of food's positions in row-column order. When a snake eats the food, its length and the game's score both increase by 1.
Each food appears one by one on the screen. For example, the second food will not appear until the first food was eaten by the snake.
When a food does appear on the screen, it is guaranteed that it will not appear on a block occupied by the snake.
Example:
Given width = 3, height = 2, and food = [[1,2],[0,1]].

Snake snake = new Snake(width, height, food);

Initially the snake appears at position (0,0) and the food at (1,2).

|S| | |
| | |F|

snake.move("R"); -> Returns 0

| |S| |
| | |F|

snake.move("D"); -> Returns 0

| | | |
| |S|F|

snake.move("R"); -> Returns 1 (Snake eats the first food and right after that, the second food appears at (0,1) )

| |F| |
| |S|S|

snake.move("U"); -> Returns 1

| |F|S|
| | |S|

snake.move("L"); -> Returns 2 (Snake eats the second food)

| |S|S|
| | |S|

snake.move("U"); -> Returns -1 (Game over because snake collides with border)

解释题意：
蛇可以上下左右移动，没吃到一个食物，蛇的长度和游戏的分数+1
蛇的起始点在屏幕的左上角，且初始长度为1
食物每次只会出现一个，下一个食物在蛇吃掉了当前食物之后才会出现
食物出现的位置不会在蛇的身上或者是出界
游戏初始化的时候input为宽，长还有食物的坐标。move function 可以take in 上下左右四个directions

游戏终止的两种情况；
蛇的头出界了
蛇自己咬到了自己

思路：
将屏幕模拟成一个二维空间，每一个位置用一个坐标表示。蛇在移动的过程中其实就是坐标的变换。
然后移动过程中，我们需要分几种情况讨论：
移动之后的坐标超出屏幕界限
移动之后的坐标，已经存在于身体的一部分（蛇自己咬到了自己）
正常的移动 （需要头部+1, 尾巴-1）
吃到了食物 （分数+1， 头部+ 1， 原来的的尾巴保持不变，食物指针移到下一个）


因此， 我们需要两个data strucutre:
set -- 快速查找是否是身体的一部分
deque -- body所占用的位置 => 可以快速更新蛇的头尾
0 L R U D F
char[][] grid
int headX
int headY
int tailX
int tailY
U -> R
 
=========game start=============
1. call constructor → build char[][] gird
2. get curr fruit → 
0000000
000RD00
000UL00
0000000
0000000
int dir
headX, headY, tailX, tailY
 
width * height
Time: O(1)
Space: O(蛇的长度)
class SnakeGame {

    /** Initialize your data structure here.
        @param width - screen width
        @param height - screen height 
        @param food - A list of food positions
        E.g food = [[1,1], [1,0]] means the first food is positioned at [1,1], the second is at [1,0]. */
    Set<Integer> set; // this copy is good for fast loop-up for eating body case
    Deque<Integer> body; // this copy is good for updating tail
    int score;
    int[][] food;
    int foodIndex;
    int width;
    int height;
    
    public SnakeGame(int width, int height, int[][] food) {
        this.width = width;
        this.height = height;
        this.food = food;
        set = new HashSet<>();
        set.add(0); //intially at [0][0]
        body = new LinkedList<>();
        body.offerLast(0);
    }
      
    public int move(String direction) {
        //case 0: game already over: do nothing
        if (score == -1) {
            return -1;
        }
        
        // compute new head
        int rowHead = body.peekFirst() / width;
        int colHead = body.peekFirst() % width;
        switch (direction) {
            case "U" : rowHead--;
                       break;
            case "D" : rowHead++;
                       break;
            case "L" : colHead--;
                       break;
            default :  colHead++;
        }
        int head = rowHead * width + colHead;
        
        //case 1: out of boundary or eating body
        set.remove(body.peekLast()); // new head is legal to be in old tail's position, remove from set temporarily 
        if (rowHead < 0 || rowHead == height || colHead < 0 || colHead == width || set.contains(head)) {
            return score = -1;
        }
        
        // add head for case3 and case4
        set.add(head); 
        body.offerFirst(head);
        
        //case2: eating food, keep tail, add head
        if (foodIndex < food.length && rowHead == food[foodIndex][0] && colHead == food[foodIndex][1]) {
            set.add(body.peekLast()); // old tail does not change, so add it back to set
            foodIndex++;
            return ++score;
        }     
        //case3: normal move, remove tail, add head
        body.pollLast();
        return score;
        
    }
}
/**
 * Your SnakeGame object will be instantiated and called as such:
 * SnakeGame obj = new SnakeGame(width, height, food);
 * int param_1 = obj.move(direction);
 */