JZ-066-Motion range of the robot

The range of motion of the robot

Topic description

There is a square with m rows and n columns on the ground. A robot starts to move from the grid of coordinates 0 and 0, and can only move one grid in four directions: left, right, up and down at a time, but cannot enter the grid where the sum of the digits of the row and column coordinates is greater than k. For example, when k is 18, the robot is able to enter square (35,37) because 3+5+3+7 = 18. However, it cannot go into square (35,38) because 3+5+3+8 = 19.

• How many squares can the robot reach?

topic link : range of motion of the robot

code

/**
 * 标题：机器人的运动范围
 * 题目描述
 * 地上有一个m行和n列的方格。一个机器人从坐标0,0的格子开始移动，每一次只能向左，右，上，下四个方向移动一格，但是不能进入行坐标和列坐标的数位
 * 之和大于k的格子。 例如，当k为18时，机器人能够进入方格（35,37），因为3+5+3+7 = 18。但是，它不能进入方格（35,38），因为3+5+3+8 = 19。
 * 请问该机器人能够达到多少个格子？
 * 题目链接：
 * https://www.nowcoder.com/practice/6e5207314b5241fb83f2329e89fdecc8?tpId=13&&tqId=11219&rp=1&ru=/ta/coding-interviews&qru=/ta/coding-interviews/question-ranking
 */
public class Jz66 {

    private static final int[][] next = {{0, -1}, {0, 1}, {-1, 0}, {1, 0}};
    private int cnt = 0;
    private int rows;
    private int cols;
    private int threshold;
    private int[][] digitSum;

    /**
     * 深度优先搜索（Depth First Search，DFS）
     * 回溯是深度优先搜索的一种特例，它在一次搜索过程中需要设置一些本次搜索过程的局部状态，并在本次搜索结束之后清除状态。
     * 而普通的深度优先搜索并不需要使用这些局部状态，虽然还是有可能设置一些全局状态。
     *
     * @param threshold
     * @param rows
     * @param cols
     * @return
     */
    public int movingCount(int threshold, int rows, int cols) {
        this.rows = rows;
        this.cols = cols;
        this.threshold = threshold;
        initDigitSum();
        boolean[][] marked = new boolean[rows][cols];
        dfs(marked, 0, 0);
        return cnt;
    }

    private void dfs(boolean[][] marked, int r, int c) {
        if (r < 0 || r >= rows || c < 0 || c >= cols || marked[r][c]) {
            return;
        }
        marked[r][c] = true;
        if (this.digitSum[r][c] > this.threshold) {
            return;
        }
        cnt++;
        for (int[] n : next) {
            dfs(marked, r + n[0], c + n[1]);
        }
    }

    private void initDigitSum() {
        int[] digitSumOne = new int[Math.max(rows, cols)];
        for (int i = 0; i < digitSumOne.length; i++) {
            int n = i;
            while (n > 0) {
                digitSumOne[i] += n % 10;
                n /= 10;
            }
        }
        this.digitSum = new int[rows][cols];
        for (int i = 0; i < this.rows; i++) {
            for (int j = 0; j < this.cols; j++) {
                this.digitSum[i][j] = digitSumOne[i] + digitSumOne[j];
            }
        }
    }

    public static void main(String[] args) {
        Jz66 jz66 = new Jz66();
        int i = jz66.movingCount(18, 20, 20);
        System.out.println(i);
        System.out.println(4 / 10);
    }
}

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