第66题——机器人的运动范围

题目：

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？

思路：

利用递归回溯的方法，写一个sum()方法，求i和j的各个位相加的和，并在移动时判断sum是否大于threshold

Java

package nowcoder;

public class S66_MovingCount {
    public int movindCount(int threshold, int rows, int cols){
        int[][] flag = new int[rows][cols];
        return moving(threshold, flag, rows, cols, 0, 0);
    }
    public int moving(int threshold, int[][] flag, int rows, int cols, int i, int j){
        if (i>=rows || j >= cols || i<0 || j<0 || threshold <0 || sum(i, j) > threshold || flag[i][j] ==1)
            return 0;
        flag[i][j] = 1;
        return moving(threshold, flag, rows, cols, i-1, j)+
                moving(threshold, flag, rows, cols, i+1, j)+
                moving(threshold, flag, rows, cols, i, j-1)+
                moving(threshold, flag, rows, cols, i, j+1)+1;
    }
    public int sum(int i, int j){
        if (i < 0 || j <0)
            return 0;
        int sum = 0;
        while (i>0 && j>0){
            sum += i%10;
            i = i/10;
            sum += j%10;
            j = j/10;
        }
        return sum;
    }
    public static void main(String[] args){
        S66_MovingCount s66 = new S66_MovingCount();
        System.out.println(s66.movindCount(2, 4, 4));
    }
}

Python

class MovingCount:
    def movingCount(self, threshold, rows, cols):
        flag = [[0] * cols for i in range(rows)]
        return self.moving(threshold, rows, cols, 0, 0, flag)
    def moving(self, threshold, rows, cols, i, j, flag):
        if i >= rows or j >= cols or i < 0 or j < 0 or self.sum(i, j) > threshold or flag[i][j] == 1:
            return 0
        flag[i][j] = 1
        return self.moving(threshold, rows, cols, i-1, j, flag) + \
               self.moving(threshold, rows, cols, i+1, j, flag) + \
               self.moving(threshold, rows, cols, i, j-1, flag) + \
               self.moving(threshold, rows, cols, i, j+1, flag) + 1
    def sum(self, i, j):
        if i < 0 or j < 0:
            return 0
        sum = 0
        while i > 0 and j > 0:
            sum += i % 10
            sum += j % 10
            i = i/10
            j = j/10
        return sum

if __name__ == '__main__':
    test = MovingCount()
    print(test.movingCount(4, 2, 2))