20190525-剑指offer13-AcWing-24.机器人的运动范围

剑指offer13-AcWing-24.机器人的运动范围

地上有一个 m 行和 n 列的方格，横纵坐标范围分别是 0∼m−1 和 0∼n−1。
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。
请问该机器人能够达到多少个格子？
样例1
输入：k=7, m=4, n=5
输出：20
样例2
输入：k=18, m=40, n=40
输出：1484
解释：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。
注意:
0<=m<=50
0<=n<=50
0<=k<=100

思路：
    回溯法！！！
C++代码：

class Solution {
public:
    bool numSum(int now_row, int now_col, int threshold){
        int sum_pos = 0;
        while(now_row){
            sum_pos += now_row % 10;
            now_row /= 10;
        }
        while(now_col){
            sum_pos += now_col % 10;
            now_col /= 10;
        }
        if(sum_pos <= threshold){
            return true;
        }else{
            return false;
        }
    }
    int count_bin(int now_row, int now_col, int rows, int cols, int threshold, vector<vector<int>>& visited){
        int count = 0;
        bool num_sum = numSum(now_row, now_col, threshold);
        if(now_row >= 0 && now_row < rows && now_col >=0 && now_col < cols && !visited[now_row][now_col] && num_sum){
            visited[now_row][now_col] = 1;
            count = 1 + count_bin(now_row + 1, now_col, rows, cols, threshold, visited) + 
                        count_bin(now_row - 1, now_col, rows, cols, threshold, visited) + 
                        count_bin(now_row, now_col + 1, rows, cols, threshold, visited) + 
                        count_bin(now_row, now_col - 1, rows, cols, threshold, visited);
            
        }
        return count;
    }
    int movingCount(int threshold, int rows, int cols)
    {
        if(threshold < 0 || rows < 1 || cols < 1){
            return 0;
        }
        int now_row = 0;
        int now_col = 0;
        
        vector<vector<int>> visited;
        
        for(int i = 0; i < rows; i++){
            visited.push_back(vector<int>(cols, 0));
        }
        
        int count = count_bin(0, 0, rows, cols, threshold, visited);
        return count;
    }
};

python代码（超时）：

class Solution(object):
    def numSum(self, now_row, now_col, threshold):
        pos_sum = 0
        while now_row:
            pos_sum += now_row % 10
            now_row = now_row // 10
        while now_col:
            pos_sum += now_col % 10
            now_col = now_col // 10 
            
        if pos_sum <= threshold:
            return True
        else:
            return False
            
    def countSum(self, now_row, now_col, rows, cols, threshold, visited):
        count = 0
        num_sum = self.numSum(now_row, now_col, threshold)
        if 0 <= now_row < rows and 0 <= now_col < cols and not visited[now_row][now_col] and num_sum:
            visited[now_row][now_col] = 1
            count = 1 + self.countSum(now_row + 1, now_col, rows, cols, threshold, visited) + self.countSum(now_row - 1, now_col, rows, cols, threshold, visited) + self.countSum(now_row, now_col + 1, rows, cols, threshold, visited)  + self.countSum(now_row, now_col - 1, rows, cols, threshold, visited) 
        return count
        
    def movingCount(self, threshold, rows, cols):
        """
        :type threshold: int
        :type rows: int
        :type cols: int
        :rtype: int
        """
        if threshold < 0 or rows <= 0 or cols <= 0:
            return 0
        
        visited = [[0] * cols for row in range(rows)]
        
        count_sum = self.countSum(0, 0, rows, cols, threshold, visited)
        return count_sum