[Sword Finger 13] Robot's range of motion

Method 1: Depth first search: time O(mn), space O(mn)

answer:

1. To simulate the direction of the robot, first judge whether it can reach the target position every time. If it can be reached, mark the position to indicate that it has been there.
2. The robot starts walking from the upper left corner [0, 0], which means dfs can only go right and down

class Solution {
    
    
public:
    int res = 0;
    bool isCorrect(int x, int y, int k)
    {
    
    
        int count = 0;
        while (x || y)
        {
    
    
            if (x)
            {
    
    
                count += x % 10;
                x /= 10;
            }
            if (y)
            {
    
    
                count += y % 10;
                y /= 10;
            }
        }
        return count <= k;
    }
    void movingboard(int m, int n, int k, int i, int j, vector<vector<bool>>& board)
    {
    
    
        if (i < 0 || i == m || j < 0 || j == n || board[i][j])
            return;
        // 先让 board[i][j]为真，再去判断该位置是否有效，如果该位置无效下次判断该时，就省去了判断位置函数的调用开销 
        board[i][j] = true;
        if (isCorrect(i, j, k))
        {
    
    
            res++;
            // 优化：只需要向右和下走
            movingboard(m, n, k, i + 1, j, board);
            movingboard(m, n, k, i, j + 1, board);
        }
    }
    int movingCount(int m, int n, int k) 
    {
    
    
        vector<vector<bool>> board(m, vector<bool>(n, false));
        movingboard(m, n, k, 0, 0, board);
        return res;
    }
};