dfs Red and Black

本文介绍了一种基于深度优先搜索的迷宫寻路算法。该算法可在二维网格中找到从起点到所有可达位置的路径,特别适用于由黑色(可通过)和红色(不可通过)方块构成的地图。通过递归方式遍历所有可能的方向,并标记已访问的位置避免重复计算。

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Description

Input

Output

Sample Input

Sample Output

Hint

Description

There is a rectangular room, covered with square tiles. Each tile is colored either red or black. A man is standing on a black tile. From a tile, he can move to one of four adjacent tiles. But he can't move on red tiles, he can move only on black tiles.

Write a program to count the number of black tiles which he can reach by repeating the moves described above.

Input

The input consists of multiple data sets. A data set starts with a line containing two positive integers W and H; W and H are the numbers of tiles in the x- and y- directions, respectively. W and H are not more than 20.

There are H more lines in the data set, each of which includes W characters. Each character represents the color of a tile as follows.

'.' - a black tile
'#' - a red tile
'@' - a man on a black tile(appears exactly once in a data set)

Output

For each data set, your program should output a line which contains the number of tiles he can reach from the initial tile (including itself).

Sample Input

6 9
....#.
.....#
......
......
......
......
......
#@...#
.#..#.
11 9
.#.........
.#.#######.
.#.#.....#.
.#.#.###.#.
.#.#..@#.#.
.#.#####.#.
.#.......#.
.#########.
...........
11 6
..#..#..#..
..#..#..#..
..#..#..###
..#..#..#@.
..#..#..#..
..#..#..#..
7 7
..#.#..
..#.#..
###.###
...@...
###.###
..#.#..
..#.#..
0 0

Sample Output

45
59
6
13
#include<stdio.h>
#include<string.h>
#include<math.h>
#include<stdlib.h>
#include<algorithm>
#include<iostream>
#include<queue>
using namespace std;
int n, m;
int chess[25][25];
bool visited[25][25];
int d[4][2] = { 0,1,1,0,-1,0,0,-1 };
int sum = 0;
void dfs(int x,int y)
{
	int tx, ty;
	for(int i=0;i<4;i++)
	{
		tx = x + d[i][0];
		ty = y + d[i][1];
		if (tx < 0 || tx >= n || ty<0 || ty>=m || chess[ty][tx]=='#' || visited [ty][tx]==true)
		{
			continue;
		}
		visited[ty][tx] = true;
		sum += 1;
		dfs(tx, ty);
	}
}
int main()
{
	while(~scanf("%d %d",&n,&m))
	{
		sum = 0;
		memset(visited, false, sizeof(visited));
		int x, y;
		if (n == 0 && m == 0) { break; }
		getchar();
		for(int i=0;i<m;i++)
		{
			for(int j=0;j<n;j++)
			{
				scanf("%c", &chess[i][j]);
				if(chess[i][j]=='@')
				{
					x = j;
					y = i;
				}
			}
			getchar();
		}
		visited[y][x] = true;
		sum+=1;
		dfs(x, y);
		printf("%d\n", sum);
	}
	return 0;
}

//by tp
"black and red problem"通常是指图论中的“黑红树”(Black-Red Tree),这是一种用于实现二叉查找树的数据结构。Python中的深度优先搜索(Depth-First Search,DFS)可以用来遍历这种特殊的树。 在处理这类问题的DFS解法中,你需要递归地访问每个节点,并维护两个颜色规则:每个节点要么是红色,要么是黑色,且根节点必须是黑色。两个额外的规则是: 1. 每个叶节点(NIL节点)都是黑色的。 2. 如果一个节点是红色的,则其子节点必须是黑色。 DFS通常会采用一种叫做预置颜色(preorder coloring)的策略,即先访问左子树,然后访问右子树。在遍历时,需要确保每次遇到红色节点时都进行了正确的调整,以保持树的平衡和黑色节点的性质。 下面是一个简单的Python DFS解法示例,假设有一个名为`Node`的类表示树节点,包含`color`(颜色)和`left`, `right`属性: ```python class Node: def __init__(self, color): self.color = color self.left = None self.right = None def is_valid_b_and_r(node): if node is None: return True # 检查当前节点是否违反规则 if node.color != 'red': return is_valid_b_and_r(node.left) and is_valid_b_and_r(node.right) # 深度检查子节点的颜色和位置 left_red = node.left and node.left.color == 'red' right_red = node.right and node.right.color == 'red' # 父亲节点为红色,子节点不能同时为红色 if left_red and right_red: return False # 深入左子树或右子树并检查它们是否有效 if left_red: return is_valid_b_and_r(node.left.left) and is_valid_b_and_r(node.left.right) elif right_red: return is_valid_b_and_r(node.right.left) and is_valid_b_and_r(node.right.right) # 如果到达这里说明所有子节点都不是红色 return True # 示例用法 root = ... # 创建一个代表树的根节点 if is_valid_b_and_r(root): print("树满足black and red规则") else: print("树不满足black and red规则") ```
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