搜索技术——广度优先搜索(BFS)

本文深入探讨了广度优先搜索(BFS)和深度优先搜索(DFS)的基本原理及应用,特别是在图和树的遍历中。通过具体实例,详细解释了如何使用队列实现BFS算法,并提供了一个关于在红黑格子世界中寻找可达黑色格子数量的编程示例。

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广度优先搜索和深度优先搜索是基本的暴力技术,常用于解决图,树的遍历问题。
算法思路为:在每个节点的可扩展处都扩散一遍,如无法继续扩展便停下,等到所有的分列都停止之后广度优先搜索便结束。
广度优先搜索的扩散一般都是用队列来进行实现。

代码实现(…为自定义操作):

void BFS(....)
{
	queue<type> q;
	..............
	q.push(n);
	while(!q.empty())
	{
		q.pop();
		............
		if(....)
		{
			.......
			q.push(m);
		}
	}
}

(如果有误还请指正)

具体实践

Red and Black
Time Limit: 2000/1000 MS (Java/Others) Memory Limit:
65536/32768 K (Java/Others) Total Submission(s): 35748 Accepted
Submission(s): 21693

Problem 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

Source Asia 2004, Ehime (Japan), Japan Domestic

Recommend Eddy

#include<queue>
#include<iostream>
using namespace std;

int width, high;
int num;//记录总数
char room[21][21];

struct node
{
	int x;
	int y;
};

int dir[4][2] = { {-1,0},{0,-1},{1,0},{0,1} };//往四面扩展

void BFS(int dx, int dy)
{
	queue<node> q;
	node start, next;
	num = 1;
	start.x = dx;
	start.y = dy;
	q.push(start);
	while (!q.empty())
	{
		start = q.front();
		q.pop();
		for (int i = 0; i < 4; i++)
		{
			next.x = start.x + dir[i][0];
			next.y = start.y + dir[i][1];
			if (next.x >= 0 && next.x < width && next.y >= 0 && next.y < high && room[next.x][next.y] == '.')
			{
				room[next.x][next.y] = '#';
				q.push(next);
				num++;
			}
		}
	}
}

int main()
{
	int x, y;
	while (cin >> width >> high)
	{
		for (int i = 0; i < high; i++)
		{
			for (int j = 0; j < width; j++)
			{
				cin >> room[j][i];
				if (room[j][i] == '@')//设置初始点
				{
					x = j;
					y = i;
				}
			}
		}
		num = 0;
		BFS(x, y);
		cout << num << endl;
	}
	return 0;
}

(题目略水)

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