广度优先搜索 BFS 模板

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摘自： 算法笔记 8.2

BFS 模板

void BFS(int s){
	queue<int> q;
	q.push(s);
	while(!q.empty()){
		取出队首元素top;
		访问队首元素top;
		将队首元素出队;
		将top下一层的结点中尚未访问的结点全部入队，并设置为已入队;
	}
}

矩阵的块（数细胞）

Sample Input:

6 7
0 1 1 1 0 0 1
0 0 1 0 0 0 0
0 0 0 0 1 0 0
0 0 0 1 1 1 0
1 1 1 0 1 0 0
1 1 1 1 0 0 0

Sample Output:

4

#include <iostream>
#include <vector>
#include <queue>
#include <algorithm>
using namespace std;
struct node {
	int x;
	int y;
}Node;

int m, n;// 矩阵大小
const int maxn = 100;
int matrix[maxn][maxn];
int inq[maxn][maxn] = { false };//是否已经入过队
int X[4] = { 0,1,0,-1 };
int Y[4] = { -1,0,1,0 };//增量数组

bool judge(int newX, int newY) {
	if (newX<0|| newX>=m||newY<0||newY>=n) {// 越界
		return false;
	}
	if (matrix[newX][newY]==0 || inq[newX][newY] == true) {// 位置非1或已经入队
		return false;
	}
	return true;
}

void BFS(int x, int y) {
	queue<node> q;
	Node.x = x, Node.y = y;
	q.push(Node);
	inq[x][y] = true;
	while (!q.empty()) {
		node top = q.front();
		q.pop();
		for (int i = 0; i < 4; i++)
		{
			int newX = top.x+ X[i];
			int newY = top.y + Y[i];
			if (judge(newX, newY)) {
				Node.x = newX;
				Node.y = newY;
				q.push(Node);
				inq[newX][newY] = true;
			}
		}
	}	
}
int main() {
	
	scanf("%d%d", &n, &m);//n 为行数，m为列数
	for (int i = 0; i < n; i++)
	{
		for (int j = 0; j < m; j++)
		{
			scanf("%d", &matrix[i][j]);
		}
	}

	int ans = 0;//块数
	for (int i = 0; i < n; i++)
	{
		for (int j = 0; j < m; j++)
		{
			if (matrix[i][j] == 1 && inq[i][j] == false) {
				ans++;
				BFS(i, j);
			}
		}
	}
	printf("%d\n", ans);
	return 0;
}

迷宫

Sample Input:

5 5
…
...
.S.
.**.
…T

Sample Output:

11

#include <iostream>
#include <vector>
#include <queue>
#include <algorithm>
#include <string>
using namespace std;
struct node {
	int x, y;
	int step;//步数（层数）
}S, T, Node;//起点、终点、临时点

int X[4] = { 0,1,0,-1 };
int Y[4] = { -1,0,1,0 };//四向

int n, m;//n行,m列
const int maxn = 100;
char maze[maxn][maxn];
bool inq[maxn][maxn] = { false };//是否已经入队

bool judge(int x, int y) {
	if (x < 0 || x >= n || y < 0 || y >= m) { //越界
		return 0;
	}
	if (maze[x][y] == '*') {// 墙
		return false;
	}
	if (inq[x][y] == true) {//回头路
		return false;
	}
	return true;
}

int BFS() {
	queue<node> q;
	q.push(S);
	inq[S.x][S.y] = true;
	while (!q.empty())
	{
		node top = q.front();
		q.pop();
		if (top.x == T.x && top.y == T.y) {
			return top.step;
		}
		for (int i = 0; i < 4; i++) {
			int newX = top.x + X[i];
			int newY = top.y + Y[i];
			if (judge(newX, newY)) {
				Node.x = newX;
				Node.y = newY;
				Node.step = top.step + 1;
				q.push(Node);
				inq[newX][newY] = true;
			}
		}
	}
	return -1;//无法到达终点
}
int main() {
	scanf("%d%d", &n, &m);
	for (int i = 0; i < n; i++)
	{
		getchar();
		for (int j = 0; j < m; j++)
		{
			maze[i][j] = getchar();
			//记录起点、终点
			if (maze[i][j] == 'S') {
				S.x = i;
				S.y = j;
			}
			if (maze[i][j] == 'T') {
				T.x = i;
				T.y = j;
			}
		}
	}

	S.step = 0;
	printf("%d", BFS());

	return 0;
}