洛谷P1457 [USACO2.1]城堡 The Castle进阶解法

这篇博客介绍了一种用于解决大型迷宫问题的算法。首先，通过输入的迷宫墙信息创建房间结构，并使用位运算进行解码。然后，通过递归标记法找出所有连通房间并计算其数量。接着，计算每个房间的大小并找出最大房间。最后，确定最大房间的边界墙并输出相关信息。该算法展示了如何高效地处理复杂迷宫问题。

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#include<iostream>
#include<algorithm>

using std::cout;
using std::cin;
using std::endl;

struct Room
{
	bool west, north, east, south;
	int  number;
} room[52][52];
struct Break
{
	int size, row, column;
	char location;
}breakwall[10005];
int n, m, list[2505], row, column, bigflag = 0;
char location;

void decode(Room& temproom, int& codedwall)
{
	if (codedwall & 8)
		temproom.south = true;
	if (codedwall & 4)
		temproom.east = true;
	if (codedwall & 2)
		temproom.north = true;
	if (codedwall & 1)
		temproom.west = true;
}

void mark(int i, int j, int k)
{
	room[i][j].number = k;
	if (!room[i][j].east && !room[i][j + 1].number)
		mark(i, j + 1, k);
	if (!room[i][j].south && !room[i + 1][j].number)
		mark(i + 1, j, k);
	if (!room[i][j].north && !room[i - 1][j].number)
		mark(i - 1, j, k);
	if (!room[i][j].west && !room[i][j - 1].number)
		mark(i, j - 1, k);
}

int count(void)
{
	int k = 1;
	for (int i = 1; i <= n; i++)
		for (int j = 1; j <= m; j++)
			if (!room[i][j].number)
			{
				mark(i, j, k);
				k++;
			}
	return k - 1;
}

void marksize(void)
{
	for (int i = 1; i <= n; i++)
		for (int j = 1; j <= m; j++)
			list[room[i][j].number]++;
}

int findmax(int num)
{
	int max = 0;
	for (int i = 0; i <= num; i++)
		if (list[i] > max)
			max = list[i];
	return max;
}

int  wall(void)
{
	int k = 0;
	for (int j = 1; j <= m; j++)
		for (int i = n; i > 0; i--)
		{
			if (room[i][j].north && room[i][j].number != room[i - 1][j].number)
			{
				breakwall[k].row = i;
				breakwall[k].column = j;
				breakwall[k].location = 'N';
				breakwall[k].size = list[room[i][j].number] + list[room[i - 1][j].number];
				k++;
			}
			if (room[i][j].east && room[i][j].number != room[i][j + 1].number)
			{
				breakwall[k].row = i;
				breakwall[k].column = j;
				breakwall[k].location = 'E';
				breakwall[k].size = list[room[i][j].number] + list[room[i][j + 1].number];
				k++;
			}
		}
	return k;
}

int sudofindmax(int num)
{
	int max = 0, temp = 0;
	for (int i = 0; i <= num; i++)
		if (breakwall[i].size > max)
		{
			max = breakwall[i].size;
			temp = i;
		}
	return temp;
}

int main()
{
	int num, num2;
	cin >> m >> n;
	for (int i = 1; i <= n; i++)
		for (int j = 1, codedwall; j <= m; j++)
		{
			cin >> codedwall;
			decode(room[i][j], codedwall);
		}
	num = count();
	cout << num << endl;
	marksize();
	cout << findmax(num) << endl;
	num = wall();
	num2 = sudofindmax(num);
	cout << breakwall[num2].size << endl << breakwall[num2].row << ' ' << breakwall[num2].column << ' ' << breakwall[num2].location << endl;
	return 0;
}