一种简单的方法是创建一个具有房间大小的数组并用“0”初始化它。
之后，您应该遍历数组。如果找到“0”，则从该点开始 BFS，并将数组结果着色为当前数字。
关于 BFS 的信息
BFS 必须查看直接邻居并检查此数组内是否有“0”。如果这是真的，BFS 必须检查两个盒子之间是否没有墙。如果中间没有墙，则使用当前颜色（开头为 1）为该框着色，并在新框上调用 BFS。
当房间完全着色时，BFS 会自动停止。然后全局颜色将增加 1，循环继续并寻找下一个“0”。
在循环之后，房间的数量存储在全局颜色值中。
这个算法在 O(n) 中工作
小例子：
//CountingRooms.h
#include <vector>
class CountingRooms
{
public:
CountingRooms();
~CountingRooms();
int Count();
void TestFill();
void Print();
private:
struct Point
{
int x = 0;
int y = 0;
};
unsigned int* m_arrFieldColors = nullptr;
unsigned int* m_arrFieldWalls = nullptr;
int m_nSizeX = 0;
int m_nSizeY = 0;
int m_nCurrentColor = 0;
unsigned int GetValue(unsigned int* field, int x, int y);
void SetValue(unsigned int* field, int x, int y, unsigned int value);
bool CanPass(int x1, int y1, int x2, int y2);
void DFS(int posX, int posY);
bool IsInsideArray(int x1, int y1);
};
//CountingRooms.cpp
#include "stdafx.h"
#include "CountingRooms.h"
#include <iostream>
CountingRooms::CountingRooms()
{
}
CountingRooms::~CountingRooms()
{
if (m_arrFieldColors)
{
delete[]m_arrFieldColors;
}
if (m_arrFieldWalls)
{
delete[]m_arrFieldWalls;
}
}
bool CountingRooms::IsInsideArray(int x, int y)
{
return x >= 0 && y >= 0 && x < m_nSizeX && y < m_nSizeY;
}
bool CountingRooms::CanPass(int x1, int y1, int x2, int y2)
{
if (IsInsideArray(x1, y1) && IsInsideArray(x2, y2)) //inside the array range
{
if (x2 - x1 == 1 && y2 - y1 == 0) // right
{
if (!(GetValue(m_arrFieldWalls, x1, y1) & 2) && !(GetValue(m_arrFieldWalls, x2, y2) & 8)) { return true; }
}
if (x2 - x1 == 0 && y2 - y1 == -1) // up
{
if (!(GetValue(m_arrFieldWalls, x1, y1) & 4) && !(GetValue(m_arrFieldWalls, x2, y2) & 1)) { return true; }
}
if (x2 - x1 == -1 && y2 - y1 == 0) // left
{
if (!(GetValue(m_arrFieldWalls, x1, y1) & 8) && !(GetValue(m_arrFieldWalls, x2, y2) & 2)) { return true; }
}
if (x2 - x1 == 0 && y2 - y1 == 1) // down
{
if (!(GetValue(m_arrFieldWalls, x1, y1) & 1) && !(GetValue(m_arrFieldWalls, x2, y2) & 4)) { return true; }
}
}
return false;
}
void CountingRooms::DFS(int posX, int posY)
{
if (GetValue(m_arrFieldColors, posX, posY)) // check if the field is already colored
{
return;
}
Point sStart;
sStart.x = posX;
sStart.y = posY;
std::vector<Point> vecList;
vecList.push_back(sStart);
m_nCurrentColor++;
while (vecList.size()) // as long as something is inside the list
{
Point sTemp = vecList[vecList.size()-1]; //get out the last element
vecList.pop_back();
if (IsInsideArray(sTemp.x, sTemp.y))
{
if (!GetValue(m_arrFieldColors, sTemp.x, sTemp.y)) // is field not colored
{
SetValue(m_arrFieldColors, sTemp.x, sTemp.y, m_nCurrentColor);
if (CanPass(sTemp.x, sTemp.y, sTemp.x + 1, sTemp.y)) /* right*/
{
Point newPoint;
newPoint.x = sTemp.x + 1;
newPoint.y = sTemp.y;
vecList.push_back(newPoint);
}
if (CanPass(sTemp.x, sTemp.y, sTemp.x - 1, sTemp.y)) /* left*/
{
Point newPoint;
newPoint.x = sTemp.x - 1;
newPoint.y = sTemp.y;
vecList.push_back(newPoint);
}
if (CanPass(sTemp.x, sTemp.y, sTemp.x, sTemp.y - 1)) /* up*/
{
Point newPoint;
newPoint.x = sTemp.x;
newPoint.y = sTemp.y - 1;
vecList.push_back(newPoint);
}
if (CanPass(sTemp.x, sTemp.y, sTemp.x, sTemp.y + 1)) /* down*/
{
Point newPoint;
newPoint.x = sTemp.x;
newPoint.y = sTemp.y + 1;
vecList.push_back(newPoint);
}
}
}
}
}
int CountingRooms::Count()
{
m_nCurrentColor = 0;
for (int i = 0; i < m_nSizeY; ++i)
{
for (int j = 0; j < m_nSizeX; ++j)
{
DFS(j, i);
}
}
return m_nCurrentColor;
}
void CountingRooms::TestFill()
{
m_arrFieldWalls = new unsigned int[42]{13, 6,13, 6,12, 5, 6,
14, 9, 6,11,10,15,10,
8, 5, 3,14,11,14,10,
11,13, 5, 1, 5, 3,11};
m_arrFieldColors = new unsigned int[42];
for (int i = 0; i < 42;i++)
{
m_arrFieldColors[i] = 0;
}
m_nSizeX = 7;
m_nSizeY = 4;
}
unsigned int CountingRooms::GetValue(unsigned int* field, int x, int y)
{
if (IsInsideArray(x, y))
{
return field[x + m_nSizeX*y];
}
return -1;
}
void CountingRooms::SetValue(unsigned int* field, int x, int y, unsigned int value)
{
if (IsInsideArray(x, y))
{
field[x + m_nSizeX*y] = value;
}
}
void CountingRooms::Print()
{
std::cout << "Walls:" << std::endl;
for (int j = 0; j < m_nSizeY;++j)
{
for (int i = 0; i < m_nSizeX;++i)
{
std::cout << GetValue(m_arrFieldWalls, i, j) << "\t";
}
std::cout << std::endl;
}
std::cout << std::endl<<"Colors:" << std::endl;
for (int j = 0; j < m_nSizeY;++j)
{
for (int i = 0; i < m_nSizeX;++i)
{
std::cout << GetValue(m_arrFieldColors, i, j) << "\t";
}
std::cout << std::endl;
}
}
//main.cpp
#include "stdafx.h"
#include <iostream>
#include "CountingRooms.h"
int main()
{
CountingRooms cr;
cr.TestFill();
std::cout<<"There are "<<cr.Count()<<" rooms"<<std::endl;
cr.Print();
char key = 0;
std::cin >> key;
return 0;
}
顺便说一句：BFS 被 DFS 取代，但两者都在工作。
输出