分而治之：残缺棋盘+染色

效果

代码

#include
#include 
using namespace std;


class ChessBoard {
private:
	int **chessBoard;
	int size;
	int xd, yd;
	int triangle;
public:
	ChessBoard(int s, int x, int y) {
		size = s;
		chessBoard = new int*[size];
		for (int i = 0; i < size; i++) {
			chessBoard[i] = new int[size];
			for (int j = 0; j < size; j++)
				chessBoard[i][j] = 0;
		}
		xd = x, yd = y;
		chessBoard[xd][yd] = -1;
		triangle = 0;
	}
	int search(int lx, int ly, int rx, int ry, int len);
	void cover(int lx, int ly, int rx, int ry, int len, int tri);
	void display();
};
int ChessBoard::search(int lx, int ly, int rx, int ry, int len) {
	int i, j;
	bool flag = false;
	for (i = lx; i <= rx; i++) {
		for (j = ly; j <= ry; j++) {
			if (chessBoard[i][j] != 0) {
				flag = true;
				break;
			}
				
		}
		if (flag) break;
	}
	int ox = lx + len;
	int oy = ly + len;
	if (i >= ox && j >= oy)
		return 4; //第四象限
	if (i < ox && j >= oy)
		return 1; //第一象限
	if (i >= ox && j < oy)
		return 3; //第三象限
	if (i < ox && j < oy)
		return 2; //第二象限
}
void ChessBoard::cover(int lx, int ly, int rx, int ry, int len, int color) {
	if (len == 0)
		return; //没有空块
	triangle++;
	if (len >= 2) color = 1;

	int quadrant = search(lx, ly, rx, ry, len);
	if (quadrant == 1) {
		chessBoard[lx + len][ly + len] = color; //4
		chessBoard[lx + len][ly + len - 1] = color; //3
		chessBoard[lx + len - 1][ly + len - 1] = color; //2
	}
	else if (quadrant == 2) {
		chessBoard[lx + len - 1][ly + len] = color; //1
		chessBoard[lx + len][ly + len] = color; //4
		chessBoard[lx + len][ly + len - 1] = color; //3
	}
	else if (quadrant == 3) {
		chessBoard[lx + len - 1][ly + len] = color; //1
		chessBoard[lx + len - 1][ly + len - 1] = color; //2
		chessBoard[lx + len][ly + len] = color; //4
	}
	else if (quadrant == 4) {
		chessBoard[lx + len - 1][ly + len] = color; //1
		chessBoard[lx + len - 1][ly + len - 1] = color; //2
		chessBoard[lx + len][ly + len - 1] = color; //3
	}
	//分治
	cover(lx, ly + len, lx + len - 1, ry, len / 2, 2); //1
	cover(lx, ly, lx + len - 1, ly + len - 1, len / 2, 3); //2
	cover(lx + len, ly, rx, ly + len - 1, len / 2, 2); //3
	cover(lx + len, ly + len, rx, ry, len / 2, 3); //4
}
void ChessBoard::display() {
	//颜色的代码： 0=黑色  1蓝色 2 绿色 3湖蓝色 4红色 5紫色 6黄色 7白色 8灰色 9淡蓝色
	enum colour { black, blue, green, lake_blue, red, purple, yellow, white, grey, baby_blue };
	int forecolour = white, backcolour;
	HANDLE handle;    //获取句柄
	handle = GetStdHandle(STD_OUTPUT_HANDLE);  //获取小黑框的句柄
	COORD coord;   //获取坐标轴结构体

	for (int i = 0; i < size; i++) {
		for (int j = 0; j < size; j++) {
			coord.X = i;
			coord.Y = j + 2;
			SetConsoleCursorPosition(handle, coord);   //移动光标到x，y处
			if (chessBoard[i][j] == -1) backcolour = white;
			else if (chessBoard[i][j] == 1) backcolour = yellow;
			else if (chessBoard[i][j] == 2) backcolour = lake_blue;
			else if (chessBoard[i][j] == 3) backcolour = red;
			SetConsoleTextAttribute(handle, forecolour + backcolour * 0x10);//改变当前光标的背景和字体颜色
			cout << " ";
		}
		cout << endl;
	}
	backcolour = black;
	SetConsoleTextAttribute(handle, forecolour + backcolour * 0x10);//改变当前光标的背景和字体颜色
	cout << "共用三隔板数: " << triangle << endl;
}


int main(void) {
	int k, x, y; 
	cout << "输入k: ";
	cin >> k;
	cout << "输入残缺位置(x,y): ";
	cin >> x >> y;
	int size = pow(2, k);
	ChessBoard chessBoard(size, x, y);
	chessBoard.cover(0, 0, size - 1, size - 1, size / 2, 1);
	chessBoard.display();


	system("pause");
	return 0;
}