棋盘覆盖问题 分治和栈实现

版权声明：本文为博主原创，未经博主允许不得转载。 https://blog.csdn.net/one_of_a_kind/article/details/83820182

#include<iostream>
#include<math.h>
#include <algorithm>
#include<string>
#include<stack>
using namespace std;

int chessboard[1024][1024];
int type = 0;
int N;
struct chess {
	int x;
	int y;
	int k;
	int cx;
	int cy;
};
stack <chess> chessStack;

void Print(int k) {
	int n = pow(2, k);
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < n; j++) {
			printf("%5d", chessboard[i][j]);
		}
		printf("\n");
	}
	printf("\n");
}

//用于给结构体赋值
void Assign(int x, int y, int k, int cx, int cy, chess & c) {
	c.x = x; c.y = y; c.cx = cx; c.cy = cy; c.k = k;
}

void ChessViaStack() {
	while (!chessStack.empty()) {
		chess ctemp;
		chess c = chessStack.top();
		chessStack.pop();
		int x = c.x, y = c.y, k = c.k, cx = c.cx, cy = c.cy;
		int n = pow(2, k);
		type++;

		if (n < 2) {
			type--;
		}
		//已被覆盖的坐标在左上方
		else if ((cx < x + n / 2) && (cy < y + n / 2)) {
			//再覆盖三个棋子
			chessboard[x + n / 2 - 1][y + n / 2] = type;
			chessboard[x + n / 2][y + n / 2 - 1] = type;
			chessboard[x + n / 2][y + n / 2] = type;

			Assign(x, y, k - 1, cx, cy, ctemp);
			chessStack.push(ctemp);
			Assign(x, y + n / 2, k - 1, x + n / 2 - 1, y + n / 2, ctemp);
			chessStack.push(ctemp);
			Assign(x + n / 2, y, k - 1, x + n / 2, y + n / 2 - 1, ctemp);
			chessStack.push(ctemp);
			Assign(x + n / 2, y + n / 2, k - 1, x + n / 2, y + n / 2, ctemp);
			chessStack.push(ctemp);
		}
		//左下
		else if ((cx >= x + n / 2) && (cy < y + n / 2)) {
			//再覆盖三个棋子
			chessboard[x + n / 2 - 1][y + n / 2 - 1] = type;
			chessboard[x + n / 2 - 1][y + n / 2] = type;
			chessboard[x + n / 2][y + n / 2] = type;

			Assign(x + n / 2, y, k - 1, cx, cy, ctemp);
			chessStack.push(ctemp);
			Assign(x, y, k - 1, x + n / 2 - 1, y + n / 2 - 1, ctemp);
			chessStack.push(ctemp);
			Assign(x, y + n / 2, k - 1, x + n / 2 - 1, y + n / 2, ctemp);
			chessStack.push(ctemp);
			Assign(x + n / 2, y + n / 2, k - 1, x + n / 2, y + n / 2, ctemp);
			chessStack.push(ctemp);
		}
		//右上
		else if ((cx < x + n / 2) && (cy >= y + n / 2)) {
			//再覆盖三个棋子
			chessboard[x + n / 2 - 1][y + n / 2 - 1] = type;
			chessboard[x + n / 2][y + n / 2 - 1] = type;
			chessboard[x + n / 2][y + n / 2] = type;

			Assign(x, y + n / 2, k - 1, cx, cy, ctemp);
			chessStack.push(ctemp);
			Assign(x, y, k - 1, x + n / 2 - 1, y + n / 2 - 1, ctemp);
			chessStack.push(ctemp);
			Assign(x + n / 2, y, k - 1, x + n / 2, y + n / 2 - 1, ctemp);
			chessStack.push(ctemp);
			Assign(x + n / 2, y + n / 2, k - 1, x + n / 2, y + n / 2, ctemp);
			chessStack.push(ctemp);
		}
		//右下
		else if ((cx >= x + n / 2) && (cy >= y + n / 2)) {
			//再覆盖三个棋子
			chessboard[x + n / 2 - 1][y + n / 2 - 1] = type;
			chessboard[x + n / 2 - 1][y + n / 2] = type;
			chessboard[x + n / 2][y + n / 2 - 1] = type;

			Assign(x + n / 2, y + n / 2, k - 1, cx, cy, ctemp);
			chessStack.push(ctemp);
			Assign(x, y, k - 1, x + n / 2 - 1, y + n / 2 - 1, ctemp);
			chessStack.push(ctemp);
			Assign(x, y + n / 2, k - 1, x + n / 2 - 1, y + n / 2, ctemp);
			chessStack.push(ctemp);
			Assign(x + n / 2, y, k - 1, x + n / 2, y + n / 2 - 1, ctemp);
			chessStack.push(ctemp);
		}
	}
	
}

void RecursiveChess(int x, int y, int k, int cx, int cy) {
	//Print(k);

	int n = pow(2, k);
	type++;

	if (n < 2) {
		type--;
		return;
	}
	//已被覆盖的坐标在左上方
	else if ((cx < x + n / 2) && (cy < y + n / 2)) {
		//再覆盖三个棋子
		chessboard[x + n / 2 - 1][y + n / 2] = type;
		chessboard[x + n / 2][y + n / 2 - 1] = type;
		chessboard[x + n / 2][y + n / 2] = type;

		RecursiveChess(x, y, k - 1, cx, cy);
		RecursiveChess(x, y + n / 2, k - 1, x + n / 2 - 1, y + n / 2);
		RecursiveChess(x + n / 2, y, k - 1, x + n / 2, y + n / 2 - 1);
		RecursiveChess(x + n / 2, y + n / 2, k - 1, x + n / 2, y + n / 2);
	}
	//左下
	else if ((cx >= x + n / 2) && (cy < y + n / 2)) {
		//再覆盖三个棋子
		chessboard[x + n / 2 - 1][y + n / 2 - 1] = type;
		chessboard[x + n / 2 - 1][y + n / 2] = type;
		chessboard[x + n / 2][y + n / 2] = type;

		RecursiveChess(x + n / 2, y, k - 1, cx, cy);
		RecursiveChess(x, y, k - 1, x + n / 2 - 1, y + n / 2 - 1);
		RecursiveChess(x, y + n / 2, k - 1, x + n / 2 - 1, y + n / 2);
		RecursiveChess(x + n / 2, y + n / 2, k - 1, x + n / 2, y + n / 2);
	}
	//右上
	else if ((cx < x + n / 2) && (cy >= y + n / 2)) {
		//再覆盖三个棋子
		chessboard[x + n / 2 - 1][y + n / 2 - 1] = type;
		chessboard[x + n / 2][y + n / 2 - 1] = type;
		chessboard[x + n / 2][y + n / 2] = type;

		RecursiveChess(x, y + n / 2, k - 1, cx, cy);
		RecursiveChess(x, y, k - 1, x + n / 2 - 1, y + n / 2 - 1);
		RecursiveChess(x + n / 2, y, k - 1, x + n / 2, y + n / 2 - 1);
		RecursiveChess(x + n / 2, y + n / 2, k - 1, x + n / 2, y + n / 2);
	}
	//右下
	else if ((cx >= x + n / 2) && (cy >= y + n / 2)) {
		//再覆盖三个棋子
		chessboard[x + n / 2 - 1][y + n / 2 - 1] = type;
		chessboard[x + n / 2 - 1][y + n / 2] = type;
		chessboard[x + n / 2][y + n / 2 - 1] = type;

		RecursiveChess(x + n / 2, y + n / 2, k - 1, cx, cy);
		RecursiveChess(x, y, k - 1, x + n / 2 - 1, y + n / 2 - 1);
		RecursiveChess(x, y + n / 2, k - 1, x + n / 2 - 1, y + n / 2);
		RecursiveChess(x + n / 2, y, k - 1, x + n / 2, y + n / 2 - 1);
	}
}

int main() {
	int k,cx, cy;
	while (cin >> k) {
		memset(chessboard, 0, 1024 * 1024 * sizeof(int));
		cin >> cx >> cy;
		N = pow(2, k);
		type = 0;
		chessboard[cx][cy] = -1;
		
		RecursiveChess(0, 0, k, cx, cy);
		
		/*
		*栈实现
		chess c;
		Assign(0, 0, k, cx, cy, c);
		chessStack.push(c);
		ChessViaStack();
		*/
		Print(k);
	}
	system("pause");
	return 0;
}