棋盘覆盖

 分治+递归

//思路：棋盘大小为2^size * 2^size,不断将棋盘划分成4部分，若特殊方格在某一部分，只需继续递归，若不在，则在此部分构造一个特殊方格。//构造特殊方格要注意：由于划分4部分中三部分无特殊方格，故构造的特殊方格必须在这三部分连成一个L型牌#include <iostream>#include <iomanip>using namespace std;int chessBoard[1 << 9][1 << 9];void fill(int row, int col, int s_row, int s_col, int size) {if(size == 1) return;static int num = 1;int cur_num = num++;int half_size = size / 2;//左上角大方格if(s_row < row + half_size && s_col < col + half_size) {fill(row, col, s_row, s_col, half_size);}else {//构造特殊方格chessBoard[row + half_size - 1][col + half_size - 1] = cur_num;fill(row, col, row + half_size - 1, col + half_size - 1, half_size);}//左下角大方格if(s_row >= row + half_size && s_col < col + half_size) {fill(row + half_size, col, s_row, s_col, half_size);}else {//构造特殊方格chessBoard[row + half_size][col + half_size - 1] = cur_num;fill(row + half_size, col, row + half_size, col + half_size - 1, half_size);}//右上角大方格if(s_row < row + half_size && s_col >= col + half_size) {fill(row, col + half_size, s_row, s_col, half_size);}else {//构造特殊方格chessBoard[row + half_size - 1][col + half_size] = cur_num;fill(row, col + half_size, row + half_size - 1, col + half_size, half_size);}//右下角大方格if(s_row >= row + half_size && s_col >= col + half_size) {fill(row + half_size, col + half_size, s_row, s_col, half_size);}else {//构造特殊方格chessBoard[row + half_size][col + half_size] = cur_num;fill(row + half_size, col + half_size, row + half_size, col + half_size, half_size);}}void print(int size) {for(int i = 0; i < size; i++) {for(int j = 0; j < size; j++) {cout << setw(3) << chessBoard[i][j];}cout << endl;}}int main() {int size;int s_col, s_row;cout << "输入棋盘的长(必须是2的n次方，你只需要输入n即可):";cin >> size;cout << "输入特殊方格的位置:";cin >> s_row >> s_col;int _size = 1 << size;while(s_row >= _size && s_col >= _size) {cout << "输入有误，请重新输入:";cin >> s_row >> s_col;}chessBoard[s_row][s_col] = 0;fill(0, 0, s_row, s_col, _size);print(_size);return 0;}