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; }