How to Use "L" dominos to conver 2^K * 2^K boxes
The code:
1 package algorithm.study.demo1; 2 3 import java.util.Arrays; 4 5 import org.junit.Test; 6 7 /** 8 * This class is to implement how use "L" dominos to bespread the 2^K * 2^K boxes. But one of the 9 * boxes has bean put a dominos 10 * 11 * for example: there is a boxes and "0" represent the boxes need filled by "L" dominos 12 * the "1" represent the box has bean filled by dominos. 13 * [0, 1, 0, 0] 14 [0, 0, 0, 0] 15 [0, 0, 0, 0] 16 [0, 0, 0, 0] 17 18 There are four types "L" dominos to used 19 20 a): b): c): d): 21 1 1 1 1 1 1 22 1 1 1 1 1 1 23 you will use the four types of domines to fill of empty boxes 24 25 * 26 * @author ygh 2017年2月23日 27 */ 28 public class LDomino { 29 30 //The domino flag,same domina will use same number 31 private int LDominos = 10; 32 33 34 /** 35 * Arithmetic thoughts:Using recursion thoughts 36 * a):We first separate the all dominos boxes to four smaller and equal 37 * dominos,one of the four domines must has a box has bean fill; 38 * 39 * [0, 1, 0, 0] 40 [0, 0, 0, 0] 41 42 [0, 0, 0, 0] 43 [0, 0, 0, 0] 44 * 45 * b):then we fill the center of four dominos with "L",but if one has 46 * the filled box,we will not to fill it. 47 * 48 * [0, 1, 0, 0] 49 [0, 0, 1, 0] 50 51 [0, 1, 1, 0] 52 [0, 0, 0, 0] 53 54 * 55 *c):we use same method to separate the four dominos to smaller dominos,then fill the center boxes 56 * except for one has a box been filled with 57 * 58 * 59 * [3, 1, 2, 2] 60 * 61 [3, 3, 1, 2] 62 63 [3, 1, 1, 2] 64 65 [3, 3, 2, 2] 66 67 you see it success,so will use program to implement it following 68 * 69 70 * @param or The boxes primary row 行 71 * @param oc The boxes primary line 列 72 * @param dr The boxes has been fill with domino row 行 73 * @param dc The boxes has been fill with domino line 列 74 * @param size The size of the box,we will use 2^size as the box's row and line 75 */ 76 public void fillBoxes(int[][] arr,int or,int oc,int dr,int dc,int size){ 77 //get boxes and initialize a box filled with domino 78 79 if(size==1){ 80 return; 81 } 82 83 //the temporary number of dominos 84 int filled = ++LDominos; 85 //the size of smaller boxes 86 int s = size / 2; 87 88 //If the box filled in the top left 89 if(dr<or+s && dc<oc+s){ 90 fillBoxes(arr,or,oc,dr,dc,s); 91 }else{//If the box filled not in the top left 92 arr[or+s-1][oc+s-1]=filled; 93 fillBoxes(arr,or, oc, or+s-1, oc+s-1, s); 94 } 95 96 //If the box filled in the top right 97 if(dr>=or+s && dc < oc+s){ 98 fillBoxes(arr,or+s, oc, dr, dc, s); 99 }else{ //If the box filled not in the top right 100 arr[or+s][oc+s-1]=filled; 101 fillBoxes(arr,or+s, oc, or+s, oc+s-1, s); 102 } 103 104 //If the box filled in the bottom left 105 if(dr<or+s && dc>=oc+s){ 106 fillBoxes(arr,or, oc+s, dr, dc, s); 107 }else{//If the box filled not in the bottom left 108 arr[or+s-1][oc+s]=filled; 109 fillBoxes(arr,or, oc+s, or+s-1, oc+s, s); 110 } 111 112 //If the box filled in the bottom right 113 if(dr>=or+s && dc>=oc+s){ 114 fillBoxes(arr,or+s, oc+s, dr, dc, s); 115 }else{//If the box filled not in the bottom right 116 arr[or+s][oc+s]=filled; 117 fillBoxes(arr,or+s, oc+s, or+s, oc+s, s); 118 } 119 120 } 121 122 123 /** 124 * return 125 * @param size 126 * @return 127 */ 128 public int[][] getBoxes(int size) { 129 int arr [][] = new int[size][size]; 130 for(int i=0;i<size;i++){ 131 Arrays.fill(arr[i], 0); 132 } 133 return arr; 134 } 135 136 /** 137 * print the boxes 138 * @param arr The boxes needed to print 139 * @param size The size of boxes,the size must be 2^k 140 */ 141 public void inputBoxes(int[][]arr,int size,String status){ 142 System.out.println(status); 143 for(int i=0;i<size;i++){ 144 System.out.println(Arrays.toString(arr[i])); 145 } 146 } 147 148 149 /** 150 * Get a random Integer,but we give it max value. 151 * 152 * @param maxValue The max value of the random integer. 153 * @return A random integer that don't than max value. 154 */ 155 public int getRandow(int maxValue) { 156 return (int) (Math.random() * maxValue); 157 } 158 159 160 /** 161 * test preparation 162 * @param size 163 */ 164 public void prepareTest(int size){ 165 int[][] arr = getBoxes(size); 166 int dr = getRandow(arr.length); 167 int dc = getRandow(arr.length); 168 //set one of the box filled as "10" 169 arr[dr][dc]=10; 170 inputBoxes(arr, size,"未处理状态："); 171 fillBoxes(arr, 0, 0, dr, dc, size); 172 inputBoxes(arr, size,"已处理状态："); 173 System.out.println("==================================="); 174 } 175 176 @Test 177 public void fun2(){ 178 for(int i=0;i<=4;i++){ 179 int size = (int) Math.pow(2, i); 180 prepareTest(size); 181 } 182 } 183 184 /* 185 * The result of test 186 * 未处理状态： 187 [10] 188 已处理状态： 189 [10] 190 =================================== 191 未处理状态： 192 [0, 10] 193 [0, 0] 194 已处理状态： 195 [11, 10] 196 [11, 11] 197 =================================== 198 未处理状态： 199 [0, 0, 0, 0] 200 [0, 0, 10, 0] 201 [0, 0, 0, 0] 202 [0, 0, 0, 0] 203 已处理状态： 204 [13, 13, 15, 15] 205 [13, 12, 10, 15] 206 [14, 12, 12, 16] 207 [14, 14, 16, 16] 208 =================================== 209 未处理状态： 210 [0, 0, 0, 0, 0, 0, 0, 0] 211 [0, 0, 0, 0, 0, 0, 0, 0] 212 [0, 0, 0, 0, 0, 0, 0, 0] 213 [0, 0, 0, 0, 0, 0, 0, 0] 214 [0, 0, 0, 0, 0, 0, 0, 0] 215 [0, 0, 0, 0, 0, 0, 0, 0] 216 [0, 10, 0, 0, 0, 0, 0, 0] 217 [0, 0, 0, 0, 0, 0, 0, 0] 218 已处理状态： 219 [19, 19, 21, 21, 29, 29, 31, 31] 220 [19, 18, 18, 21, 29, 28, 28, 31] 221 [20, 18, 22, 22, 30, 30, 28, 32] 222 [20, 20, 22, 17, 17, 30, 32, 32] 223 [24, 24, 26, 26, 17, 34, 36, 36] 224 [24, 23, 23, 26, 34, 34, 33, 36] 225 [25, 10, 23, 27, 35, 33, 33, 37] 226 [25, 25, 27, 27, 35, 35, 37, 37] 227 =================================== 228 未处理状态： 229 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 230 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 231 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 232 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 233 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 234 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 235 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 236 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 237 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 238 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 239 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0] 240 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 241 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 242 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 243 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 244 [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] 245 已处理状态： 246 [41, 41, 43, 43, 51, 51, 53, 53, 83, 83, 85, 85, 93, 93, 95, 95] 247 [41, 40, 40, 43, 51, 50, 50, 53, 83, 82, 82, 85, 93, 92, 92, 95] 248 [42, 40, 44, 44, 52, 52, 50, 54, 84, 82, 86, 86, 94, 94, 92, 96] 249 [42, 42, 44, 39, 39, 52, 54, 54, 84, 84, 86, 81, 81, 94, 96, 96] 250 [46, 46, 48, 39, 56, 56, 58, 58, 88, 88, 90, 90, 81, 98, 100, 100] 251 [46, 45, 48, 48, 56, 55, 55, 58, 88, 87, 87, 90, 98, 98, 97, 100] 252 [47, 45, 45, 49, 57, 55, 59, 59, 89, 89, 87, 91, 99, 97, 97, 101] 253 [47, 47, 49, 49, 57, 57, 59, 38, 38, 89, 91, 91, 99, 99, 101, 101] 254 [62, 62, 64, 64, 72, 72, 74, 38, 104, 104, 106, 106, 114, 114, 116, 116] 255 [62, 61, 61, 64, 72, 71, 74, 74, 104, 103, 103, 106, 114, 113, 113, 116] 256 [63, 61, 65, 65, 73, 71, 71, 75, 105, 103, 107, 107, 115, 10, 113, 117] 257 [63, 63, 65, 60, 73, 73, 75, 75, 105, 105, 107, 102, 115, 115, 117, 117] 258 [67, 67, 69, 60, 60, 77, 79, 79, 109, 109, 111, 102, 102, 119, 121, 121] 259 [67, 66, 69, 69, 77, 77, 76, 79, 109, 108, 111, 111, 119, 119, 118, 121] 260 [68, 66, 66, 70, 78, 76, 76, 80, 110, 108, 108, 112, 120, 118, 118, 122] 261 [68, 68, 70, 70, 78, 78, 80, 80, 110, 110, 112, 112, 120, 120, 122, 122] 262 =================================== 263 264 */ 265 266 267 }
