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| 1 | +package divideconquer; |
| 2 | + |
| 3 | +/** |
| 4 | +
|
| 5 | +* For a set of points in a coordinates system (10000 maximum), |
| 6 | +* ClosestPair class calculates the two closest points. |
| 7 | +
|
| 8 | +* @author: anonymous |
| 9 | +* @author: Marisa Afuera |
| 10 | +*/ |
| 11 | + |
| 12 | + public final class ClosestPair { |
| 13 | + |
| 14 | + |
| 15 | + /** Number of points */ |
| 16 | + int numberPoints = 0; |
| 17 | + /** Input data, maximum 10000. */ |
| 18 | + private Location[] array; |
| 19 | + /** Minimum point coordinate. */ |
| 20 | + Location point1 = null; |
| 21 | + /** Minimum point coordinate. */ |
| 22 | + Location point2 = null; |
| 23 | + /** Minimum point length. */ |
| 24 | + private static double minNum = Double.MAX_VALUE; |
| 25 | + /** secondCount */ |
| 26 | + private static int secondCount = 0; |
| 27 | + |
| 28 | + /** |
| 29 | + * Constructor. |
| 30 | + */ |
| 31 | + ClosestPair(int points) { |
| 32 | + numberPoints = points; |
| 33 | + array = new Location[numberPoints]; |
| 34 | + } |
| 35 | + |
| 36 | + /** |
| 37 | + Location class is an auxiliary type to keep points coordinates. |
| 38 | + */ |
| 39 | + |
| 40 | + public static class Location { |
| 41 | + |
| 42 | + double x = 0; |
| 43 | + double y = 0; |
| 44 | + |
| 45 | + /** |
| 46 | + * @param xpar (IN Parameter) x coordinate <br/> |
| 47 | + * @param ypar (IN Parameter) y coordinate <br/> |
| 48 | + */ |
| 49 | + |
| 50 | + Location(final double xpar, final double ypar) { //Save x, y coordinates |
| 51 | + this.x = xpar; |
| 52 | + this.y = ypar; |
| 53 | + } |
| 54 | + |
| 55 | + } |
| 56 | + |
| 57 | + public Location[] createLocation(int numberValues) { |
| 58 | + return new Location[numberValues]; |
| 59 | + |
| 60 | + } |
| 61 | + |
| 62 | + public Location buildLocation(double x, double y){ |
| 63 | + return new Location(x,y); |
| 64 | + } |
| 65 | + |
| 66 | + |
| 67 | + /** xPartition function: arrange x-axis. |
| 68 | + * @param a (IN Parameter) array of points <br/> |
| 69 | + * @param first (IN Parameter) first point <br/> |
| 70 | + * @param last (IN Parameter) last point <br/> |
| 71 | + * @return pivot index |
| 72 | + */ |
| 73 | + |
| 74 | + public int xPartition( |
| 75 | + final Location[] a, final int first, final int last) { |
| 76 | + |
| 77 | + Location pivot = a[last]; // pivot |
| 78 | + int pIndex = last; |
| 79 | + int i = first - 1; |
| 80 | + Location temp; // Temporarily store value for position transformation |
| 81 | + for (int j = first; j <= last - 1; j++) { |
| 82 | + if (a[j].x <= pivot.x) { // Less than or less than pivot |
| 83 | + i++; |
| 84 | + temp = a[i]; // array[i] <-> array[j] |
| 85 | + a[i] = a[j]; |
| 86 | + a[j] = temp; |
| 87 | + } |
| 88 | + } |
| 89 | + i++; |
| 90 | + temp = a[i]; // array[pivot] <-> array[i] |
| 91 | + a[i] = a[pIndex]; |
| 92 | + a[pIndex] = temp; |
| 93 | + return i; // pivot index |
| 94 | + } |
| 95 | + |
| 96 | + /** yPartition function: arrange y-axis. |
| 97 | + * @param a (IN Parameter) array of points <br/> |
| 98 | + * @param first (IN Parameter) first point <br/> |
| 99 | + * @param last (IN Parameter) last point <br/> |
| 100 | + * @return pivot index |
| 101 | + */ |
| 102 | + |
| 103 | + public int yPartition( |
| 104 | + final Location[] a, final int first, final int last) { |
| 105 | + |
| 106 | + Location pivot = a[last]; // pivot |
| 107 | + int pIndex = last; |
| 108 | + int i = first - 1; |
| 109 | + Location temp; // Temporarily store value for position transformation |
| 110 | + for (int j = first; j <= last - 1; j++) { |
| 111 | + if (a[j].y <= pivot.y) { // Less than or less than pivot |
| 112 | + i++; |
| 113 | + temp = a[i]; // array[i] <-> array[j] |
| 114 | + a[i] = a[j]; |
| 115 | + a[j] = temp; |
| 116 | + } |
| 117 | + } |
| 118 | + i++; |
| 119 | + temp = a[i]; // array[pivot] <-> array[i] |
| 120 | + a[i] = a[pIndex]; |
| 121 | + a[pIndex] = temp; |
| 122 | + return i; // pivot index |
| 123 | + } |
| 124 | + |
| 125 | + /** xQuickSort function: //x-axis Quick Sorting. |
| 126 | + * @param a (IN Parameter) array of points <br/> |
| 127 | + * @param first (IN Parameter) first point <br/> |
| 128 | + * @param last (IN Parameter) last point <br/> |
| 129 | + */ |
| 130 | + |
| 131 | + public void xQuickSort( |
| 132 | + final Location[] a, final int first, final int last) { |
| 133 | + |
| 134 | + if (first < last) { |
| 135 | + int q = xPartition(a, first, last); // pivot |
| 136 | + xQuickSort(a, first, q - 1); // Left |
| 137 | + xQuickSort(a, q + 1, last); // Right |
| 138 | + } |
| 139 | + } |
| 140 | + |
| 141 | + /** yQuickSort function: //y-axis Quick Sorting. |
| 142 | + * @param a (IN Parameter) array of points <br/> |
| 143 | + * @param first (IN Parameter) first point <br/> |
| 144 | + * @param last (IN Parameter) last point <br/> |
| 145 | + */ |
| 146 | + |
| 147 | + public void yQuickSort( |
| 148 | + final Location[] a, final int first, final int last) { |
| 149 | + |
| 150 | + if (first < last) { |
| 151 | + int q = yPartition(a, first, last); // pivot |
| 152 | + yQuickSort(a, first, q - 1); // Left |
| 153 | + yQuickSort(a, q + 1, last); // Right |
| 154 | + } |
| 155 | + } |
| 156 | + |
| 157 | + /** closestPair function: find closest pair. |
| 158 | + * @param a (IN Parameter) array stored before divide <br/> |
| 159 | + * @param indexNum (IN Parameter) number coordinates divideArray <br/> |
| 160 | + * @return minimum distance <br/> |
| 161 | + */ |
| 162 | + |
| 163 | + public double closestPair(final Location[] a, final int indexNum) { |
| 164 | + |
| 165 | + Location[] divideArray = new Location[indexNum]; |
| 166 | + System.arraycopy(a, 0, divideArray, 0, indexNum); // Copy previous array |
| 167 | + int totalNum = indexNum; // number of coordinates in the divideArray |
| 168 | + int divideX = indexNum / 2; // Intermediate value for divide |
| 169 | + Location[] leftArray = new Location[divideX]; //divide - left array |
| 170 | + //divide-right array |
| 171 | + Location[] rightArray = new Location[totalNum - divideX]; |
| 172 | + if (indexNum <= 3) { // If the number of coordinates is 3 or less |
| 173 | + return bruteForce(divideArray); |
| 174 | + } |
| 175 | + //divide-left array |
| 176 | + System.arraycopy(divideArray, 0, leftArray, 0, divideX); |
| 177 | + //divide-right array |
| 178 | + System.arraycopy( |
| 179 | + divideArray, divideX, rightArray, 0, totalNum - divideX); |
| 180 | + |
| 181 | + double minLeftArea = 0; //Minimum length of left array |
| 182 | + double minRightArea = 0; //Minimum length of right array |
| 183 | + double minValue = 0; //Minimum lengt |
| 184 | + |
| 185 | + minLeftArea = closestPair(leftArray, divideX); // recursive closestPair |
| 186 | + minRightArea = closestPair(rightArray, totalNum - divideX); |
| 187 | + // window size (= minimum length) |
| 188 | + minValue = Math.min(minLeftArea, minRightArea); |
| 189 | + |
| 190 | + // Create window. Set the size for creating a window |
| 191 | + // and creating a new array for the coordinates in the window |
| 192 | + for (int i = 0; i < totalNum; i++) { |
| 193 | + double xGap = Math.abs(divideArray[divideX].x - divideArray[i].x); |
| 194 | + if (xGap < minValue) { |
| 195 | + secondCount++; // size of the array |
| 196 | + } else { |
| 197 | + if (divideArray[i].x > divideArray[divideX].x) { |
| 198 | + break; |
| 199 | + } |
| 200 | + } |
| 201 | + } |
| 202 | + // new array for coordinates in window |
| 203 | + Location[] firstWindow = new Location[secondCount]; |
| 204 | + int k = 0; |
| 205 | + for (int i = 0; i < totalNum; i++) { |
| 206 | + double xGap = Math.abs(divideArray[divideX].x - divideArray[i].x); |
| 207 | + if (xGap < minValue) { // if it's inside a window |
| 208 | + firstWindow[k] = divideArray[i]; // put in an array |
| 209 | + k++; |
| 210 | + } else { |
| 211 | + if (divideArray[i].x > divideArray[divideX].x) { |
| 212 | + break; |
| 213 | + } |
| 214 | + } |
| 215 | + } |
| 216 | + yQuickSort(firstWindow, 0, secondCount - 1); // Sort by y coordinates |
| 217 | + /* Coordinates in Window */ |
| 218 | + double length = 0; |
| 219 | + // size comparison within window |
| 220 | + for (int i = 0; i < secondCount - 1; i++) { |
| 221 | + for (int j = (i + 1); j < secondCount; j++) { |
| 222 | + double xGap = Math.abs(firstWindow[i].x - firstWindow[j].x); |
| 223 | + double yGap = Math.abs(firstWindow[i].y - firstWindow[j].y); |
| 224 | + if (yGap < minValue) { |
| 225 | + length = Math.sqrt(Math.pow(xGap, 2) + Math.pow(yGap, 2)); |
| 226 | + // If measured distance is less than current min distance |
| 227 | + if (length < minValue) { |
| 228 | + // Change minimum distance to current distance |
| 229 | + minValue = length; |
| 230 | + // Conditional for registering final coordinate |
| 231 | + if (length < minNum) { |
| 232 | + minNum = length; |
| 233 | + point1 = firstWindow[i]; |
| 234 | + point2 = firstWindow[j]; |
| 235 | + } |
| 236 | + } |
| 237 | + } |
| 238 | + else { |
| 239 | + break; |
| 240 | + } |
| 241 | + } |
| 242 | + } |
| 243 | + secondCount = 0; |
| 244 | + return minValue; |
| 245 | + } |
| 246 | + |
| 247 | + /** bruteForce function: When the number of coordinates is less than 3. |
| 248 | + * @param arrayParam (IN Parameter) array stored before divide <br/> |
| 249 | + * @return <br/> |
| 250 | + */ |
| 251 | + |
| 252 | + public double bruteForce(final Location[] arrayParam) { |
| 253 | + |
| 254 | + double minValue = Double.MAX_VALUE; // minimum distance |
| 255 | + double length = 0; |
| 256 | + double xGap = 0; // Difference between x coordinates |
| 257 | + double yGap = 0; // Difference between y coordinates |
| 258 | + double result = 0; |
| 259 | + |
| 260 | + if (arrayParam.length == 2) { |
| 261 | + // Difference between x coordinates |
| 262 | + xGap = (arrayParam[0].x - arrayParam[1].x); |
| 263 | + // Difference between y coordinates |
| 264 | + yGap = (arrayParam[0].y - arrayParam[1].y); |
| 265 | + // distance between coordinates |
| 266 | + length = Math.sqrt(Math.pow(xGap, 2) + Math.pow(yGap, 2)); |
| 267 | + // Conditional statement for registering final coordinate |
| 268 | + if (length < minNum) { |
| 269 | + minNum = length; |
| 270 | + |
| 271 | + } |
| 272 | + point1 = arrayParam[0]; |
| 273 | + point2 = arrayParam[1]; |
| 274 | + result = length; |
| 275 | + } |
| 276 | + if (arrayParam.length == 3) { |
| 277 | + for (int i = 0; i < arrayParam.length - 1; i++) { |
| 278 | + for (int j = (i + 1); j < arrayParam.length; j++) { |
| 279 | + // Difference between x coordinates |
| 280 | + xGap = (arrayParam[i].x - arrayParam[j].x); |
| 281 | + // Difference between y coordinates |
| 282 | + yGap = (arrayParam[i].y - arrayParam[j].y); |
| 283 | + // distance between coordinates |
| 284 | + length = |
| 285 | + Math.sqrt(Math.pow(xGap, 2) + Math.pow(yGap, 2)); |
| 286 | + // If measured distance is less than current min distance |
| 287 | + if (length < minValue) { |
| 288 | + // Change minimum distance to current distance |
| 289 | + minValue = length; |
| 290 | + if (length < minNum) { |
| 291 | + // Registering final coordinate |
| 292 | + minNum = length; |
| 293 | + point1 = arrayParam[i]; |
| 294 | + point2 = arrayParam[j]; |
| 295 | + } |
| 296 | + } |
| 297 | + } |
| 298 | + } |
| 299 | + result = minValue; |
| 300 | + |
| 301 | + } |
| 302 | + return result; // If only one point returns 0. |
| 303 | + } |
| 304 | + |
| 305 | + /** main function: execute class. |
| 306 | + * @param args (IN Parameter) <br/> |
| 307 | + * @throws IOException If an input or output |
| 308 | + * exception occurred |
| 309 | + */ |
| 310 | + |
| 311 | + public static void main(final String[] args) { |
| 312 | + |
| 313 | + //Input data consists of one x-coordinate and one y-coordinate |
| 314 | + |
| 315 | + ClosestPair cp = new ClosestPair(12); |
| 316 | + cp.array[0]=cp.buildLocation(2,3); |
| 317 | + cp.array[1]=cp.buildLocation(2,16); |
| 318 | + cp.array[2]=cp.buildLocation(3,9); |
| 319 | + cp.array[3]=cp.buildLocation(6,3); |
| 320 | + cp.array[4]=cp.buildLocation(7,7); |
| 321 | + cp.array[5]=cp.buildLocation(19,4); |
| 322 | + cp.array[6]=cp.buildLocation(10,11); |
| 323 | + cp.array[7]=cp.buildLocation(15,2); |
| 324 | + cp.array[8]=cp.buildLocation(15,19); |
| 325 | + cp.array[9]=cp.buildLocation(16,11); |
| 326 | + cp.array[10]=cp.buildLocation(17,13); |
| 327 | + cp.array[11]=cp.buildLocation(9,12); |
| 328 | + |
| 329 | + System.out.println("Input data"); |
| 330 | + System.out.println("Number of points: "+ cp.array.length); |
| 331 | + for (int i=0;i<cp.array.length;i++){ |
| 332 | + System.out.println("x: " + cp.array[i].x + ", y: " + cp.array[i].y); |
| 333 | + } |
| 334 | + |
| 335 | + cp.xQuickSort(cp.array, 0, cp.array.length-1); // Sorting by x value |
| 336 | + |
| 337 | + double result; // minimum distance |
| 338 | + |
| 339 | + result = cp.closestPair(cp.array, cp.array.length); |
| 340 | + // ClosestPair start |
| 341 | + // minimum distance coordinates and distance output |
| 342 | + System.out.println("Output Data"); |
| 343 | + System.out.println("(" + cp.point1.x + ", " + cp.point1.y + ")"); |
| 344 | + System.out.println("(" + cp.point2.x + ", " + cp.point2.y + ")"); |
| 345 | + System.out.println("Minimum Distance : " + result); |
| 346 | + |
| 347 | + } |
| 348 | +} |
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