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286 lines
7.9 KiB
Java
286 lines
7.9 KiB
Java
import java.util.Arrays;
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import java.util.Random;
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// https://en.wikipedia.org/wiki/R-tree
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public class PointLocationRtree {
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static Random random = new Random(1);
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static class Polygon {
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final int[] x;
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final int[] y;
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final int centerX;
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final int centerY;
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final int id;
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public Polygon(int[] x, int[] y, int id) {
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this.x = x;
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this.y = y;
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this.centerX = average(x);
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this.centerY = average(y);
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this.id = id;
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}
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static int average(int[] a) {
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long res = 0;
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for (int v : a)
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res += v;
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return (int) (res / a.length);
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}
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}
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static class RTree {
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final Polygon[] polygons;
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final int[] minx, maxx, miny, maxy;
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public RTree(Polygon[] polygons) {
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int n = polygons.length;
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this.polygons = polygons;
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minx = new int[n];
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maxx = new int[n];
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miny = new int[n];
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maxy = new int[n];
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Arrays.fill(minx, Integer.MAX_VALUE);
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Arrays.fill(maxx, Integer.MIN_VALUE);
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Arrays.fill(miny, Integer.MAX_VALUE);
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Arrays.fill(maxy, Integer.MIN_VALUE);
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build(0, n, true);
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}
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void build(int low, int high, boolean divX) {
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if (low >= high)
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return;
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int mid = (low + high) >>> 1;
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nth_element(polygons, low, high, mid, divX);
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for (int i = low; i < high; i++) {
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for (int j = 0; j < polygons[i].x.length; j++) {
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minx[mid] = Math.min(minx[mid], polygons[i].x[j]);
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miny[mid] = Math.min(miny[mid], polygons[i].y[j]);
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maxx[mid] = Math.max(maxx[mid], polygons[i].x[j]);
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maxy[mid] = Math.max(maxy[mid], polygons[i].y[j]);
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}
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}
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build(low, mid, !divX);
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build(mid + 1, high, !divX);
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}
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// See: http://www.cplusplus.com/reference/algorithm/nth_element
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static void nth_element(Polygon[] a, int low, int high, int n, boolean divX) {
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while (true) {
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int k = partition(a, low, high, low + random.nextInt(high - low), divX);
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if (n < k)
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high = k;
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else if (n > k)
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low = k + 1;
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else
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return;
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}
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}
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static int partition(Polygon[] a, int fromInclusive, int toExclusive, int separatorIndex, boolean divX) {
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int i = fromInclusive;
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int j = toExclusive - 1;
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if (i >= j) return j;
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double separator = divX ? a[separatorIndex].centerX : a[separatorIndex].centerY;
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swap(a, i++, separatorIndex);
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while (i <= j) {
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while (i <= j && (divX ? a[i].centerX : a[i].centerY) < separator)
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++i;
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while (i <= j && (divX ? a[j].centerX : a[j].centerY) > separator)
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--j;
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if (i >= j)
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break;
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swap(a, i++, j--);
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}
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swap(a, j, fromInclusive);
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return j;
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}
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static void swap(Polygon[] a, int i, int j) {
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Polygon t = a[i];
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a[i] = a[j];
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a[j] = t;
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}
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int foundPolygon;
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public int findEnclosingPolygon(int x, int y) {
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foundPolygon = -1;
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findEnclosingPolygon(0, polygons.length, x, y, true);
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return foundPolygon;
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}
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void findEnclosingPolygon(int low, int high, int x, int y, boolean divX) {
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if (low >= high)
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return;
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int mid = (low + high) >>> 1;
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if (x < minx[mid] || x > maxx[mid] || y < miny[mid] || y > maxy[mid])
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return;
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int location = pointInPolygon(x, y, polygons[mid].x, polygons[mid].y);
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if (location != -1) {
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foundPolygon = polygons[mid].id;
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return;
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}
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findEnclosingPolygon(low, mid, x, y, !divX);
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findEnclosingPolygon(mid + 1, high, x, y, !divX);
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}
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}
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public static int[] locatePoints(int[][] polygonX, int[][] polygonY, int[] qx, int[] qy) {
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int n = polygonX.length;
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Polygon[] polygons = new Polygon[n];
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for (int i = 0; i < n; i++) {
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polygons[i] = new Polygon(polygonX[i], polygonY[i], i);
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}
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RTree rTree = new RTree(polygons);
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int[] res = new int[qx.length];
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for (int i = 0; i < qx.length; i++) {
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res[i] = rTree.findEnclosingPolygon(qx[i], qy[i]);
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}
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return res;
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}
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// random test
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public static void main(String[] args) {
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for (int step = 0; step < 10_000; step++) {
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int range = 10;
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int R = 3;
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int C = 3;
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int[][] polygonX = new int[R * C][];
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int[][] polygonY = new int[R * C][];
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for (int r = 0; r < R; r++) {
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for (int c = 0; c < C; c++) {
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int n = random.nextInt(10) + 3;
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int[][] xy = getRandomPolygon(n, range, range);
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polygonX[r * C + c] = xy[0];
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polygonY[r * C + c] = xy[1];
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for (int i = 0; i < n; i++) {
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polygonX[r * C + c][i] += c * (range + 1);
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polygonY[r * C + c][i] += r * (range + 1);
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}
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}
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}
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int queries = random.nextInt(10) + 1;
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queries = 1;
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int[] qx = new int[queries];
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int[] qy = new int[queries];
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int[] res1 = new int[queries];
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Arrays.fill(res1, -1);
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for (int i = 0; i < queries; i++) {
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qx[i] = random.nextInt((C + 2) * (range + 1)) - range;
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qy[i] = random.nextInt((R + 2) * (range + 1)) - range;
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for (int j = 0; j < polygonX.length; j++) {
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int v = pointInPolygon(qx[i], qy[i], polygonX[j], polygonY[j]);
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if (v >= 0) {
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res1[i] = j;
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break;
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}
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}
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}
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int[] res2 = locatePoints(polygonX, polygonY, qx, qy);
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if (!Arrays.equals(res1, res2))
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throw new RuntimeException();
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}
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}
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static int pointInPolygon(int qx, int qy, int[] x, int[] y) {
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int n = x.length;
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int cnt = 0;
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for (int i = 0, j = n - 1; i < n; j = i++) {
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if (y[i] == qy && (x[i] == qx || y[j] == qy && (x[i] <= qx || x[j] <= qx) && (x[i] >= qx || x[j] >= qx)))
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return 0; // boundary
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if ((y[i] > qy) != (y[j] > qy)) {
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long det = (long) (x[i] - qx) * (y[j] - qy) - (long) (x[j] - qx) * (y[i] - qy);
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if (det == 0)
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return 0; // boundary
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if ((det > 0) != (y[j] - y[i] > 0))
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++cnt;
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}
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}
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return cnt % 2 == 0 ? -1 /* exterior */ : 1 /* interior */;
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}
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static int[][] getRandomPolygon(int n, int maxWidth, int maxHeight) {
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int[] x = new int[n];
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int[] y = new int[n];
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int[] p = new int[n];
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while (true) {
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for (int i = 0; i < n; i++) {
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x[i] = random.nextInt(maxWidth);
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y[i] = random.nextInt(maxHeight);
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p[i] = i;
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}
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for (boolean improved = true; improved; ) {
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improved = false;
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < n; j++) {
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int[] p1 = p.clone();
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reverse(p1, i, j);
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if (len(x, y, p) > len(x, y, p1)) {
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p = p1;
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improved = true;
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}
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}
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}
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}
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int[] tx = x.clone();
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int[] ty = y.clone();
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for (int i = 0; i < n; i++) {
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x[i] = tx[p[i]];
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y[i] = ty[p[i]];
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}
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boolean ok = true;
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for (int i = 0; i < n; i++) {
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long x1 = x[(i - 1 + n) % n] - x[i];
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long y1 = y[(i - 1 + n) % n] - y[i];
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long x2 = x[(i + 1) % n] - x[i];
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long y2 = y[(i + 1) % n] - y[i];
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ok &= x1 * y2 - x2 * y1 != 0 || x1 * x2 + y1 * y2 <= 0;
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}
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for (int i2 = 0, i1 = p.length - 1; i2 < p.length; i1 = i2++)
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for (int j2 = 0, j1 = p.length - 1; j2 < p.length; j1 = j2++)
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ok &= i1 == j1 || i1 == j2 || i2 == j1
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|| !isCrossOrTouchIntersect(x[i1], y[i1], x[i2], y[i2], x[j1], y[j1], x[j2], y[j2]);
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if (ok)
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return new int[][]{x, y};
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}
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}
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// http://en.wikipedia.org/wiki/2-opt
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static void reverse(int[] p, int i, int j) {
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int n = p.length;
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// reverse order from i to j
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while (i != j) {
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int t = p[j];
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p[j] = p[i];
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p[i] = t;
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i = (i + 1) % n;
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if (i == j) break;
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j = (j - 1 + n) % n;
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}
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}
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static double len(int[] x, int[] y, int[] p) {
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double res = 0;
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for (int i = 0, j = p.length - 1; i < p.length; j = i++) {
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double dx = x[p[i]] - x[p[j]];
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double dy = y[p[i]] - y[p[j]];
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res += Math.sqrt(dx * dx + dy * dy);
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}
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return res;
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}
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static boolean isCrossOrTouchIntersect(long x1, long y1, long x2, long y2, long x3, long y3, long x4, long y4) {
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if (Math.max(x1, x2) < Math.min(x3, x4) || Math.max(x3, x4) < Math.min(x1, x2)
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|| Math.max(y1, y2) < Math.min(y3, y4) || Math.max(y3, y4) < Math.min(y1, y2))
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return false;
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long z1 = (x2 - x1) * (y3 - y1) - (y2 - y1) * (x3 - x1);
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long z2 = (x2 - x1) * (y4 - y1) - (y2 - y1) * (x4 - x1);
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long z3 = (x4 - x3) * (y1 - y3) - (y4 - y3) * (x1 - x3);
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long z4 = (x4 - x3) * (y2 - y3) - (y4 - y3) * (x2 - x3);
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return (z1 <= 0 || z2 <= 0) && (z1 >= 0 || z2 >= 0) && (z3 <= 0 || z4 <= 0) && (z3 >= 0 || z4 >= 0);
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}
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}
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