377 lines
10 KiB
Java
377 lines
10 KiB
Java
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import java.util.*;
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// https://en.wikipedia.org/wiki/Point_location
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public class PointLocation {
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public static int[] locatePoints(int[][] polygonX, int[][] polygonY, int[] qx, int[] qy) {
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// preprocessing
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Map<Long, Integer> endPoints = new HashMap<>();
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Map<Integer, NavigableSet<Segment>> verticalSegments = new HashMap<>();
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List<Event> events = new ArrayList<>();
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for (int k = 0; k < polygonX.length; ++k) {
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int n = polygonX[k].length;
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for (int i = 0, j = n - 1; i < n; j = i++) {
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endPoints.put(((long) polygonX[k][i] << 32) + polygonY[k][i], k);
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Segment s = new Segment(polygonX[k][i], polygonY[k][i], polygonX[k][j], polygonY[k][j], k);
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if (s.x1 != s.x2) {
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events.add(new Event(s.x1, s.y1, 1, s));
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events.add(new Event(s.x2, s.y2, -1, s));
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} else {
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if (!verticalSegments.containsKey(s.x1)) {
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verticalSegments.put(s.x1, new TreeSet<>(segmentComparator));
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}
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verticalSegments.get(s.x1).add(s);
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}
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}
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}
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Collections.sort(events, eventComparator);
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int[] eventsX = new int[events.size()];
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Treap[] treaps = new Treap[events.size()];
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int cnt = 0;
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Treap treap = null;
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for (Event event : events) {
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if (cnt == 0 || eventsX[cnt - 1] < event.x)
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++cnt;
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if (event.type == 1) {
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treap = insert(treap, event.segment);
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} else if (event.type == -1) {
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treap = remove(treap, event.segment);
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}
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eventsX[cnt - 1] = event.x;
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treaps[cnt - 1] = treap;
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}
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// answering queries
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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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Integer polygonId = endPoints.get(((long) qx[i] << 32) + qy[i]);
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if (polygonId != null) {
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res[i] = polygonId;
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continue;
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}
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NavigableSet<Segment> vSegments = verticalSegments.get(qx[i]);
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if (vSegments != null) {
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SortedSet<Segment> head = vSegments.headSet(new Segment(qx[i], qy[i], qx[i], qy[i], 0), true);
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if (!head.isEmpty() && head.last().contains(qx[i], qy[i])) {
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res[i] = head.last().polygonId;
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continue;
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}
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}
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int lo = Arrays.binarySearch(eventsX, 0, cnt, qx[i]);
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if (lo < 0) lo = -lo - 2;
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if (lo == -1 || lo == cnt - 1) {
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res[i] = -1;
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continue;
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}
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Segment minRight = new Segment(qx[i], qy[i], qx[i], qy[i], 0);
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TreapPair treapPair = split(treaps[lo], minRight, true);
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Treap max = max(treapPair.left);
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Treap min = min(treapPair.right);
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if (min != null && min.key.contains(qx[i], qy[i])) {
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res[i] = min.key.polygonId;
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} else if (max != null && max.key.contains(qx[i], qy[i])) {
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res[i] = max.key.polygonId;
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} else if (getSize(treapPair.left) % 2 == 1) {
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res[i] = max.key.polygonId;
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} else {
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res[i] = -1;
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}
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}
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return res;
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}
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static final Comparator<Segment> segmentComparator = (a, b) -> {
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if (a.x1 == b.x1 && a.y1 == b.y1) {
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long v = cross(a.x1, a.y1, a.x2, a.y2, b.x2, b.y2);
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if (v != 0)
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return v > 0 ? -1 : 1;
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} else if (a.x1 < b.x1) {
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long v = cross(a.x1, a.y1, a.x2, a.y2, b.x1, b.y1);
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if (v != 0)
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return v > 0 ? -1 : 1;
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} else {
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long v = cross(b.x1, b.y1, b.x2, b.y2, a.x1, a.y1);
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if (v != 0)
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return v < 0 ? -1 : 1;
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}
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return Integer.compare(a.y1, b.y1);
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};
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static class Segment {
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final int x1, y1, x2, y2, polygonId;
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public Segment(int x1, int y1, int x2, int y2, int polygonId) {
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if (x1 < x2 || x1 == x2 && y1 < y2) {
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this.x1 = x1;
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this.y1 = y1;
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this.x2 = x2;
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this.y2 = y2;
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} else {
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this.x1 = x2;
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this.y1 = y2;
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this.x2 = x1;
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this.y2 = y1;
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}
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this.polygonId = polygonId;
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}
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public boolean contains(int x, int y) {
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long a = y2 - y1;
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long b = x1 - x2;
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long c = -a * x1 - b * y1;
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return x >= x1 && x <= x2 && (y >= y1 || y >= y2) && (y <= y1 || y <= y2) && a * x + b * y + c == 0;
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}
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}
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static final Comparator<Event> eventComparator = (a, b) -> {
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if (a.x != b.x)
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return a.x < b.x ? -1 : 1;
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if (a.type != b.type)
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return a.type < b.type ? -1 : 1;
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return Integer.compare(a.y, b.y);
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};
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static class Event {
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final int x, y;
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final int type;
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final Segment segment;
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public Event(int x, int y, int type, Segment segment) {
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this.x = x;
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this.y = y;
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this.type = type;
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this.segment = segment;
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}
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}
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static long cross(long ax, long ay, long bx, long by, long cx, long cy) {
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return (bx - ax) * (cy - ay) - (by - ay) * (cx - ax);
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}
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static Random random = new Random(1);
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// persistent treap
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static class Treap {
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final Segment key;
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final Treap left;
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final Treap right;
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final int size;
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Treap(Segment key) {
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this.key = key;
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left = null;
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right = null;
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size = 1;
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}
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public Treap(Segment key, Treap left, Treap right) {
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this.key = key;
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this.left = left;
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this.right = right;
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this.size = getSize(left) + getSize(right) + 1;
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}
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}
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static int getSize(Treap root) {
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return root == null ? 0 : root.size;
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}
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static class TreapPair {
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Treap left;
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Treap right;
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TreapPair(Treap left, Treap right) {
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this.left = left;
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this.right = right;
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}
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}
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static TreapPair split(Treap root, Segment minRight, boolean inclusive) {
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if (root == null)
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return new TreapPair(null, null);
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int cmp = segmentComparator.compare(root.key, minRight);
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if (cmp > 0 || cmp == 0 && inclusive) {
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TreapPair leftSplit = split(root.left, minRight, inclusive);
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return new TreapPair(leftSplit.left, new Treap(root.key, leftSplit.right, root.right));
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} else {
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TreapPair rightSplit = split(root.right, minRight, inclusive);
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return new TreapPair(new Treap(root.key, root.left, rightSplit.left), rightSplit.right);
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}
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}
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static Treap merge(Treap left, Treap right) {
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if (left == null)
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return right;
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if (right == null)
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return left;
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if (random.nextInt(left.size + right.size) < left.size) {
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return new Treap(left.key, left.left, merge(left.right, right));
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} else {
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return new Treap(right.key, merge(left, right.left), right.right);
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}
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}
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static Treap insert(Treap root, Segment x) {
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TreapPair t = split(root, x, true);
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return merge(merge(t.left, new Treap(x)), t.right);
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}
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static Treap remove(Treap root, Segment x) {
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TreapPair t = split(root, x, true);
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return merge(t.left, split(t.right, x, false).right);
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}
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static Treap min(Treap root) {
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while (root != null && root.left != null)
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root = root.left;
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return root;
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}
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static Treap max(Treap root) {
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while (root != null && root.right != null)
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root = root.right;
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return root;
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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 = 20;
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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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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;
|
||
|
|
// reverse order from i to j
|
||
|
|
while (i != j) {
|
||
|
|
int t = p[j];
|
||
|
|
p[j] = p[i];
|
||
|
|
p[i] = t;
|
||
|
|
i = (i + 1) % n;
|
||
|
|
if (i == j) break;
|
||
|
|
j = (j - 1 + n) % n;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
static double len(int[] x, int[] y, int[] p) {
|
||
|
|
double res = 0;
|
||
|
|
for (int i = 0, j = p.length - 1; i < p.length; j = i++) {
|
||
|
|
double dx = x[p[i]] - x[p[j]];
|
||
|
|
double dy = y[p[i]] - y[p[j]];
|
||
|
|
res += Math.sqrt(dx * dx + dy * dy);
|
||
|
|
}
|
||
|
|
return res;
|
||
|
|
}
|
||
|
|
|
||
|
|
static boolean isCrossOrTouchIntersect(long x1, long y1, long x2, long y2, long x3, long y3, long x4, long y4) {
|
||
|
|
if (Math.max(x1, x2) < Math.min(x3, x4) || Math.max(x3, x4) < Math.min(x1, x2)
|
||
|
|
|| Math.max(y1, y2) < Math.min(y3, y4) || Math.max(y3, y4) < Math.min(y1, y2))
|
||
|
|
return false;
|
||
|
|
long z1 = (x2 - x1) * (y3 - y1) - (y2 - y1) * (x3 - x1);
|
||
|
|
long z2 = (x2 - x1) * (y4 - y1) - (y2 - y1) * (x4 - x1);
|
||
|
|
long z3 = (x4 - x3) * (y1 - y3) - (y4 - y3) * (x1 - x3);
|
||
|
|
long z4 = (x4 - x3) * (y2 - y3) - (y4 - y3) * (x2 - x3);
|
||
|
|
return (z1 <= 0 || z2 <= 0) && (z1 >= 0 || z2 >= 0) && (z3 <= 0 || z4 <= 0) && (z3 >= 0 || z4 >= 0);
|
||
|
|
}
|
||
|
|
}
|