Collinear Points

Point.java

照要求补API即可。

import java.util.Comparator;
import edu.princeton.cs.algs4.StdDraw;public class Point implements Comparable<Point> {private final int x;     // x-coordinate of this pointprivate final int y;     // y-coordinate of this point/*** Initializes a new point.** @param  x the <em>x</em>-coordinate of the point* @param  y the <em>y</em>-coordinate of the point*/public Point(int x, int y) {/* DO NOT MODIFY */this.x = x;this.y = y;}/*** Draws this point to standard draw.*/public void draw() {/* DO NOT MODIFY */StdDraw.point(x, y);}/*** Draws the line segment between this point and the specified point* to standard draw.** @param that the other point*/public void drawTo(Point that) {/* DO NOT MODIFY */StdDraw.line(this.x, this.y, that.x, that.y);}/*** Returns the slope between this point and the specified point.* Formally, if the two points are (x0, y0) and (x1, y1), then the slope* is (y1 - y0) / (x1 - x0). For completeness, the slope is defined to be* +0.0 if the line segment connecting the two points is horizontal;* Double.POSITIVE_INFINITY if the line segment is vertical;* and Double.NEGATIVE_INFINITY if (x0, y0) and (x1, y1) are equal.** @param  that the other point* @return the slope between this point and the specified point*/public double slopeTo(Point that) {if (compareTo(that) == 0) {return Double.NEGATIVE_INFINITY;}if (this.x == that.x) {return Double.POSITIVE_INFINITY;}if (this.y == that.y) {return +0.0;}return 1.0 * (this.y - that.y) / (this.x - that.x);}/*** Compares two points by y-coordinate, breaking ties by x-coordinate.* Formally, the invoking point (x0, y0) is less than the argument point* (x1, y1) if and only if either y0 < y1 or if y0 = y1 and x0 < x1.** @param  that the other point* @return the value <tt>0</tt> if this point is equal to the argument*         point (x0 = x1 and y0 = y1);*         a negative integer if this point is less than the argument*         point; and a positive integer if this point is greater than the*         argument point*/public int compareTo(Point that) {if (this.y < that.y) {return -1;} else if (this.y > that.y) {return 1;} else if (this.x < that.x) {return -1;} else if (this.x > that.x) {return 1;} else {return 0;}}/*** Compares two points by the slope they make with this point.* The slope is defined as in the slopeTo() method.** @return the Comparator that defines this ordering on points*/public Comparator<Point> slopeOrder() {return new SlopeComparator();}/*** Returns a string representation of this point.* This method is provide for debugging;* your program should not rely on the format of the string representation.** @return a string representation of this point*/public String toString() {/* DO NOT MODIFY */return "(" + x + ", " + y + ")";}private class SlopeComparator implements Comparator<Point> {@Overridepublic int compare(Point o1, Point o2) {if (slopeTo(o1) < slopeTo(o2)) {return -1;} else if (slopeTo(o1) > slopeTo(o2)) {return 1;} else {return 0;}}}/*** Unit tests the Point data type.*/public static void main(String[] args) {}
}

BruteCollinearPoints.java

暴力四重循环就完事了。

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;public class BruteCollinearPoints {private final List<LineSegment> segments;public BruteCollinearPoints(Point[] points) {if (points == null) {throw new IllegalArgumentException();}Point[] copy = new Point[points.length];segments = new ArrayList<>();// 避免修改原数组，需要先复制下来for (int i = 0; i < points.length; i++) {if (points[i] == null) {throw new IllegalArgumentException();}copy[i] = points[i];}Arrays.sort(copy);for (int i = 0; i < copy.length - 1; i++) {if (copy[i].compareTo(copy[i + 1]) == 0) {throw new IllegalArgumentException();}}run(copy);}public int numberOfSegments() {return segments.size();}public LineSegment[] segments() {LineSegment[] res = new LineSegment[segments.size()];int i = 0;for (LineSegment segment : segments) {res[i++] = segment;}return res;}private void run(Point[] points) {int n = points.length;// 直接四重遍历for (int i = 0; i < n - 3; i++) {for (int j = i + 1; j < n - 2; j++) {double s1 = points[i].slopeTo(points[j]);for (int k = j + 1; k < n - 1; k++) {double s2 = points[i].slopeTo(points[k]);if (s1 == s2) {for (int m = k + 1; m < n; m++) {double s3 = points[i].slopeTo(points[m]);if (s1 == s3) {LineSegment temp = new LineSegment(points[i], points[m]);segments.add(temp);}}}}}}}
}

FastCollinearPoints.java

基本方法是以某一个点为基准，将其余点按照斜率大小进行排序，遍历得到的数组，相同斜率的点排在一起，即共线。问题在于如何找到线的端点以及排除重复端点对。思路如下：

一条线段的端点，与线段上其余点相比，其x/y值必然是最大/小的。所以可以直接用compareTo()来找到端点。
从基准点数组中，每次按顺序取一个基准点来排序斜率数组。在找到端点后，只保存以当前基准点为较小端点的线段，这样就可以避免端点对的重复。

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;public class FastCollinearPoints {private final List<LineSegment> segments;public FastCollinearPoints(Point[] points) {if (points == null) {throw new IllegalArgumentException();}Point[] copy = new Point[points.length];segments = new ArrayList<>();for (int i = 0; i < points.length; i++) {if (points[i] == null) {throw new IllegalArgumentException();}copy[i] = points[i];}Arrays.sort(copy);for (int i = 0; i < copy.length - 1; i++) {if (copy[i].compareTo(copy[i + 1]) == 0) {throw new IllegalArgumentException();}}run(copy);}public int numberOfSegments() {return segments.size();}public LineSegment[] segments() {LineSegment[] res = new LineSegment[segments.size()];int i = 0;for (LineSegment segment : segments) {res[i++] = segment;}return res;}private void run(Point[] points) {int n = points.length;Point[] bases = Arrays.copyOf(points, n);   // 基准点数组int current = 0;while (current < n) {Point base = bases[current++];      // 选取下一个基准点Point min = base;       // 共线线段较小端点Point max = base;       // 贡献线段较大端点int count = 2;          // 线段中至少会有两个点Arrays.sort(points, base.slopeOrder());        // 按照与基准点的斜率进行排序for (int i = 0; i < n - 1; i++) {double s1 = base.slopeTo(points[i]);double s2 = base.slopeTo(points[i + 1]);if (s1 == s2) {count++;// 在新加入共线点的情况下更新小端点和大端点if (max.compareTo(points[i + 1]) < 0) {max = points[i + 1];} else if (min.compareTo(points[i + 1]) > 0) {min = points[i + 1];}// 当点i、i+1为最后两个点时，需要进行判断// 只保存以base为小端点的线段if (i == n - 2 && count >= 4 && base.compareTo(min) == 0) {LineSegment temp = new LineSegment(min, max);segments.add(temp);}} else {// 当相同斜率序列中断时，需要进行判断// 只保存以base为小端点的线段if (count >= 4 && base.compareTo(min) == 0) {LineSegment temp = new LineSegment(min, max);segments.add(temp);}// 开始新斜率序列时，需要将base与新斜率的第一个点进行比较，重置min和maxif (base.compareTo(points[i + 1]) > 0) {min = points[i + 1];max = base;} else {min = base;max = points[i + 1];}count = 2;}}}}
}

参考

SHICHENG - 【Algorithms, Part I】Week3 Collinear Points

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Collinear Points

Collinear Points

Point.java

BruteCollinearPoints.java

FastCollinearPoints.java

参考

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