Max Points on a Line

问题描述

Given n points on a 2D plane, find the maximum number of points that lie on the same straight line.

 

解决思路

1. 定义Line类

{slope; intercept; isVertical; isHorizontal}

定义hashcode(), equals()方法

2. 遍历每两两的点，记录下数目最多的Line；

3. 遍历所有的点，记录下在该Line上的点的数目，即为共线的最大数目；

注意：点集中有可能有重合的点。

 

程序

class Line {
	static double epsilo = 0.00001;
	double slope;
	double intercept;
	boolean isVertical;
	boolean isHorizontal;

	public Line(double x1, double y1, double x2, double y2) {
		if (isEquals(x1, x2)) {
			isVertical = true;
			intercept = x1;
		} else if (isEquals(y1, y2)) {
			isHorizontal = true;
			intercept = y1;
		} else {
			slope = (y1 - y2) / (x1 - x2);
			intercept = x1 - y1 / slope;
		}
	}

	public static boolean isEquals(double d1, double d2) {
		return Math.abs(d1 - d2) < epsilo;
	}

	@Override
	public boolean equals(Object obj) {
		if (!(obj instanceof Line)) {
			return false;
		}
		Line line = (Line) obj;
		if (isEquals(line.slope, this.slope)
				&& isEquals(line.intercept, this.intercept)
				&& line.isVertical == this.isVertical
				&& line.isHorizontal == this.isHorizontal) {
			return true;
		}
		return false;
	}

	@Override
	public int hashCode() {
		return (int) (slope * 1000) | (int) (intercept * 1000);
	}
}

public class Solution {
    public int maxPoints(Point[] points) {
		if (points == null) {
			return 0;
		}
		if (points.length <= 2) {
			return points.length;
		}

		HashMap<Line, Integer> map = new HashMap<Line, Integer>();
		for (int i = 0; i < points.length - 1; i++) {
			for (int j = i + 1; j < points.length; j++) {
				Point p1 = points[i];
				Point p2 = points[j];
				Line line = new Line(p1.x, p1.y, p2.x, p2.y);
				if (map.containsKey(line)) {
					map.put(line, map.get(line) + 1);
				} else {
					map.put(line, 1);
				}
			}
		}

		int max = 0;
		Line maxLine = null;
		for (Line l : map.keySet()) {
			if (map.get(l) > max) {
				max = map.get(l);
				maxLine = l;
			}
		}

		if (maxLine == null) {
			return -1;
		}

		int cnt = 0;
		if (maxLine.isVertical) {
			for (Point point : points) {
				if (Line.isEquals(point.x, maxLine.intercept)) {
					++cnt;
				}
			}
		} else if (maxLine.isHorizontal) {
			for (Point point : points) {
				if (Line.isEquals(point.y, maxLine.intercept)) {
					++cnt;
				}
			}
		} else {
			for (Point point : points) {
				if (Line.isEquals(point.y, maxLine.slope
						* (point.x - maxLine.intercept))) {
					++cnt;
				}
			}
		}
		return cnt;
	}
}