LeetCode之Max Points on a Line Total
1.问题描述
Given n points on a 2D plane, find the maximum number of points that lie on the same straight line.
2.翻译
对于在一个平面上的N个点，找出在同一条直线的最多的点的数目
3.思路分析
我们知道任意的两个点可以构成一条直线，对于一条在直线的上的点，他们必然具有相同的斜率，这个我初中都知道了。因为找出最多的点的方法也就比较简单了，我们只要依次遍历这些点，并且记录相同的斜率的点的数目，这样数目最大的那个斜率对应的值就是我们所需要的那个最大值了，因为我们需要一个HashMap,key用来存放斜率，value用来记录点的数目，最后我们只需要拿出value最大的那个 值就可以了。因为HashMap的底层采用hash实现，所以在查找比对的过程中效率还是比较高的。
4.实现代码
Solution.java()（实现过程借鉴了别人的实现，但是解题的思路是自己的）
package maxPoints;
import java.util.HashMap;
public class Solution {
public int maxPoints(Point[] points) {
if(points.length <= 2) {//如果点的数目小于等于2，那么一直线上的点就是数组的长度了
return points.length;
}
double k = 0.0;//斜率
int maxPointNum = 0;
int tempMaxPointNum = 0;
int samePointNum = 0;//坐标完全相同点的个数
int parallelPointNum = 0; //与x轴平行
HashMap<Double,Integer> slopeMap = new HashMap<Double,Integer>();
for(int i=0;i<points.length-1;i++) {
samePointNum = 1; //代表起始点，会被累加上
parallelPointNum = 0;
tempMaxPointNum = 0;
slopeMap.clear();
for(int j=i+1;j<points.length;j++) {
if((points[i].x == points[j].x)&&((points[i].y == points[j].y))) {//坐标完全相同
samePointNum++;
continue;
}
if(points[i].x == points[j].x) { //与y轴平行
parallelPointNum++;
} else {
if(points[i].y == points[j].y) {
k = 0;
} else {
k = ((double)(points[i].y - points[j].y))/(points[i].x - points[j].x);
}
if(slopeMap.get(k) == null) {//斜率不存在
slopeMap.put(k, new Integer(1));
if(1>tempMaxPointNum) {
tempMaxPointNum = 1;
}
}else {//斜率已存在
int number = slopeMap.get(k);
number++;
slopeMap.put(k, new Integer(number));
if(number>tempMaxPointNum) {
tempMaxPointNum = number;
}
}
}
}
if(parallelPointNum > 1) {
if(parallelPointNum>tempMaxPointNum) {
tempMaxPointNum = parallelPointNum;
}
}
tempMaxPointNum += samePointNum;//加上起始点和具有相同坐标的点
if(tempMaxPointNum>maxPointNum) {
maxPointNum = tempMaxPointNum;
}
}
return maxPointNum;
}
}
SoultionTest.java
package maxPoints;
import java.util.Random;
public class SolutionTest {
/**
* @param args
*/
public static void main(String[] args) {
// TODO Auto-generated method stub
Point []pointArr = new Point[100];
for(int index = 0;index < 100;index++){
Point point = new Point(index,new Random(index).nextInt());
pointArr[index] = point;
System.out.println("Point("+point.x+","+point.y+")");
}
System.out.println(new Solution().maxPoints(pointArr));
}
}
结果：
Point(0,-1155484576) Point(1,-1155869325) Point(2,-1154715079) Point(3,-1155099828) Point(4,-1157023572) Point(5,-1157408321) Point(6,-1156254074) Point(7,-1156638823) Point(8,-1158562568) Point(9,-1158947317) Point(10,-1157793070) Point(11,-1158177819) Point(12,-1160101563) Point(13,-1160486312) Point(14,-1159332065) Point(15,-1159716814) Point(16,-1149328594) Point(17,-1149713343) Point(18,-1148559096) Point(19,-1148943845) Point(20,-1150867590) Point(21,-1151252339) Point(22,-1150098092) Point(23,-1150482841) Point(24,-1152406585) Point(25,-1152791334) Point(26,-1151637087) Point(27,-1152021836) Point(28,-1153945581) Point(29,-1154330330) Point(30,-1153176083) Point(31,-1153560832) Point(32,-1167796541) Point(33,-1168181290) Point(34,-1167027043) Point(35,-1167411792) Point(36,-1169335537) Point(37,-1169720286) Point(38,-1168566039) Point(39,-1168950788) Point(40,-1170874532) Point(41,-1171259281) Point(42,-1170105035) Point(43,-1170489784) Point(44,-1172413528) Point(45,-1172798277) Point(46,-1171644030) Point(47,-1172028779) Point(48,-1161640559) Point(49,-1162025308) Point(50,-1160871061) Point(51,-1161255810) Point(52,-1163179554) Point(53,-1163564303) Point(54,-1162410057) Point(55,-1162794806) Point(56,-1164718550) Point(57,-1165103299) Point(58,-1163949052) Point(59,-1164333801) Point(60,-1166257546) Point(61,-1166642295) Point(62,-1165488048) Point(63,-1165872797) Point(64,-1180108506) Point(65,-1180493255) Point(66,-1179339008) Point(67,-1179723757) Point(68,-1181647502) Point(69,-1182032251) Point(70,-1180878004) Point(71,-1181262753) Point(72,-1183186497) Point(73,-1183571246) Point(74,-1182416999) Point(75,-1182801748) Point(76,-1184725493) Point(77,-1185110242) Point(78,-1183955995) Point(79,-1184340744) Point(80,-1173952524) Point(81,-1174337273) Point(82,-1173183026) Point(83,-1173567775) Point(84,-1175491519) Point(85,-1175876268) Point(86,-1174722021) Point(87,-1175106770) Point(88,-1177030515) Point(89,-1177415264) Point(90,-1176261017) Point(91,-1176645766) Point(92,-1178569510) Point(93,-1178954259) Point(94,-1177800013) Point(95,-1178184762) Point(96,-1192420471) Point(97,-1192805220) Point(98,-1191650973) Point(99,-1192035722) 6
从结果输出了可以看出在通一条直线上最多的点是6个。
5.这个题的解决方法很暴力，可是还有很多细节需要注意，比如斜率为0 的情况，斜率不存在的情况，还有点重合的情况，等等。
