10. Max Points on a Line
Given n points on a 2D plane, find the maximum number of points that lie on the same straight line.
主要思想:O(n2),固定一个点,遍历其余 n 个点, 计算与该点相同的点的个数,和其余所有点的斜率,相同斜率的点视为同一直线。
初步 AC 代码:
/**
* Definition for a point.
* struct Point {
* int x;
* int y;
* Point() : x(0), y(0) {}
* Point(int a, int b) : x(a), y(b) {}
* };
*/
class Solution {
public:
int maxPoints(vector<Point> &points) {
unordered_map<float, int> mp;
int maxNumber = 0;
for(size_t i = 0; i < points.size(); ++i) {
int repeat = 1;
int sameX = 0;
for(size_t j = 0; j < points.size(); ++j) {
if(j == i) continue;
if(points[j].x == points[i].x) {
if(points[j].y == points[i].y) ++repeat;
else ++sameX;
}
else {
float k = (float)(points[i].y - points[j].y) / (points[i].x - points[j].x);// key.
mp[k]++;
}
}
unordered_map<float, int>::iterator it = mp.begin();
while(it != mp.end()) {
if(it->second + repeat > maxNumber) maxNumber = it->second + repeat;
++it;
}
maxNumber = (repeat + sameX) > maxNumber ? (repeat + sameX) : maxNumber;
mp.clear();
}
return maxNumber;
}
};
但是里面的 hash map 使用了 浮点值做键值是个非常拙劣的方法。如下所述:
Testing equality with float ou double is always a bad idea because of rounding errors, so don't use them as a hash. Never.
For it's floating point arithmetic, Java uses a subset of IEEE754. IEEE754 is full of beautiful tricks to mimic the behavior of real numbers and do a wonderful job at it, so sometimes we forget that is has limitations. The main troubles are (in no specific order):
- there is a gap between 0.0 and the next value (so non-zero numbers can be rounded to 0 if they are in this gap)
- there are special values for +infinity and -infinity (so there is no overflow, but you can get "stuck" on an infinite value. Imagine
a*b
evaluates toinfinity
, thena*b/b
will also evaluate to infinity and not to à`)- there is a special value
NaN
that means not a number. (0.0 / 0.0
evaluates toNaN
)- there are signed zeroes (
+0.0
and-0.0
) Signed zeroes are usually not that painful (-0.0 == +0.0
for the primitive typesdouble
andfloat
but not for their object wrappersDouble
andFloat
)To come back to your question, using
Double
as a key in the map is a terrible idea because of rounding problems. You do not need to useMath.PI
for infinity sinceDouble.POSITIVE_INFINITY
is a legitimate value. Be careful though, you don't want to have positive and negative infinity mixed up. Look at the previous questions, the trick here is to represent a line by an equation ax+by+c=0 with a,b, and c of typeint
.As a final note, I think it is important to know the limitations of the encoding you are using (overflow for int, signed zeroes, infinity, and NaN of floating point numbers, surrogate pair for UTF-16…)
所以待重新写答案 AC 一次。
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