从N个2D点返回成对的点，其中每两个点定义一条线

Question

I have a List of 2D points: (x1, y1), (x2, y2) … (xN, yN) - N 2D points. Each two points define a 2D line.

Return a list of all unique 2D lines, which you can build using pairs of points from the list.

How can I implement using hash table/map - to keep unique lines (there are infinite lines)

I am trying to find the slope and intercept then point of intersection.

slope = y2 -y1 / x2 - x1 intercept = y1 - slope * x1;

(trying to do this in c++)

Answer 1

you didn't specify language, so I will use python here for the sake of easiness. it will look like a joke to python:

import itertools


def slope(p1, p2):
    return (p1[1]-p2[1]) / (p1[0]-p2[0])


def slp_intrcpt(p1, p2):
    """
    return the tuple of slope and intercept
    """
    slp = slope(p1, p2)
    return slp, p1[1] - slp * p1[0]


def uniq_lines(points):
    return set(slp_intrcpt(p1, p2) for p1, p2 in itertools.combinations(points, 2))

since (slope, intercept) pair is good enough to determine a line, so i would say that finished your requirement.

if you want to keep track of all pairs that produce the lines, you may

import collections

def uniq_lines(points):
    d = collections.defaultdict(lambda: [])
    for p1, p2 in itertools.combinations(points, 2):
        d[slp_intrcpt(p1, p2)].append((p1, p2))
    return d