Problem Statement: You are given n points in a plane. Whenever we find three points that are collinear, we draw a line through them. How many different lines are there? Come up with an efficient algorithm. First, explain your solution. Then provide a code written in C++ or JAVA or python. Or you can just give me a clearly written pseudocode. Hints: 0. We take three points and see if they are collinear or not. If they are collinear, we determine the line's equation. And we store the slope and x intercept of that line in a map data structure. We store the pair (m,c) in a map of pairs. We store (m,c) because this pair defines the line. 1. Every time we find such a line, we save it's slope and x intercept. Suppose Pi,Pj and Pk are collinear. And the equation of the line is: y=mx+c Where m=yj−yixj−xi and c=yi(xj−xi)−xi(yj−yi)xj−xi We can store m and c as floating point values but that is prone to small errors. So, we can store m and c as irreducible fractions. Suppose m=m1m2 and c=c1c2 where gcd(m1,m2)=1 and gcd(c1,c2)=1. We can store the pair (m,c) as a pair of pairs ((m1,m2),(c1,c2)). 2. For an efficient solution, remember the angular sort technique we used in Graham's Scan algorithm? Can we do the same here? Of course. 3. All values in the input will be integers.
Problem Statement: You are given n points in a plane. Whenever we find three points that are collinear, we draw a line through them. How many different lines are there? Come up with an efficient
Hints:
0. We take three points and see if they are collinear or not. If they are collinear, we determine the line's equation. And we store the slope and x intercept of that line in a map data structure. We store the pair (m,c) in a map of pairs. We store (m,c) because this pair defines the line.
1. Every time we find such a line, we save it's slope and x intercept.
Suppose Pi,Pj and Pk are collinear. And the equation of the line is: y=mx+c
Where m=yj−yixj−xi
and c=yi(xj−xi)−xi(yj−yi)xj−xi
We can store m and c as floating point values but that is prone to small errors. So, we can store m and c as irreducible fractions.
Suppose m=m1m2 and c=c1c2 where gcd(m1,m2)=1 and gcd(c1,c2)=1.
We can store the pair (m,c) as a pair of pairs ((m1,m2),(c1,c2)).
2. For an efficient solution, remember the angular sort technique we used in Graham's Scan algorithm? Can we do the same here? Of course.
3. All values in the input will be integers.
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