Given N lines are in the form a*x + b*y = c (a>0 or a==0 & b>0). Find the number of pairs of lines intersecting at a point.
x + 2y = 2
x + 2y = 4
- Parallel lines never intersect so a method is needed to exclude parallel lines for each line.
- The slope of a line can be represented as pair(a, b). Construct a map with key as slope and value as a set with c as entries in it so that it has an account of the parallel lines.
- Iterate over the lines add them to the map and maintain a variable Tot which counts the total number of lines till now.
- Now for each line update the Tot variable then add Tot to the answer and subtract the number of parallel lines to that line including itself.
Below is the implementation of the above approach:
- Number of pairs of lines having integer intersection points
- Program for Point of Intersection of Two Lines
- Find intersection point of lines inside a section
- Maximum distinct lines passing through a single point
- Count ways to divide circle using N non-intersecting chord | Set-2
- Count ways to divide circle using N non-intersecting chords
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- Count pairs (A, B) such that A has X and B has Y number of set bits and A+B = C
- Count pairs with Bitwise AND as ODD number
- Given two arrays count all pairs whose sum is an odd number
- Count pairs with sum as a prime number and less than n
- Count number of ordered pairs with Even and Odd Product
- Count number of ordered pairs with Even and Odd Sums
- Count number of pairs in array having sum divisible by K | SET 2
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