Practice Problems on Basic Geometry for Competitive Programming

What are Geometric Algorithms?

Geometric algorithms are a set of computational techniques used in Competitive Programming to solve problems related to geometry and spatial relationships. These problems often involve points, lines, polygons, and other geometric objects....

Why to use Geometric Algorithms?

There are several questions which require basic geometric algorithms like:...

1. Vector Addition/Subtraction:

Operations like addition and subtraction of two vectors can be simply done by performing the operation on the individual components of the vectors. Like if we have two vectors (x1, y1) and (x2, y2), then the sum of the two vectors is (x1+x2, y1+y2) and the difference between them is (x1-x2, y1-y2)....

2. Dot Product and Cross Product:

The dot product of two vectors is simply the sum of the products of the corresponding elements. If we have two vectors (x1, y1) and (x2, y2), then the dot product of the two vectors is (x1 * x2) + (y1 * y2). The dot product of two vectors is a scalar quantity....

3. Distance from a point to a line:

Suppose we are given point A and a line L and we need to calculate the distance between the point and the line (say h), we can simply do it using Cross Product of vectors....

4. Intersection Point of two lines:

We can find the intersection point of two lines in 2D using parametric equations. Parametric equations are a way of representing a curve in terms of one or more parameters. For a line in 2D, we can use the following parametric equation:...

Practice Problems on Basic Geometry for Competitive Programming:

Problem Problem Link Check if two line segments intersect Practice Now Line Passing through two points Practice Now Find the missing point of parallelogram Practice Now...