Table of Contents
- 1 How do you ensure that even the points across the boundary are checked to identify the closest pair of points while using divide and conquer strategy?
- 2 How do you check if points are on the same line?
- 3 What is closest pair problem in DAA?
- 4 Who said impera et?
- 5 What does it mean if three points are collinear?
- 6 What is the best way to calculate the distance between points?
How do you ensure that even the points across the boundary are checked to identify the closest pair of points while using divide and conquer strategy?
Closest Pair of Points using Divide and Conquer algorithm
- Find the middle point in the sorted array, we can take P[n/2] as middle point.
- Divide the given array in two halves.
- Recursively find the smallest distances in both subarrays.
- From the above 3 steps, we have an upper bound d of minimum distance.
How do you check if points are on the same line?
Explanation: To find out if a point is on a line, you can plug the points back into an equation. If the values equal one another, then the point must be on a line.
How do you find the closest pair of points?
Closest Pair of Points | O(nlogn) Implementation
- 1) We sort all points according to x coordinates.
- 2) Divide all points in two halves.
- 3) Recursively find the smallest distances in both subarrays.
- 4) Take the minimum of two smallest distances.
How do you determine if points are on the same line in 3d?
There are three methods to find wether the 3 points are collinear or not. (1) The slope of line segment joining point A , B equalls to the slope of line segment joining point B,C. (2) Area bounded by the triangle joining points A,B,C is zero. (3) The sum of distance between AB and BC is equall to the distance AC.
What is closest pair problem in DAA?
In this problem, a set of n points are given on the 2D plane. In this problem, we have to find the pair of points, whose distance is minimum. To solve this problem, we have to divide points into two halves, after that smallest distance between two points is calculated in a recursive way.
Who said impera et?
The maxim divide et impera has been attributed to Philip II of Macedon. It was utilised by the Roman ruler Julius Caesar and the French emperor Napoleon (together with the maxim divide ut regnes).
Is it possible to find two points whose distance is $sqrt2$?
Prove that given 5 points inside a square of side length 2, it is always possible to find two of them whose distance apart is at most $\\sqrt2$. This looks to me like I should try to apply the Pigeonhole Principle, though I can’t see a way to do it.
What is the largest distance that the $2$ points in this square can be?
And the largest distance that the $2$ points in this square can be is the length of the diagonal – $\\sqrt{1+1}=\\sqrt{2}$. Thanks for giving just the right amount of hint.$\\endgroup$
What does it mean if three points are collinear?
It means that if three points are collinear, then they cannot form a triangle. Suppose, the three points P (x 1, y 1 ), Q (x 2, y 2) and R (x 3, y 3) are collinear, then by remembering the formula of area of triangle formed by three points we get; Example: Find if P (2, 3), Q (4, 0) and R (6, -3) are collinear points.
What is the best way to calculate the distance between points?
The best way would be to cover the maximum possible distance in a diagonal direction and remaining in horizontal or vertical direction. If we look closely this just reduces to the maximum of abs (x2-x1) and abs (y2-y1). Traverse for all points and summation of all diagonal distance will be the answer.