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Which problem identify the closest pair of points in a plane?
The closest pair of points problem or closest pair problem is a problem of computational geometry: given n points in metric space, find a pair of points with the smallest distance between them.
What is the optimal time required for solving the closest pair problem using divide and conquer approach 2 points?
Explanation: The optimal time for solving using a divide and conquer approach is mathematically found to be O(N log N). Explanation: The time taken for merging the smaller subproblems in a divide and conquer approach is mathematically found to be O(N log N).
What approach is being followed in Floyd warshall algorithm?
What approach is being followed in Floyd Warshall Algorithm? Explanation: Floyd Warshall Algorithm follows dynamic programming approach because the all pair shortest paths are computed in bottom up manner.
How to find the closest pair of points?
Now we need to consider the pairs such that one point in pair is from the left half and the other is from the right half. Consider the vertical line passing through P [n/2] and find all points whose x coordinate is closer than d to the middle vertical line. Build an array strip [] of all such points.
How to calculate the distance between two points?
For example, in air-traffic control, you may want to monitor planes that come too close together, since this may indicate a possible collision. Recall the following formula for distance between two points p and q. The Brute force solution is O (n^2), compute the distance between each pair and return the smallest.
Can a point be closer in one direction than another?
The trick is that by definition the distance in one direction must be less than or equal to the euclidean distance. So if the distance in one direction is greater than our current closest distance of the closest known point then that point cannot be closer, and more importantly all points in that direction cannot be greater.
What’s the fastest way to find the closest distance?
So if we have a point at a known closest distance of 13 then we can abort checking in the +x, -x, +y, -y, directions as soon as the distance in just that direction exceeds our closest known distance. Because if it is further +x than our current m, all the remaining values of +x can be mathematically be proven to be further away.