Closest Pair
From Algorithmist
[edit] Line Sweep Algorithm
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[edit] Divide and Conquer
The problem can be solved in O(n log n) time using the recursive divide and conquer approach, e.g., as follows[1]:
- Sort points along the x-coordinate
- Split the set of points into two equal-sized subsets by a vertical line
- Solve the problem recursively in the left and right subsets. This will give the left-side and right-side minimal distances.
- Find the minimal distance among the pair of points in which one point lies on the left of the dividing vertical and the second point lies to the right.
- The final answer is the minimum among the left, middle, and right deltas.
Originally taken from: http://en.wikipedia.org/wiki/Closest_pair_of_points_problem
[edit] Example Problems
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