Let us say I have 50000 "3D spatial coordinates" in a 1D array. I want two know if there are two points that are coinciding. If yes, which ones, or how many pairs?
I know I can use the distance formula but that would be really costly and will create a 2D array of 50k X 50k i.e. each column for relative distance of every single point w.r.t other points.
I am looking for an efficient algorithm.
The first way: use hashtable/map/dictionary. O(n) amortized complexity, O(n) memory
Put points there one-by-one. If there is no such key in dictionary yet, add pair (coordinates; value=1), otherwise increment value field.
In Python, for example, there is Counter intended for this kind of problems.
The second way: sorting. O(nlogn) usual complexity.
Sort points, using special comparator: compare X-coordinate first, in case of eqiality compare Y-coordinate, in case of equality compare Z. After that walk through sorted array, similar points will stand together.
In Python default comparator for such structures works as needed.