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Find the two points with the lowest and highest x-coordinates, and the two points with the lowest and highest y-coordinates. (Each of these operations takes O ( n ).) These four points form a convex quadrilateral , and all points that lie in this quadrilateral (except for the four initially chosen vertices) are not part of the convex hull.
Then A[I] is equivalent to an array of the first 10 elements of A. A practical example of this is a sorting operation such as: I = array_sort(A); % Obtain a list of sort indices B = A[I]; % B is the sorted version of A C = A[array_sort(A)]; % Same as above but more concise.
Each possible contiguous sub-array is represented by a point on a colored line. That point's y-coordinate represents the sum of the sample. Its x-coordinate represents the end of the sample, and the leftmost point on that colored line represents the start of the sample. In this case, the array from which samples are taken is [2, 3, -1, -20, 5, 10].
In this algorithm, one recursively draws a line to split the vertices into two sets. The Delaunay triangulation is computed for each set, and then the two sets are merged along the splitting line. Using some clever tricks, the merge operation can be done in time O( n ) , so the total running time is O( n log n ) .
In array languages, operations are generalized to apply to both scalars and arrays. Thus, a+b expresses the sum of two scalars if a and b are scalars, or the sum of two arrays if they are arrays. An array language simplifies programming but possibly at a cost known as the abstraction penalty.
In some of these languages an extra keyword is used to declare no return value; for example void in C, C++ and C#. In some languages, such as Python, the difference is whether the body contains a return statement with a value, and a particular callable may return with or without a value based on control flow.
If the value of this is positive then the ideal line is below the midpoint and closer to the candidate point (+, +); i.e. the y coordinate should increase. Otherwise, the ideal line passes through or above the midpoint, and the y coordinate should stay the same; in which case the point ( x 0 + 1 , y 0 ) {\displaystyle (x_{0}+1,y_{0})} is chosen.
The Bentley–Ottmann algorithm will insert a new segment s into this data structure when the sweep line L crosses the left endpoint p of this segment (i.e. the endpoint of the segment with the smallest x-coordinate, provided the sweep line L starts from the left, as explained above in this article).