Search results
Results from the WOW.Com Content Network
Deterministically, one can use median-of-3 pivot strategy (as in the quicksort), which yields linear performance on partially sorted data, as is common in the real world. However, contrived sequences can still cause worst-case complexity; David Musser describes a "median-of-3 killer" sequence that allows an attack against that strategy, which ...
The time for this method is dominated by the sorting step, which requires () time using a comparison sort. [2] [3] Even when integer sorting algorithms may be used, these are generally slower than the linear time that may be achieved using specialized selection algorithms. Nevertheless, the simplicity of this approach makes it attractive ...
Consider the example of [5, 2, 3, 1, 0], following the scheme, after the first partition the array becomes [0, 2, 1, 3, 5], the "index" returned is 2, which is the number 1, when the real pivot, the one we chose to start the partition with was the number 3. With this example, we see how it is necessary to include the returned index of the ...
A further relaxation requiring only a list of the k smallest elements, but without requiring that these be ordered, makes the problem equivalent to partition-based selection; the original partial sorting problem can be solved by such a selection algorithm to obtain an array where the first k elements are the k smallest, and sorting these, at a total cost of O(n + k log k) operations.
Quicksort is a divide-and-conquer algorithm which relies on a partition operation: to partition an array, an element called a pivot is selected. [30] [31] All elements smaller than the pivot are moved before it and all greater elements are moved after it. This can be done efficiently in linear time and in-place. The lesser and greater sublists ...
In computer science, the median of medians is an approximate median selection algorithm, frequently used to supply a good pivot for an exact selection algorithm, most commonly quickselect, that selects the kth smallest element of an initially unsorted array. Median of medians finds an approximate median in linear time.
The 3-partition problem remains NP-complete even when the integers in S are bounded above by a polynomial in n. In other words, the problem remains NP-complete even when representing the numbers in the input instance in unary. i.e., 3-partition is NP-complete in the strong sense or strongly NP-complete. This property, and 3-partition in general ...
The solution to this problem is of interest for designing sorting algorithms; in particular, variants of the quicksort algorithm that must be robust to repeated elements may use a three-way partitioning function that groups items less than a given key (red), equal to the key (white) and greater than the key (blue). Several solutions exist that ...