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A sorting algorithm is stable if whenever there are two records R and S with the same key, and R appears before S in the original list, then R will always appear before S in the sorted list. When equal elements are indistinguishable, such as with integers, or more generally, any data where the entire element is the key, stability is not an issue.
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.
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 ...
Sorting a set of unlabelled weights by weight using only a balance scale requires a comparison sort algorithm. A comparison sort is a type of sorting algorithm that only reads the list elements through a single abstract comparison operation (often a "less than or equal to" operator or a three-way comparison) that determines which of two elements should occur first in the final sorted list.
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Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the input list element by element, comparing the current element with the one after it, swapping their values if needed. These passes through the list are repeated until no swaps have to be performed during a pass, meaning that the ...
The problem of testing whether two of the pairs in the + sorting problem have equal sums can be solved by sorting the pairs and then testing consecutive pairs for equality. In turn, it could be used to solve the 3SUM problem, implying that it is unlikely to have a strongly subquadratic algorithm.
def cycle_sort (array)-> int: """Sort an array in place and return the number of writes.""" writes = 0 # Loop through the array to find cycles to rotate. # Note that the last item will already be sorted after the first n-1 cycles. for cycle_start in range (0, len (array)-1): item = array [cycle_start] # Find where to put the item. pos = cycle_start for i in range (cycle_start + 1, len (array ...