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An example of stable sort on playing cards. When the cards are sorted by rank with a stable sort, the two 5s must remain in the same order in the sorted output that they were originally in. When they are sorted with a non-stable sort, the 5s may end up in the opposite order in the sorted output.
Stable sorting algorithms maintain the relative order of records with equal keys (i.e. values). That is, a sorting algorithm is stable if whenever there are two records R and S with the same key and with R appearing before S in the original list, R will appear before S in the sorted list.
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 ...
For example, addresses could be sorted using the city as primary sort key, and the street as secondary sort key. If the sort key values are totally ordered, the sort key defines a weak order of the items: items with the same sort key are equivalent with respect to sorting. See also stable sorting. If different items have different sort key ...
Hence, the Babylonian method is numerically stable, while Method X is numerically unstable. Numerical stability is affected by the number of the significant digits the machine keeps. If a machine is used that keeps only the four most significant decimal digits, a good example on loss of significance can be given by the two equivalent functions
In computer science, a stable sorting algorithm preserves the order of records with equal keys. In numerical analysis, a numerically stable algorithm avoids magnifying small errors. An algorithm is stable if the result produced is relatively insensitive to perturbations during computation.
Comparison-based sorting algorithms have traditionally dealt with achieving an optimal bound of O(n log n) when dealing with time complexity.Adaptive sort takes advantage of the existing order of the input to try to achieve better times, so that the time taken by the algorithm to sort is a smoothly growing function of the size of the sequence and the disorder in the sequence.
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.