QuickSort

QuickSort - -To form L, E we sort at both ends Complexity...

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Quick Sort -A popular algorithm that also used “divde/conquer” -an “in place” algorithm that no additional memory is necessary to store temporary results QuickSort(s) → input: unsorted array s → output: sorted array s 1. Divide if s has only one element, return; otherwise -choose randomly an element “x” in s called the “pivot” -Divide s into three sets: L, E, G L → all elements < x E → all elements == x G → all elements > x 2. Resurse quicksort(L); quicksort(G); //At this point, L and G are sorted 3. Conquer put elements of L, E, and G back into s In-Place Quick Sort -We use the same array s to store L, E and G at each step -We use sub-ranges to represent each set -Last element in array is used as pivot
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Unformatted text preview: -To form L, E we sort at both ends Complexity of Quicksort-in the expected case at every call of quicksort, the pivot x will divide L and G in two sets that will, on average, be the same size-The work done in the algorithm for one element is the number of times the element is moved-in every call to qsSubrange we move each element only once in the subrange. Therefore an element is moved at most log(n) times-However in the worst case we could choose x (the pivot) such that either L or G are empty-Will only happen when the array is already sorted-Even with this problem, quicksort is very popular because it's fast and the common case is O(n log(n))...
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