Sorting is considered as one of the important issues of computer science. Although there is a huge number of sorting algorithms, sorting problem has attracted a great deal of research; because efficient sorting is important to optimize the use of other algorithms. It is also often in producing human-readable output. This paper presents a new sorting algorithm called SMS-algorithm (Scan, Move, a...

The first complete running time analysis of a stochastic divide and conquer algorithm was given for Quicksort, a sorting algorithm invented 1961 by Hoare. We analyse here the variant Random Median Quicksort. The analysis includes the expectation, the asymptotic distribution, the moments and exponential moments. The asymptotic distribution is characterized by a stochastic fixed point equation. T...

In this lecture we consider two related algorithms for sorting that achieve a much better running time than the selection sort from last lecture: mergesort and quicksort. We developed quicksort and its invariants in detail. As usual, contracts and loop invariants will bridge the gap between the abstract idea of the algorithm and its implementation. We will revisit many of the computational thin...

In this lecture we consider two related algorithms for sorting that achieve a much better running time than the selection sort from last lecture: mergesort and quicksort. We developed quicksort and its invariants in detail. As usual, contracts and loop invariants will bridge the gap between the abstract idea of the algorithm and its implementation. We will revisit many of the computational thin...

In this lecture we consider two related algorithms for sorting that achieve a much better running time than the selection sort from an earlier lecture: mergesort and quicksort. We develop quicksort and its invariants in detail. As usual, contracts and loop invariants will bridge the gap between the abstract idea of the algorithm and its implementation. We will revisit many of the computational ...

This paper introduces a new, faster sorting algorithm (ARL – Adaptive Left Radix) that does in-place, non-stable sorting. Left Radix, often called MSD (Most Significant Digit) radix, is not new in itself, but the adaptive feature and the in-place sorting ability are new features. ARL does sorting with only internal moves in the array, and uses a dynamically defined radix for each pass. ALR is a...

The first complete running time analysis of a stochastic divide and conquer algorithm was given for Quicksort, a sorting algorithm invented 1961 by Hoare. We analyse here the variant Random Median Quicksort. The analysis includes the expectation, the asymptotic distribution, the moments and exponential moments. The asymptotic distribution is characterized by a stochastic fixed point equation. T...

In this paper, we proposed a new efficient sorting algorithm based on insertion sort concept. The proposed algorithm called Bidirectional Conditional Insertion Sort (BCIS). It is in-place sorting algorithm and it has remarkably efficient average case time complexity when compared with classical insertion sort (IS). By comparing our new proposed algorithm with the Quicksort algorithm, BCIS indic...

We study probability distributions of several characteristic parameters on various forms of Quicksort algorithm: median-of-k, cutting of small lists. A constant use of generating functions leads to a more synthetic description and analysis of the combinatorial structure of the algorithm. This approach allows us in particular to extend the known results for the distributions of running times. We...

Exercise 1 Comparisons in Quicksort To begin with, note that when we talk about the ’number of comparisons’, we mean the number of times one element is compared to another element of the sequence to sort. We do not count internal comparisons of the algorithm (like when the algorithm compares the index of an element to another index). Let a, b be two distinct elements of rank i and j, respective...