As a result words with the same word count remain sorted lexicographically. Since we already had sorted the list lexicographically, using a stable sort to by word count does not change the order of equal elements anymore. That’s where the stable sort comes into the picture. Second pass, sorted by count using an unstable sort:Īs we have used an unstable sort, the second pass does not maintain the lexicographical order. Second step – sort the whole list lexicographically, then by word count: First pass, sorted lexicographically: How much wood would woodchuck chuck if woodchuck could chuck wood When Stability Mattersįirst step – compute the word count: Input: Stable sorting maintains the order of the two equal balls numbered 8, whereas unstable sorting may invert the relative order of the two 8s. Let’s represent our array using color-coded balls, where any two balls with the same integer will have a different color which would help us keep track of equal elements (8 in our case): Let’s understand the concept with the help of an example. We can classify the sorting as stable if: i < j and A = A and m < n Let’s consider two equal elements in A at indices i and j, i.e, A and A, that end up at indices m and n respectively in B. Further, let B be the collection of elements in A in the sorted order. Let A be a collection of elements and < be a strict weak ordering on the elements.

In other words, stable sorting maintains the position of two equals elements relative to one another. For the decimal system, the radix is 10 (it uses ten digits to represent all numbers - from 0 to 9).

For the binary system, the radix is 2 (it uses only two digits - 0 and 1). Stable sorting algorithms preserve the relative order of equal elements, while unstable sorting algorithms don’t. Radix Sort in Python Dimitrije Stamenic Introduction to Radix Sort The radix (or base) is the number of digits used to represent numbers in a positional numeral system. The stability of a sorting algorithm is concerned with how the algorithm treats equal (or repeated) elements.

Radix sort msd in python