Question

The C++ book I’m reading described a sort algo, saying it is the Bubblesort yet I cannot find a single variation of bubblesort just like it. I understand the differences are minor, but is it exactly as efficient as a regular bubblesort ?

BubbleSort(int A[], int length)
for (j=0; j < length-1; j++)
  for (i=j+1; i < length; i++)
    if (A[i] < A[j])
      Swap()

Basically, instead of comparing two adjacent values, it compares the first A[0] with every entry, on the next pass it compares A[1] with the remaining entries, then A[2] etc.

Is it really just a regular bubblesort, is the characteristics and performance exactly the same?

Answer 1

This is selection sort. On each pass you find the i’th smallest element and put it in position i. After the first pass, it is not necessary to look at A[0] anymore, and so on. Selection sort is worst-case O(n²) and best-case O(n), just like bubble sort, but it has a smaller constant factor than bubble sort. Insertion sort, an additional refinement, is even better, to the point where it’s faster than most O(n log n) algorithms for very small arrays (fewer than ten elements or so) and so serious library sort primitives will cut over to it for small subproblems.