7.4. The Selection SortΒΆ

The selection sort improves on the bubble sort by making only one exchange for every pass through the first part of the vector. We will call this a step. In order to do this, a selection sort looks for the largest value as it makes a partial pass and, after completing the partial pass, places it in the proper location, ending the step. As with a bubble sort, after the first step, the largest item is in the correct place. After the second step, the next largest is in place. This process continues and requires \(n-1\) steps to sort n items, since the final item must be in place after the \((n-1)\) st step.

On each step, the largest remaining item is selected and then placed in its proper location. The first pass places 93, the second pass places 77, the third places 55, and so on. The function is shown in ActiveCode 1 .

This visualization allows you to step through the algorithm. Yellow bars represent the current element, red represents the element being looked at, and blue represents the last element to look at during a step.

You may see that the selection sort makes the same number of comparisons as the bubble sort and is therefore also \(O(n^{2})\). However, due to the reduction in the number of exchanges, the selection sort typically executes faster in benchmark studies. In fact, for our particular vector, the bubble sort makes 20 exchanges, while the selection sort makes only 8.

Self Check

    Q-2: Suppose you have the following vector of numbers to sort: [11, 7, 12, 14, 19, 1, 6, 18, 8, 20] which vector represents the partially sorted (ascending) vector after three steps of selection sort?
  • [7, 11, 12, 1, 6, 14, 8, 18, 19, 20]
  • Selection sort is similar to bubble sort (which you appear to have done) but uses fewer swaps
  • [7, 11, 12, 14, 19, 1, 6, 18, 8, 20]
  • This looks like an insertion sort.
  • [11, 7, 12, 14, 1, 6, 8, 18, 19, 20]
  • This one looks similar to the correct answer but instead of swapping the numbers have been shifted to the left to make room for the correct numbers.
  • [11, 7, 12, 14, 8, 1, 6, 18, 19, 20]
  • Selection sort improves upon bubble sort by making fewer swaps.
Next Section - 7.5. The Insertion Sort