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Selection Sort


Selection Sorting

Selection sort algorithm starts by compairing first two elements of an array and swapping if necessary, i.e., if you want to sort the elements of array in ascending order and if the first element is greater than second then, you need to swap the elements but, if the first element is smaller than second, leave the elements as it is. Then, again first element and third element are compared and swapped if necessary. This process goes on until first and last element of an array is compared. This completes the first step of selection sort.
If there are n elements to be sorted then, the process mentioned above should be repeated n-1 times to get required result. But, for better performance, in second step, comparison starts from second element because after first step, the required number is automatically placed at the first (i.e, In case of sorting in ascending order, smallest element will be at first and in case of sorting in descending order, largest element will be at first.). Similarly, in third step, comparison starts from third element and so on.
The following image will help you understand the algo..
Time Complexity Analysis
Selection sort stops, when unsorted part becomes empty. As we know, on every step number of unsorted elements decreased by one. Therefore, selection sort makes n steps (n is number of elements in array) of outer loop, before stop. Every step of outer loop requires finding minimum in unsorted part. Summing up, n + (n - 1) + (n - 2) + ... + 1, results in O(n2) number of comparisons. Number of swaps may vary from zero (in case of sorted array) to n - 1 (in case array was sorted in reversed order), which results in O(n) number of swaps. Overall algorithm complexity is O(n2).
Fact, that selection sort requires n - 1 number of swaps at most, makes it very efficient in situations, when write operation is significantly more expensive, than read operation.
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