Sorting Algorithms part 1

Transcription

1 Sorting Algorithms part 1 1. Bubble sort Description Bubble sort is a simple sorting algorithm. It works by repeatedly stepping through the array to be sorted, comparing two items at a time, swapping these two items if they are in the wrong order. The pass through the array is repeated until no swaps are needed, which means the array is sorted. The algorithm gets its name from the way smaller elements "bubble" to the top (i.e. head) of the array via the swaps. [0] [1] [2] [3] [4] [5] The element in red is the element that has to be sorted. The element in green is the element to be sorted and it has been swapped with the neighbor element. The element in blue is the element to be sorted and it is sorted, i.e. is place at the right place. The sorting algorithm starts at the second element of the array, i.e. index 1. 1

2 Another version of the bubble sort is presented below: Flag issorted shows if the array is sorted. Its value starts from true. If there are any swap operations between the elements of the array during one loop of the array, the flag is turned to false. i shows which element is analyzed. numberoftimeslooped shows how many times the array has been analyzed. This variable is used in order to determine the number of iterations for the next loop. [0] [1] [2] [3] [4] [5] i issorted numberof TimesLooped true false true true 2 8 false true false true true 3 5 false 1 true 4 2

3 Code /** Bubble sort data The array to be sorted */ public void sort(integer[] data) //Flag showing if the array is sorted boolean issorted; //A temporary variable that is used when two elements are swapped int tempvariable; //Counter that shows how many times the loop has been executed int numberoftimeslooped = 0; do issorted = true; for (int i = 1; i < data.length - numberoftimeslooped; i++) //Check if the elements has to be swapped if (data[i] < data[i - 1]) //Swap the elements tempvariable = data[i]; data[i] = data[i - 1]; data[i - 1] = tempvariable; issorted = false; //Increase the loop counter numberoftimeslooped++; while (!issorted); 3

4 2. Selection sort Description The selection sort algorithm sorts an array by repeatedly finding the smallest element of the unsorted tail region and moving it to the front. Algorithm: 1) i = 0 the first element of the array; 2) Finds the minimum value in the not sorted array; 3) Swaps the found value with the value in the i-th position; 4) i++; 5) Step 2, if there are any not sorted elements left. [0] [1] [2] [3] [4] [5] The element in red is the smallest element of the unsorted part of the array. The element in blue is the found smallest element that is placed in the right spot of the sorted part of the array. The element in green is the element that has been swapped with the smallest element. 4

5 Code private void sort(integer[] a) for (int i = 0; i < a.length - 1; i++) //Find the smallest element in the unsorted array //(the tail range) //Get the position of the smallest element int minpos = i; for (int j = i + 1; j < a.length; j++) if (a[j] < a[minpos]) minpos = j; //Swap the smallest element with the element in //position i int temp = a[minpos]; a[minpos] = a[i]; a[i] = temp; 5

6 3. Insertion sort Description Insertion sort is a sorting algorithm that is appropriate for small inputs. It is generally considered to be a good solution if only a few elements need sorting. However, if we are dealing with a large amount of data, insertion sort is a poor choice because it is time consuming. The iteration of the insertion sort removes an element from the input data, inserting it at the correct position in the already sorted list, until no elements are left in the input. In the initial state the first element, itself, is sorted. In the final state all elements, considered as a group, have been sorted. The basic action of the insertion sort is to sort the elements in positions 0 through p. In each stage p is increased by 1. Code: [0] [1] [2] [3] [4] [5] The dark shading indicates the sorted area. The first element is considered sorted. The algorithm starts from the second element of the array (index 1). The red color indicates which element is to be sorted. The blue color indicates where the element is placed in the sorted array. private void sort(integer[] a) for (int p = 1; p < a.length; p++) Integer temp = a[p]; int j = p; for (; j > 0 && temp.compareto(a[j-1]) < 0; j--) a[j] = a[j - 1]; a[j] = temp; 6