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Bubble Sorting:
Bubble sort is a simple sorting algorithm. This sorting algorithm is comparison-based algorithm in which each pair of adjacent elements is compared and the elements are swapped if they are not in order. This algorithm is not suitable for large data sets as its average and worst case complexity are of O(n^2 ) where n is the number of items.
Bubble Sort Working Concept:
We take an unsorted array for our example. Bubble sort takes Ο(n^2 ) time so we're keeping it short and precise.
Bubble sort starts with very first two elements, comparing them to check which one is greater.
In this case, value 33 is greater than 14, so it is already in sorted locations. Next, we compare 33 with 27.
We find that 27 is smaller than 33 and these two values must be swapped.
The new array should look like this −
Next we compare 33 and 35. We find that both are in already sorted positions.
Then we move to the next two values, 35 and 10.
We know then that 10 is smaller 35. Hence they are not sorted.
We swap these values. We find that we have reached the end of the array. After one iteration, the array should look like this −
Algorithm:
We assume list is an array of n elements. We further assume that swap function swaps the values of the given array elements.
begin BubbleSort(list)
for all elements of list if list[i] > list[i+1] swap(list[i], list[i+1]) end if end for
return list
end BubbleSort
Bubble Sort Program in C:
Implementation in C
#include <stdio.h> #include <stdbool.h>
#define MAX 10 int list[MAX] = {1,8,4,6,0,3,5,2,7,9};
void display(){ int i; printf("[");
// navigate through all items for(i = 0; i < MAX; i++){ printf("%d ",list[i]); }
printf("]\n"); }
void bubbleSort() { int temp; int i,j;
bool swapped = false;
// loop through all numbers for(i = 0; i < MAX-1; i++) { swapped = false;
// loop through numbers falling ahead for(j = 0; j < MAX-1-i; j++) { printf(" Items compared: [ %d, %d ] ", list[j],list[j+1]);
// check if next number is lesser than current no // swap the numbers. // (Bubble up the highest number)
if(list[j] > list[j+1]) { temp = list[j]; list[j] = list[j+1]; list[j+1] = temp;
swapped = true; printf(" => swapped [%d, %d]\n",list[j],list[j+1]); }else { printf(" => not swapped\n"); }
Iteration 1#: [1 4 6 0 3 5 2 7 8 9 ]
Items compared: [ 1, 4 ] => not swapped Items compared: [ 4, 6 ] => not swapped Items compared: [ 6, 0 ] => swapped [0, 6] Items compared: [ 6, 3 ] => swapped [3, 6] Items compared: [ 6, 5 ] => swapped [5, 6] Items compared: [ 6, 2 ] => swapped [2, 6] Items compared: [ 6, 7 ] => not swapped Items compared: [ 7, 8 ] => not swapped Iteration 2#: [1 4 0 3 5 2 6 7 8 9 ]
Items compared: [ 1, 4 ] => not swapped Items compared: [ 4, 0 ] => swapped [0, 4] Items compared: [ 4, 3 ] => swapped [3, 4] Items compared: [ 4, 5 ] => not swapped Items compared: [ 5, 2 ] => swapped [2, 5] Items compared: [ 5, 6 ] => not swapped Items compared: [ 6, 7 ] => not swapped
Iteration 3#: [1 0 3 4 2 5 6 7 8 9 ] Items compared: [ 1, 0 ] => swapped [0, 1] Items compared: [ 1, 3 ] => not swapped Items compared: [ 3, 4 ] => not swapped Items compared: [ 4, 2 ] => swapped [2, 4] Items compared: [ 4, 5 ] => not swapped Items compared: [ 5, 6 ] => not swapped
Iteration 4#: [0 1 3 2 4 5 6 7 8 9 ] Items compared: [ 0, 1 ] => not swapped Items compared: [ 1, 3 ] => not swapped Items compared: [ 3, 2 ] => swapped [2, 3] Items compared: [ 3, 4 ] => not swapped Items compared: [ 4, 5 ] => not swapped
Iteration 5#: [0 1 2 3 4 5 6 7 8 9 ]
Items compared: [ 0, 1 ] => not swapped Items compared: [ 1, 2 ] => not swapped Items compared: [ 2, 3 ] => not swapped Items compared: [ 3, 4 ] => not swapped Output Array: [0 1 2 3 4 5 6 7 8 9 ]
22. Insertion
Insertion Sort:
This is an in-place comparison-based sorting algorithm. Here, a sub-list is maintained which is always sorted. For example, the lower part of an array is maintained to be sorted. An element which is to be 'insert'ed in this sorted sub-list, has to find its appropriate place and then it has to be inserted there. Hence the name, insertion sort.
The array is searched sequentially and unsorted items are moved and inserted into the sorted sub-list (in the same array). This algorithm is not suitable for large data sets as its average and worst case complexity are of Ο(n^2 ), where n is the number of items.
Insertion Sort Working:
We take an unsorted array for our example.
Insertion sort compares the first two elements.
It finds that both 14 and 33 are already in ascending order. For now, 14 is in sorted sub- list.
Insertion sort moves ahead and compares 33 with 27.
And finds that 33 is not in the correct position.
We swap them again. By the end of third iteration, we have a sorted sub-list of 4 items.
This process goes on until all the unsorted values are covered in a sorted sub-list.
Algorithm
Now we have a bigger picture of how this sorting technique works, so we can derive simple steps by which we can achieve insertion sort.
Step 1 − If it is the first element, it is already sorted. return 1; Step 2 − Pick next element Step 3 − Compare with all elements in the sorted sub-list Step 4 − Shift all the elements in the sorted sub-list that is greater than the value to be sorted Step 5 − Insert the value Step 6 − Repeat until list is sorted
Insertion Sort Program in C:
#include <stdio.h> #include <stdbool.h> #define MAX 7
int intArray[MAX] = {4,6,3,2,1,9,7};
void printline(int count){ int i;
for(i = 0;i <count-1;i++){ printf("="); }
printf("=\n");
}
void display(){ int i; printf("[");
// navigate through all items for(i = 0;i<MAX;i++){ printf("%d ",intArray[i]); }
printf("]\n");
}
void insertionSort(){
int valueToInsert; int holePosition; int i;
// loop through all numbers for(i = 1; i < MAX; i++){
// select a value to be inserted. valueToInsert = intArray[i];
// select the hole position where number is to be inserted holePosition = i;
// check if previous no. is larger than value to be inserted while (holePosition > 0 && intArray[holePosition-1] > valueToInsert){ intArray[holePosition] = intArray[holePosition-1]; holePosition--; printf(" item moved : %d\n" , intArray[holePosition]); }
item moved : item moved : item inserted :1, at position : iteration 4#: [1, 2, 3, 4, 6, 9, 7]
iteration 5#: [1, 2, 3, 4, 6, 9, 7] item moved : item moved : item inserted :7, at position : iteration 6#: [1, 2, 3, 4, 7, 6, 9] Output Array: [1, 2, 3, 4, 7, 6, 9]
==================================================
Selection sort:
Selection sort is a simple sorting algorithm. This sorting algorithm is an in-place comparison-based algorithm in which the list is divided into two parts, the sorted part at the left end and the unsorted part at the right end. Initially, the sorted part is empty and the unsorted part is the entire list.
The smallest element is selected from the unsorted array and swapped with the leftmost element, and that element becomes a part of the sorted array. This process continues moving unsorted array boundary by one element to the right.
This algorithm is not suitable for large data sets as its average and worst case complexities are of O(n^2 ), where n is the number of items.
Selection Sort Working:
Consider the following depicted array as an example.
For the first position in the sorted list, the whole list is scanned sequentially. The first position where 14 is stored presently, we search the whole list and find that 10 is the lowest value.
So we replace 14 with 10. After one iteration 10, which happens to be the minimum value in the list, appears in the first position of the sorted list.
For the second position, where 33 is residing, we start scanning the rest of the list in a linear manner.
We find that 14 is the second lowest value in the list and it should appear at the second place. We swap these values.
Algorithm
Step 1 − Set MIN to location 0 Step 2 − Search the minimum element in the list Step 3 − Swap with value at location MIN Step 4 − Increment MIN to point to next element Step 5 − Repeat until list is sorted
Selection Sort Program in C:
#include <stdio.h> #include <stdbool.h> #define MAX 7
int intArray[MAX] = {4,6,3,2,1,9,7};
void printline(int count){ int i;
for(i = 0;i <count-1;i++){ printf("="); }
printf("=\n"); }
void display(){ int i; printf("[");
// navigate through all items for(i = 0;i<MAX;i++){ printf("%d ", intArray[i]); }
printf("]\n");
}
void selectionSort(){
int indexMin,i,j;
// loop through all numbers for(i = 0; i < MAX-1; i++){
// set current element as minimum indexMin = i;
// check the element to be minimum for(j = i+1;j<MAX;j++){ if(intArray[j] < intArray[indexMin]){ indexMin = j; } }
if(indexMin != i){ printf("Items swapped: [ %d, %d ]\n" , intArray[i], intArray[indexMin]);
// swap the numbers int temp = intArray[indexMin]; intArray[indexMin] = intArray[i]; intArray[i] = temp; }
printf("Iteration %d#:",(i+1)); display(); }
}
- Merge
Merge sort:
Merge sort is a sorting technique based on divide and conquer technique. With worst- case time complexity being Ο(n log n), it is one of the most respected algorithms.
Merge sort first divides the array into equal halves and then combines them in a sorted manner.
Merge Sort Working:
To understand merge sort, we take an unsorted array as the following −
We know that merge sort first divides the whole array iteratively into equal halves unless the atomic values are achieved. We see here that an array of 8 items is divided into two arrays of size 4.
This does not change the sequence of appearance of items in the original. Now we divide these two arrays into halves.
We further divide these arrays and we achieve atomic value which can no more be divided.
Now, we combine them in exactly the same manner as they were broken down. Please note the color codes given to these lists.
We first compare the element for each list and then combine them into another list in a sorted manner. We see that 14 and 33 are in sorted positions. We compare 27 and 10 and in the target list of 2 values we put 10 first, followed by 27. We change the order of 19 and 35 whereas 42 and 44 are placed sequentially.
In the next iteration of the combining phase, we compare lists of two data values, and merge them into a list of found data values placing all in a sorted order.
After the final merging, the list should look like this −
Algorithm
Merge sort keeps on dividing the list into equal halves until it can no more be divided. By definition, if it is only one element in the list, it is sorted. Then, merge sort combines the smaller sorted lists keeping the new list sorted too.
Step 1 − if it is only one element in the list it is already sorted, return. Step 2 − divide the list recursively into two halves until it can no more be divided. Step 3 − merge the smaller lists into new list in sorted order.
