C # Implement Bubble sorting,

C # Implement Bubble sorting,

I. algorithm principles

 

1. Compare adjacent elements. If the first is bigger than the second, exchange the two of them.

2. perform the same operation on each adjacent element, starting from the first pair to the last one at the end. At this point, the final element should be the largest number.

3. Repeat the preceding steps for all elements except the last one.

4. Continue to repeat the above steps for fewer and fewer elements until there is no need to compare any number.

 

Ii. Algorithm Analysis

 

Average time complexity: The best time for Bubble Sorting is O (n), the worst is O (n ²), and the average time complexity is O (n ²)

 

Space complexity: O (1) (used for exchange)

 

Iii. algorithm Stability

 

Bubble Sorting is to call a small element forward or a large element backward. The comparison is an adjacent comparison between two elements, and the Exchange also occurs between these two elements. Therefore, if the two elements are equal, I think you will not be bored to exchange them. If the two equal elements are not adjacent, even if the two are adjacent through the previous two exchanges, at this time, the sequence of the same elements is not changed, so the Bubble Sorting is a stable sorting algorithm.

 

Iv. Bubble Sorting has two obvious advantages

1. "programming complexity" is very low and it is easy to write code;

2. stability. The stability here means that the relative sequence of the same elements in the original sequence is still maintained to the sorted sequence, but the heap sorting and quick sorting are not stable.

V. C # Bubble Sorting Algorithm

C # code Replication

// Bubble sort

void BubbleSort(int array[],int n)

{Int I = 0; int j = 0; int temp = 0; int flag = 0; for (I = 0; I <n-1; I ++) /* total number of workers in the External Loop Control sorting */{flag = 0;/* Before the start of this sort, the switch flag should be false */for (j = n-1; j> I; j --)/* control the inner loop of a sort */{if (array [j] <array [J-1])/* compare adjacent elements, if the reverse order is switched */{temp = array [j]; array [j] = array [J-1]; array [J-1] = temp; flag = 1; /* if (flag = 0)/* if (flag = 0)/* this sort has not been exchanged, terminate the algorithm */break in advance; /* printf ("% d: \ n", I + 1); PrintArray (array, n );*/}}

 

Application of Algorithms

C # code Replication

// Print the Array

void PrintArray(int  array[] , int n)

{  int i;  for(i=0;i<n;i++)   printf(" %d ",array[i]);  printf("\\n");}void TestBubbleSort(){    int array[8] ={38,20,46,38,74,91,12,25};    BubbleSort(array,8);    PrintArray(array,8);}

 

Output Format

 

1st trip 2nd trip 3rd trip 4th trip 5th trip 6th trip 7th trip

12 12 12 12 12 12 12

38 20 20 20 20 20

20 38 25 25 25 25 25

46 25 38 38 38 38 38

38 46 38 38 38 38 38

74 38 46 46 46 46

91 74 74 74 74

25 91 91 91 91 91 91

A simple program of C language Bubble Sorting

Main ()
{
Int I, j, temp;
Int a [10];
For (I = 0; I <10; I ++)
Scanf ("% d,", & a [I]);
For (j = 0; j <= 9; j ++)
{For (I = 0; I <10-j; I ++)
If (a [I]> a [I + 1])
{Temp = a [I];
A [I] = a [I + 1];
A [I + 1] = temp ;}
}
For (I = 1; I <11; I ++)
Printf ("% 5d,", a [I]);
Printf ("\ n ");
}

--------------
Bubble Algorithm
Algorithm Analysis and Improvement of Bubble Sorting
The basic idea of exchanging sorting is to compare the keywords of the records to be sorted in pairs. If the order of the two records is the opposite, the two records are exchanged until there is no reverse order record.
The basic concepts of application exchange sorting include Bubble sorting and quick sorting.

Bubble Sorting

1. Sorting Method
Vertically arrange the sorted record array R [1. n]. Each record R is considered as a bubble with the weight of R. key. According to the principle that a Light Bubble cannot be under a heavy bubble, scan the array R from the bottom up: Any Light Bubble scanned to a violation of this principle will make it "float" up ". This is repeated until the last two bubbles are light and heavy.
(1) initial
R [1. n] is an unordered area.

(2) First scan
The weights of two adjacent bubbles are compared from the bottom of the unordered area to the top. If the light bubbles are found to be in the lower and severe bubbles, the positions of the two bubbles are exchanged. That is, compare (R [n], R [n-1]), (R [n-1], R [N-2]),…, (R [2], R [1]); for each pair of bubbles (R [j + 1], R [j]), if R [j + 1]. key <R [j]. key, then the contents of R [j + 1] and R [j] are exchanged.
When the first scan is complete, the "lightest" bubble floated to the top of the interval, that is, the record with the smallest keyword is placed on the highest position R [1.

(3) second scan
Scan R [2. n]. When scanning is completed, the "light" bubble floated to the R [2] position ......
Finally, the sequential area R [1. n] can be obtained through n-1 scanning.
Note:
During the I-trip scan, R [1 .. I-1] and R [I.. n] are the current sequential and disordered areas, respectively. The scan continues from the bottom of the unordered area to the top of the area. When scanning is completed, the shortest bubbles in the area float to the top position R. The result is that R [1. I] is changed to a new ordered area.

2. Bubble sorting process example
Bubble Sorting of files whose keyword sequence is 49 38 65 97 76 13 27 49

3. Sorting Algorithm
(1) Analysis
Because each sort adds a bubble to the ordered area, there are n-1 bubbles in the ordered area after N-1 sort, in the disordered area, the bubble weight is always greater than or equal to the bubble weight in the ordered area. Therefore, the entire Bubble sorting process requires at most n-1 sorting.
If no bubble position exchange is found in a sorting, it means that all bubbles in the unordered area to be sorted meet the principle of being light and heavy. Therefore, the Bubble sorting process can be terminated after this sorting. Therefore, in the following algorithm, a Boolean exchange is introduced, which is set to FALSE before each sort starts. If an exchange occurs during the sorting process, set it to TRUE. Check exchange at the end of sorting. If exchange has not occurred, terminate the algorithm and no longer perform the next sorting.

(2) specific algorithms
Void BubbleSort (SeqList R)
{// R (l. n) is the file to be sorted. It uses bottom-up scanning to perform Bubble Sorting on R.
Int I, j;
Boolean exchange; // exchange flag
For (I = 1; I <G id = "1">

A simple program of C language Bubble Sorting

Main ()
{
Int I, j, temp;
Int a [10];
For (I = 0; I <10; I ++)
Scanf ("% d,", & a [I]);
For (j = 0; j <= 9; j ++)
{For (I = 0; I <10-j; I ++)
If (a [I]> a [I + 1])
{Temp = a [I];
A [I] = a [I + 1];
A [I + 1] = temp ;}
}
For (I = 1; I <11; I ++)
Printf ("% 5d,", a [I]);
Printf ("\ n ");
}

--------------
Bubble Algorithm
Algorithm Analysis and Improvement of Bubble Sorting
The basic idea of exchanging sorting is to compare the keywords of the records to be sorted in pairs. If the order of the two records is the opposite, the two records are exchanged until there is no reverse order record.
The basic concepts of application exchange sorting include Bubble sorting and quick sorting.

Bubble Sorting

1. Sorting Method
Vertically arrange the sorted record array R [1. n]. Each record R is considered as a bubble with the weight of R. key. According to the principle that a Light Bubble cannot be under a heavy bubble, scan the array R from the bottom up: Any Light Bubble scanned to a violation of this principle will make it "float" up ". This is repeated until the last two bubbles are light and heavy.
(1) initial
R [1. n] is an unordered area.

(2) First scan
The weights of two adjacent bubbles are compared from the bottom of the unordered area to the top. If the light bubbles are found to be in the lower and severe bubbles, the positions of the two bubbles are exchanged. That is, compare (R [n], R [n-1]), (R [n-1], R [N-2]),…, (R [2], R [1]); for each pair of bubbles (R [j + 1], R [j]), if R [j + 1]. key <R [j]. key, then the contents of R [j + 1] and R [j] are exchanged.
When the first scan is complete, the "lightest" bubble floated to the top of the interval, that is, the record with the smallest keyword is placed on the highest position R [1.

(3) second scan
Scan R [2. n]. When scanning is completed, the "light" bubble floated to the R [2] position ......
Finally, the sequential area R [1. n] can be obtained through n-1 scanning.
Note:
During the I-trip scan, R [1 .. I-1] and R [I.. n] are the current sequential and disordered areas, respectively. The scan continues from the bottom of the unordered area to the top of the area. When scanning is completed, the shortest bubbles in the area float to the top position R. The result is that R [1. I] is changed to a new ordered area.

2. Bubble sorting process example
Bubble Sorting of files whose keyword sequence is 49 38 65 97 76 13 27 49

3. Sorting Algorithm
(1) Analysis
Because each sort adds a bubble to the ordered area, there are n-1 bubbles in the ordered area after N-1 sort, in the disordered area, the bubble weight is always greater than or equal to the bubble weight in the ordered area. Therefore, the entire Bubble sorting process requires at most n-1 sorting.
If no bubble position exchange is found in a sorting, it means that all bubbles in the unordered area to be sorted meet the principle of being light and heavy. Therefore, the Bubble sorting process can be terminated after this sorting. Therefore, in the following algorithm, a Boolean exchange is introduced, which is set to FALSE before each sort starts. If an exchange occurs during the sorting process, set it to TRUE. Check exchange at the end of sorting. If exchange has not occurred, terminate the algorithm and no longer perform the next sorting.

(2) specific algorithms
Void BubbleSort (SeqList R)
{// R (l. n) is the file to be sorted. It uses bottom-up scanning to perform Bubble Sorting on R.
Int I, j;
Boolean exchange; // exchange flag
For (I = 1; I <G id = "1">