(1) Sorting algorithm: the simplest sorting algorithm------bubble sorting

Key points: Scan the data from left to right, select the largest data, and put it on the right

 

Code:

#include <iostream>

using namespace std;

void bubble_sort(int list[], int n)
{
	for (int i = 0; i < n - 1; i++)  //比较n-1次
	{
		for (int j = 0; j < n - 1 - i; j++) //每一次循环少比较一次
		{
			if(list[j]> list[j + 1])
				swap(list[j], list[j + 1]);
		}
			
	}

}


int main()
{
	int arry[10] = {2,1,4,5,9,8,6,7,3,0};

	bubble_sort(arry,sizeof(arry)/sizeof(arry[0]));

	for (int i = 0; i < sizeof(arry) / sizeof(arry[0]); i++)
		cout << arry[i] << " ";

	cout << endl;

	return 0;
}

operation result:

 

Time complexity of bubble sorting method:

Number of comparisons: 1 + 2 +...+N-3 + N-2 + N-1 = (1 + (N-1)) * (N-1) / 2 = N^2/2-N/ 2

Number of exchanges: 1 + 2 +...+N-3 + N-2 + N-1 = (1 + (N-1)) * (N-1) / 2 = N^2/2-N/ 2

So the time complexity of bubbling is (N^2/2-N/2) + (N^2/2-N/2) = N^2-N

The final time complexity is: O(N^2)