气泡排序是最简单的排序算法，如果相邻元素的顺序错误，则重复交换相邻元素。 例子： 第一关： ( 5. 1. 4 2 8 ) –> ( 1. 5. 4.2.8），这里，算法比较前两个元素，并从5>1开始交换。 ( 1 5. 4. 2 8 ) –> ( 1 4. 5. 2.8），从5>4开始交换 ( 1 4 5. 2. 8 ) –> ( 1 4 2. 5. 8），从5>2开始交换 ( 1 4 2 5. 8. ) –> ( 1 4 2 5. 8. )现在，由于这些元素已经按顺序排列（8>5），所以算法不会交换它们。 第二关： ( 1. 4. 2 5 8 ) –> ( 1. 4. 2 5 8 ) ( 1 4. 2. 5 8 ) –> ( 1 2. 4. 5.8），从4>2开始交换 ( 1 2 4. 5. 8 ) –> ( 1 2 4. 5. 8 ) ( 1 2 4 5. 8. ) –> ( 1 2 4 5. 8. ) 现在，数组已经排序，但我们的算法不知道它是否完成。算法需要一个 整体 不经过 任何 交换以知道它已排序。 第三关： ( 1. 2. 4 5 8 ) –> ( 1. 2. 4 5 8 ) ( 1 2. 4. 5 8 ) –> ( 1 2. 4. 5 8 ) ( 1 2 4. 5. 8 ) –> ( 1 2 4. 5. 8 ) ( 1 2 4 5. 8. ) –> ( 1 2 4 5. 8. )
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下面是冒泡排序的实现。
C++
// C++ program for implementation of Bubble sort #include <bits/stdc++.h> using namespace std; void swap( int *xp, int *yp) { int temp = *xp; *xp = *yp; *yp = temp; } // A function to implement bubble sort void bubbleSort( int arr[], int n) { int i, j; for (i = 0; i < n-1; i++) // Last i elements are already in place for (j = 0; j < n-i-1; j++) if (arr[j] > arr[j+1]) swap(&arr[j], &arr[j+1]); } /* Function to print an array */ void printArray( int arr[], int size) { int i; for (i = 0; i < size; i++) cout << arr[i] << " " ; cout << endl; } // Driver code int main() { int arr[] = {64, 34, 25, 12, 22, 11, 90}; int n = sizeof (arr)/ sizeof (arr[0]); bubbleSort(arr, n); cout<< "Sorted array: " ; printArray(arr, n); return 0; } // This code is contributed by rathbhupendra |
C
// C program for implementation of Bubble sort #include <stdio.h> void swap( int *xp, int *yp) { int temp = *xp; *xp = *yp; *yp = temp; } // A function to implement bubble sort void bubbleSort( int arr[], int n) { int i, j; for (i = 0; i < n-1; i++) // Last i elements are already in place for (j = 0; j < n-i-1; j++) if (arr[j] > arr[j+1]) swap(&arr[j], &arr[j+1]); } /* Function to print an array */ void printArray( int arr[], int size) { int i; for (i=0; i < size; i++) printf ( "%d " , arr[i]); printf ( "" ); } // Driver program to test above functions int main() { int arr[] = {64, 34, 25, 12, 22, 11, 90}; int n = sizeof (arr)/ sizeof (arr[0]); bubbleSort(arr, n); printf ( "Sorted array: " ); printArray(arr, n); return 0; } |
JAVA
// Java program for implementation of Bubble Sort class BubbleSort { void bubbleSort( int arr[]) { int n = arr.length; for ( int i = 0 ; i < n- 1 ; i++) for ( int j = 0 ; j < n-i- 1 ; j++) if (arr[j] > arr[j+ 1 ]) { // swap arr[j+1] and arr[j] int temp = arr[j]; arr[j] = arr[j+ 1 ]; arr[j+ 1 ] = temp; } } /* Prints the array */ void printArray( int arr[]) { int n = arr.length; for ( int i= 0 ; i<n; ++i) System.out.print(arr[i] + " " ); System.out.println(); } // Driver method to test above public static void main(String args[]) { BubbleSort ob = new BubbleSort(); int arr[] = { 64 , 34 , 25 , 12 , 22 , 11 , 90 }; ob.bubbleSort(arr); System.out.println( "Sorted array" ); ob.printArray(arr); } } /* This code is contributed by Rajat Mishra */ |
python
# Python program for implementation of Bubble Sort def bubbleSort(arr): n = len (arr) # Traverse through all array elements for i in range (n): # Last i elements are already in place for j in range ( 0 , n - i - 1 ): # traverse the array from 0 to n-i-1 # Swap if the element found is greater # than the next element if arr[j] > arr[j + 1 ] : arr[j], arr[j + 1 ] = arr[j + 1 ], arr[j] # Driver code to test above arr = [ 64 , 34 , 25 , 12 , 22 , 11 , 90 ] bubbleSort(arr) print ( "Sorted array is:" ) for i in range ( len (arr)): print ( "%d" % arr[i]), |
C#
// C# program for implementation // of Bubble Sort using System; class GFG { static void bubbleSort( int []arr) { int n = arr.Length; for ( int i = 0; i < n - 1; i++) for ( int j = 0; j < n - i - 1; j++) if (arr[j] > arr[j + 1]) { // swap temp and arr[i] int temp = arr[j]; arr[j] = arr[j + 1]; arr[j + 1] = temp; } } /* Prints the array */ static void printArray( int []arr) { int n = arr.Length; for ( int i = 0; i < n; ++i) Console.Write(arr[i] + " " ); Console.WriteLine(); } // Driver method public static void Main() { int []arr = {64, 34, 25, 12, 22, 11, 90}; bubbleSort(arr); Console.WriteLine( "Sorted array" ); printArray(arr); } } // This code is contributed by Sam007 |
PHP
<?php // PHP program for implementation // of Bubble Sort function bubbleSort(& $arr ) { $n = sizeof( $arr ); // Traverse through all array elements for ( $i = 0; $i < $n ; $i ++) { // Last i elements are already in place for ( $j = 0; $j < $n - $i - 1; $j ++) { // traverse the array from 0 to n-i-1 // Swap if the element found is greater // than the next element if ( $arr [ $j ] > $arr [ $j +1]) { $t = $arr [ $j ]; $arr [ $j ] = $arr [ $j +1]; $arr [ $j +1] = $t ; } } } } // Driver code to test above $arr = array (64, 34, 25, 12, 22, 11, 90); $len = sizeof( $arr ); bubbleSort( $arr ); echo "Sorted array : " ; for ( $i = 0; $i < $len ; $i ++) echo $arr [ $i ]. " " ; // This code is contributed by ChitraNayal. ?> |
Javascript
<script> function swap(arr, xp, yp) { var temp = arr[xp]; arr[xp] = arr[yp]; arr[yp] = temp; } // An optimized version of Bubble Sort function bubbleSort( arr, n) { var i, j; for (i = 0; i < n-1; i++) { for (j = 0; j < n-i-1; j++) { if (arr[j] > arr[j+1]) { swap(arr,j,j+1); } } } } /* Function to print an array */ function printArray(arr, size) { var i; for (i=0; i < size; i++) document.write(arr[i]+ " " ); document.write( "" ); } // Driver program to test above functions var arr = [64, 34, 25, 12, 22, 11, 90]; var n = 7; document.write( "UnSorted array: " ); printArray(arr, n); bubbleSort(arr, n); document.write( "Sorted array: " ); printArray(arr, n); </script> |
输出：
Sorted array: 11 12 22 25 34 64 90
插图：
—> 优化实施： 即使数组已排序，上述函数也始终运行O（n^2）次。如果内环没有引起任何交换，可以通过停止算法来优化。
C++
// Optimized implementation of Bubble sort #include <bits/stdc++.h> using namespace std; void swap( int *xp, int *yp) { int temp = *xp; *xp = *yp; *yp = temp; } // An optimized version of Bubble Sort void bubbleSort( int arr[], int n) { int i, j; bool swapped; for (i = 0; i < n-1; i++) { swapped = false ; for (j = 0; j < n-i-1; j++) { if (arr[j] > arr[j+1]) { swap(&arr[j], &arr[j+1]); swapped = true ; } } // IF no two elements were swapped by inner loop, then break if (swapped == false ) break ; } } /* Function to print an array */ void printArray( int arr[], int size) { int i; for (i = 0; i < size; i++) cout << " " << arr[i]; cout << " n" ; } // Driver program to test above functions int main() { int arr[] = {64, 34, 25, 12, 22, 11, 90}; int n = sizeof (arr)/ sizeof (arr[0]); bubbleSort(arr, n); cout << "Sorted array: " ; printArray(arr, n); return 0; } // This code is contributed by shivanisinghss2110 |
C
// Optimized implementation of Bubble sort #include <stdio.h> #include <stdbool.h> void swap( int *xp, int *yp) { int temp = *xp; *xp = *yp; *yp = temp; } // An optimized version of Bubble Sort void bubbleSort( int arr[], int n) { int i, j; bool swapped; for (i = 0; i < n-1; i++) { swapped = false ; for (j = 0; j < n-i-1; j++) { if (arr[j] > arr[j+1]) { swap(&arr[j], &arr[j+1]); swapped = true ; } } // IF no two elements were swapped by inner loop, then break if (swapped == false ) break ; } } /* Function to print an array */ void printArray( int arr[], int size) { int i; for (i=0; i < size; i++) printf ( "%d " , arr[i]); printf ( "n" ); } // Driver program to test above functions int main() { int arr[] = {64, 34, 25, 12, 22, 11, 90}; int n = sizeof (arr)/ sizeof (arr[0]); bubbleSort(arr, n); printf ( "Sorted array: " ); printArray(arr, n); return 0; } |
JAVA
// Optimized java implementation // of Bubble sort import java.io.*; class GFG { // An optimized version of Bubble Sort static void bubbleSort( int arr[], int n) { int i, j, temp; boolean swapped; for (i = 0 ; i < n - 1 ; i++) { swapped = false ; for (j = 0 ; j < n - i - 1 ; j++) { if (arr[j] > arr[j + 1 ]) { // swap arr[j] and arr[j+1] temp = arr[j]; arr[j] = arr[j + 1 ]; arr[j + 1 ] = temp; swapped = true ; } } // IF no two elements were // swapped by inner loop, then break if (swapped == false ) break ; } } // Function to print an array static void printArray( int arr[], int size) { int i; for (i = 0 ; i < size; i++) System.out.print(arr[i] + " " ); System.out.println(); } // Driver program public static void main(String args[]) { int arr[] = { 64 , 34 , 25 , 12 , 22 , 11 , 90 }; int n = arr.length; bubbleSort(arr, n); System.out.println( "Sorted array: " ); printArray(arr, n); } } // This code is contributed // by Nikita Tiwari. |
Python3
# Python3 Optimized implementation # of Bubble sort # An optimized version of Bubble Sort def bubbleSort(arr): n = len (arr) # Traverse through all array elements for i in range (n): swapped = False # Last i elements are already # in place for j in range ( 0 , n - i - 1 ): # traverse the array from 0 to # n-i-1. Swap if the element # found is greater than the # next element if arr[j] > arr[j + 1 ] : arr[j], arr[j + 1 ] = arr[j + 1 ], arr[j] swapped = True # IF no two elements were swapped # by inner loop, then break if swapped = = False : break # Driver code to test above arr = [ 64 , 34 , 25 , 12 , 22 , 11 , 90 ] bubbleSort(arr) print ( "Sorted array :" ) for i in range ( len (arr)): print ( "%d" % arr[i],end = " " ) # This code is contributed by Shreyanshi Arun |
C#
// Optimized C# implementation // of Bubble sort using System; class GFG { // An optimized version of Bubble Sort static void bubbleSort( int []arr, int n) { int i, j, temp; bool swapped; for (i = 0; i < n - 1; i++) { swapped = false ; for (j = 0; j < n - i - 1; j++) { if (arr[j] > arr[j + 1]) { // swap arr[j] and arr[j+1] temp = arr[j]; arr[j] = arr[j + 1]; arr[j + 1] = temp; swapped = true ; } } // IF no two elements were // swapped by inner loop, then break if (swapped == false ) break ; } } // Function to print an array static void printArray( int []arr, int size) { int i; for (i = 0; i < size; i++) Console.Write(arr[i] + " " ); Console.WriteLine(); } // Driver method public static void Main() { int []arr = {64, 34, 25, 12, 22, 11, 90}; int n = arr.Length; bubbleSort(arr,n); Console.WriteLine( "Sorted array" ); printArray(arr,n); } } // This code is contributed by Sam007 |
PHP
<?php // PHP Optimized implementation // of Bubble sort // An optimized version of Bubble Sort function bubbleSort(& $arr ) { $n = sizeof( $arr ); // Traverse through all array elements for ( $i = 0; $i < $n ; $i ++) { $swapped = False; // Last i elements are already // in place for ( $j = 0; $j < $n - $i - 1; $j ++) { // traverse the array from 0 to // n-i-1. Swap if the element // found is greater than the // next element if ( $arr [ $j ] > $arr [ $j +1]) { $t = $arr [ $j ]; $arr [ $j ] = $arr [ $j +1]; $arr [ $j +1] = $t ; $swapped = True; } } // IF no two elements were swapped // by inner loop, then break if ( $swapped == False) break ; } } // Driver code to test above $arr = array (64, 34, 25, 12, 22, 11, 90); $len = sizeof( $arr ); bubbleSort( $arr ); echo "Sorted array : " ; for ( $i = 0; $i < $len ; $i ++) echo $arr [ $i ]. " " ; // This code is contributed by ChitraNayal. ?> |
Javascript
<script> // Optimized javaScript implementation // of Bubble sort // An optimized version of Bubble Sort function bubbleSort(arr, n) { var i, j, temp; var swapped; for (i = 0; i < n - 1; i++) { swapped = false ; for (j = 0; j < n - i - 1; j++) { if (arr[j] > arr[j + 1]) { // swap arr[j] and arr[j+1] temp = arr[j]; arr[j] = arr[j + 1]; arr[j + 1] = temp; swapped = true ; } } // IF no two elements were // swapped by inner loop, then break if (swapped == false ) break ; } } // Function to print an array function printArray(arr, size) { var i; for (i = 0; i < size; i++) document.write(arr[i] + " " ); document.writeln(); } // Driver program var arr = [ 64, 34, 25, 12, 22, 11, 90 ]; var n = arr.length; bubbleSort(arr, n); document.write( "Sorted array: " ); printArray(arr, n); // This code is contributed shivanisinghss2110 </script> |
输出：
Sorted array: 11 12 22 25 34 64 90
最差和平均情况时间复杂度： O（n*n）。最坏的情况发生在数组被反向排序时。 最佳情况下的时间复杂度： O（n）。最好的情况是数组已经排序。 辅助空间： O（1） 边界情况： 当元素已经排序时，冒泡排序所需的时间最短（n的顺序）。 分类到位： 对 稳定的： 对 由于其简单性，气泡排序通常用于引入排序算法的概念。 在计算机图形学中，它很受欢迎，因为它能够在几乎排序的数组中检测一个非常小的错误（如仅交换两个元素），并以线性复杂度（2n）修复它。例如，它用于多边形填充算法，其中边界线在特定扫描线（平行于x轴的线）处按其x坐标排序，随着y的增加，其顺序更改（两个元素交换）仅在两条线的交点处（来源： 维基百科 )
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