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The Bubble Sortbyby
Mr. Dave ClausenMr. Dave ClausenLa Cañada High SchoolLa Cañada High School
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The Bubble SortAlgorithm
The Bubble Sort compares adjacent elements in a The Bubble Sort compares adjacent elements in a list, and “swaps” them if they are not in order. list, and “swaps” them if they are not in order. Each pair of adjacent elements is compared and Each pair of adjacent elements is compared and swapped until the largest element “bubbles” to the swapped until the largest element “bubbles” to the bottom. Repeat this process each time stopping bottom. Repeat this process each time stopping one indexed element less, until you compare only one indexed element less, until you compare only the first two elements in the list. We know that the first two elements in the list. We know that the array is sorted after both of the nested loops the array is sorted after both of the nested loops have finished.have finished.
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A Bubble Sort Example
654321
Compare
We start by comparing the first two elements in the List.
This list is an example of a “worst case” scenario for sorting, because the List is in the exact opposite order from the way we want it sorted (the computer program does not know this).
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A Bubble Sort Example
564321
Swap
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A Bubble Sort Example
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Compare
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A Bubble Sort Example
546321
Swap
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A Bubble Sort Example
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A Bubble Sort Example
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A Bubble Sort Example
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A Bubble Sort Example
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Swap
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A Bubble Sort Example
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A Bubble Sort Example
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Swap
As you can see, the largest number has “bubbled” down to the bottom of the List after the first pass through the List.
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A Bubble Sort Example
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For our second pass through the List, we start by comparing these first two elements in the List.
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A Bubble Sort Example
453216
Swap
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A Bubble Sort Example
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A Bubble Sort Example
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A Bubble Sort Example
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A Bubble Sort Example
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A Bubble Sort Example
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A Bubble Sort Example
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Swap
At the end of the second pass, we stop at element number n - 1, because the largest element in the List is already in the last position.
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A Bubble Sort Example
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We start with the first two elements again at the beginning of the third pass.
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A Bubble Sort Example
342156
Swap
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A Bubble Sort Example
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A Bubble Sort Example
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A Bubble Sort Example
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A Bubble Sort Example
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Swap
At the end of the third pass, we stop comparing and swapping at element number n - 2.
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A Bubble Sort Example
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The beginning of the fourth pass...
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A Bubble Sort Example
231456
Swap
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A Bubble Sort Example
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A Bubble Sort Example
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The end of the fourth pass stops at element number n - 3.
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A Bubble Sort Example
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The beginning of the fifth pass...
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A Bubble Sort Example
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Swap
The last pass compares only the first two elements of the List. After this comparison and possible swap, the smallest element has “bubbled” to the top.
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What “Swapping” Means654321
TEMP
Place the first element into the Temporary Variable.
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What “Swapping” Means554321
TEMP
Replace the first element with the second element.
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What “Swapping” Means564321
TEMP
Replace the second element with the Temporary Variable.
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Java Code For Bubble Sortpublic static void bubbleSort(int[ ] list){
int k = 0;boolean exchangeMade = true;
// Make up to n - 1 passes through array, exit early if no exchanges// are made on previous pass
while ((k < list.length - 1) && exchangeMade){exchangeMade = false;k++;for (int j = 0; j < list.length - k; j++)
if (list[j] > list[j + 1]){swap(list, j, j + 1);exchangeMade = true;
}}
}
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Java Code for Swap Procedure
public static void swap(int[] list, int x, int y){
int temp = list[x];list[x] = list[y];list[y] = temp;
}
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C++ Code For Bubble Sort
void Bubble_Sort (int array, int length)void Bubble_Sort (int array, int length){{
int element, index;int element, index;
for (element = 1; element < length; ++element)for (element = 1; element < length; ++element)for (index = lengthfor (index = length--1; index >= element; 1; index >= element; ----index)index)if (array[indexif (array[index--1] > array[index])1] > array[index])Swap_Data (array[indexSwap_Data (array[index--1], array[index]);1], array[index]);
} //} //BubbleSortBubbleSort
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C++ Code for Swap Procedure
void Swap_Data (int &number1, int &number2)void Swap_Data (int &number1, int &number2){{
int temp;int temp;
temp = number1;temp = number1;number1 = number2;number1 = number2;number2 = temp;number2 = temp;
} } //Swap_Data//Swap_Data
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Pascal Code For Bubble Sort
procedureprocedure BubbleSortBubbleSort ((var IntArrayvar IntArray:: IntNumbersIntNumbers););varvarelement, index: integer;element, index: integer;
beginbeginfor element := 1 tofor element := 1 to MaxNumMaxNum dodofor index :=for index := MaxNum downtoMaxNum downto (element + 1) do(element + 1) doifif IntArrayIntArray [index] <[index] < IntArrayIntArray [index [index -- 1]1]then Swap (then Swap (IntArrayIntArray [index],[index], IntArrayIntArray [index [index -- 1])1])
end; {end; {BubbleSortBubbleSort}}
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Pascal Code for Swap Procedure
procedure Swap (procedure Swap (varvar number1, number2: integer);number1, number2: integer);varvartemp: integer;temp: integer;
beginbegintemp := number1;temp := number1;number1 := number2;number1 := number2;number2 := tempnumber2 := temp
end; {Swap}end; {Swap}
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BASIC Code For Bubble Sort8000 REM #################8000 REM #################8010 REM Bubble Sort8010 REM Bubble Sort8020 REM #################8020 REM #################8030 FOR ELEMENT = 1 TO MAXNUM 8030 FOR ELEMENT = 1 TO MAXNUM -- 118040 ::FOR INDEX = 1 TO MAXNUM 8040 ::FOR INDEX = 1 TO MAXNUM -- 118050 ::::::IF N (INDEX) < = N (INDEX + 1) THEN GOTO 80908050 ::::::IF N (INDEX) < = N (INDEX + 1) THEN GOTO 80908060 ::::::TEMP = N (INDEX + 1)8060 ::::::TEMP = N (INDEX + 1)8070 ::::::N (INDEX + 1) = N (INDEX)8070 ::::::N (INDEX + 1) = N (INDEX)8080 ::::::N (INDEX) = TEMP8080 ::::::N (INDEX) = TEMP8090 ::NEXT INDEX8090 ::NEXT INDEX8100 NEXT ELEMENT 8100 NEXT ELEMENT 8110 RETURN 8110 RETURN
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Big - O Notation
Big Big -- O notation is used to describe the efficiency O notation is used to describe the efficiency of a search or sort. The actual time necessary to of a search or sort. The actual time necessary to complete the sort varies according to the speed of complete the sort varies according to the speed of your system.your system. Big Big -- O notation is an approximate O notation is an approximate mathematical formula to determine how many mathematical formula to determine how many operations are necessary to perform the search or operations are necessary to perform the search or sort. The Big sort. The Big -- O notation for the Bubble Sort is O notation for the Bubble Sort is O(nO(n22), because it takes approximately n), because it takes approximately n22 passes to passes to sort the elements.sort the elements.
