bubble sort · 2013. 11. 6. · bubble sort with thanks to bill leahy, gatech for original slide...

Bubble Sort

With thanks to Bill Leahy, GaTech for original slide deck

Sorting

• Sorting takes an unordered collection and makes it an ordered one.

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Sorting

• Lots of algorithms for sorting– Selection sort (video lecture and textbook)– Insertion sort (textbook)– Bubble sort– Merge sort – Radix sort– ...

"Bubbling Up" the Largest Element

• Traverse a collection of elements (array)– Move from the front to the end– “Bubble” the largest value to the end using

pair-wise comparisons and swapping

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• Traverse a collection of elements– Move from the front to the end– “Bubble” the largest value to the end using


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No need to swap

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Largest value correctly placed

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The “Bubble Up” Algorithm

Given some array, a

for(int i = 0; i < a.length-1; i++) { if(a[i] > a[i+1]) {

int temp = a[i];

a[i] = a[i+1];

a[i+1] = temp; }}

Items of Interest

• Notice that only the largest value is correctly placed

• All other values are still out of order• So we need to repeat this process

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Largest value correctly placed

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Repeat “Bubble Up” How Many Times?

• If we have N elements…

• And if each time we bubble an element, we place it in its correct location…

• Then we repeat the “bubble up” process N – 1 times.

• This guarantees we’ll correctly place all N elements.

“Bubbling” All the Elements

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N -

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Reducing the Number of Comparisons

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Reducing the Number of Comparisons• On the Nth “bubble up”, we only need to

do MAX-N comparisons.

• For example:– This is the 4th “bubble up”– MAX is 6 (total number of elements in array)– Thus we have 2 comparisons to do

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Putting It All Together

public static void Bubblesort(int[] a){ int to_do = a.length-1;

while (to_do != 0) { for(int i = 0; i < to_do; i++) { if(a[i] > a[i+1]) { int temp = a[i];

a[i] = a[i+1];

a[i+1] = temp; } } to_do = to_do - 1} //end method

Inne

r lo

op

Out

er lo

op

Already Sorted Collections?

• What if the collection was already sorted?• What if only a few elements were out of place and

after a couple of “bubble ups,” the collection was sorted?

• We want to be able to detect this and “stop early”!

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101

Using a Boolean “Flag”

• We can use a boolean variable to determine if any swapping occurred during the “bubble up.”

• If no swapping occurred, then we know that the collection is already sorted!

• This boolean “flag” needs to be reset after each “bubble up.”

public static void Bubblesort(int[] a){ int to_do = a.length-1; boolean did_swap = true;

while (to_do != 0 && did_swap) { did_swap = false; for(int i = 0; i < to_do; i++) { if(a[i] > a[i+1]) { did_swap = true; int temp = a[i];

a[i] = a[i+1];

a[i+1] = temp; } } to_do = to_do - 1} //end method

An Animated Example

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An Animated Example

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An Animated Example

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An Animated Example

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An Animated Example

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An Animated Example

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An Animated Example

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After First Pass of Outer Loop

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did_swap true

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The Second “Bubble Up”

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No Swap

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After Second Pass of Outer Loop

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Finished second “Bubble Up”

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The Third “Bubble Up”

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After Third Pass of Outer Loop

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Finished third “Bubble Up”

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The Fourth “Bubble Up”

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No Swap

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After Fourth Pass of Outer Loop

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Finished fourth “Bubble Up”

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The Fifth “Bubble Up”

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After Fifth Pass of Outer Loop

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Finished fifth “Bubble Up”

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Finished “Early”

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did_swap false We didn’t do any swapping,so all of the other elementsmust be correctly placed.

We can “skip” the last twopasses of the outer loop.

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Summary

• “Bubble Up” algorithm will move largest value to its correct location (to the right/end of array)

• Repeat “Bubble Up” until all elements are correctly placed:– Maximum of N-1 times– Can finish early if no swapping occurs

• We reduce the number of elements we compare each time one is correctly placed

Truth in CS Act

• NOBODY EVER USES BUBBLE SORT

• NOBODY

• NOT EVER

• BECAUSE IT IS EXTREMELY INEFFICIENT

LB

Questions?

Bubble Sort Merge SortSortingSlide 3"Bubbling Up" the Largest ElementSlide 5Slide 6Slide 7Slide 8Slide 9Slide 10The “Bubble Up” AlgorithmItems of InterestRepeat “Bubble Up” How Many Times?“Bubbling” All the ElementsReducing the Number of ComparisonsSlide 16Putting It All TogetherSlide 18Already Sorted Collections?Using a Boolean “Flag”Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42After First Pass of Outer LoopThe Second “Bubble Up”Slide 45Slide 46Slide 47Slide 48Slide 49Slide 50Slide 51Slide 52Slide 53Slide 54Slide 55Slide 56Slide 57Slide 58Slide 59After Second Pass of Outer LoopThe Third “Bubble Up”Slide 62Slide 63Slide 64Slide 65Slide 66Slide 67Slide 68Slide 69Slide 70Slide 71Slide 72Slide 73Slide 74After Third Pass of Outer LoopThe Fourth “Bubble Up”Slide 77Slide 78Slide 79Slide 80Slide 81Slide 82Slide 83Slide 84After Fourth Pass of Outer LoopThe Fifth “Bubble Up”Slide 87Slide 88Slide 89Slide 90Slide 91After Fifth Pass of Outer LoopSlide 93SummaryTruth in CS ActQuestions?

bubble sort · 2013. 11. 6. · bubble sort with thanks to bill leahy, gatech for original slide...

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