Bubblesort and permutations. Mike Atkinson. Michael Albert, Mathilde Bouvel,
Anders Claesson, Mark Dukes. New Zealand Mathematical Society Colloquium.
Bubble sort (1). • An easy to understand and implement algorithm. • Keep
passing through the input and exchange adjacent elements which are unsorted.
[Fine, Wilf, 1965] see Algebraic Combinatorics on Words [Lothaire, 2002] ...... 310
pages. [3] See also http://monge.univ-mlv.fr/ mac/REC/text-algorithms.pdf.
Buckyball from 120 of. Tom Hull's PHiZZ unit. Fullerene from 90 of. Robert
Neale's penultimate unit. Large icosahedron from. 270 Sonobe units.
Jeet Kune Do encourages development of a uniquely ... In comparison with JKD,
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Patrick Fricker. Example: Feature Tree Imposed. Mutschler, E., G. Geisslinger,
H.K. Kroemer, and M. Schäfer-. Korting, Mutschler Arzneimittelwirkungen. 8 ed.
8 Aug 2013 ... new york times | square dance scottish country | dancing clubs | melbourne tony
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Theorem. The modal logic KD4+KD4 is sound and complete w.r.t. the bi-
topological rational plane QxQ with the horizontal and vertical topologies.
Algorithms and Computation in. Signal Processing special topic course 18-799B
spring 2005. 9th Lecture Feb. 8, 2005. Instructor: Markus Pueschel. TA: Srinivas ...
Stephan Dürr (Jülich, BMW). Andreas Jüttner (Mainz, RBC/UKQCD). Laurent
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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. – .
Bubble Sort
With thanks to Bill Leahy, GaTech for original slide deck
Sorting • Sorting takes an unordered collection and makes it an ordered one. 0
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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 0
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"Bubbling Up" the Largest Element • Traverse a collection of elements – Move from the front to the end – “Bubble” the largest value to the end using pair-wise comparisons and swapping 0
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"Bubbling Up" the Largest Element • Traverse a collection of elements – Move from the front to the end – “Bubble” the largest value to the end using pair-wise comparisons and swapping 0 42
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"Bubbling Up" the Largest Element • Traverse a collection of elements – Move from the front to the end – “Bubble” the largest value to the end using pair-wise comparisons and swapping 0
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"Bubbling Up" the Largest Element • Traverse a collection of elements – Move from the front to the end – “Bubble” the largest value to the end using pair-wise comparisons and swapping 0
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No need to swap
"Bubbling Up" the Largest Element • Traverse a collection of elements – Move from the front to the end – “Bubble” the largest value to the end using pair-wise comparisons and swapping 0
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"Bubbling Up" the Largest Element • Traverse a collection of elements – Move from the front to the end – “Bubble” the largest value to the end using pair-wise comparisons and swapping 0
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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 0
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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.
N-1
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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 0 12
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Putting It All Together
to_do = to_do - 1 } //end method
Outer loop
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; } }
Inner loop
public static void Bubblesort(int[] a){ int to_do = a.length-1;
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”! 0 5
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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 did_swap false to_do 7 i
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An Animated Example did_swap to_do i
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An Animated Example did_swap to_do i
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An Animated Example did_swap to_do i
true 7 1 Swap 23 45 98 14 0
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An Animated Example did_swap to_do i
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An Animated Example did_swap to_do i
true 7 2 Swap 23 45 98 14 0
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An Animated Example did_swap to_do i
true 7 2 Swap 23 45 14 98 0
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An Animated Example did_swap to_do i
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An Animated Example did_swap to_do i
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An Animated Example did_swap to_do i
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true 7 Finished first “Bubble Up”
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The Second “Bubble Up” did_swap to_do i
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After Second Pass of Outer Loop did_swap to_do i
true 6 Finished second “Bubble Up”
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true 5 1 Swap 14 23 6 0
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true 5 1 Swap 14 6 0
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The Third “Bubble Up” did_swap to_do i
true 5 2
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The Third “Bubble Up” did_swap to_do i
true 5 2 No Swap 14 6 0
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The Third “Bubble Up” did_swap to_do i
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The Third “Bubble Up” did_swap to_do i
true 5 3 Swap 14 6 0
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The Third “Bubble Up” did_swap to_do i
true 5 4
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The Third “Bubble Up” did_swap to_do i
true 5 4 Swap 14 6 0
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true 5 4 Swap 14 6 0
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After Third Pass of Outer Loop did_swap to_do i
true 5 Finished third “Bubble Up”
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The Fourth “Bubble Up” did_swap false to_do 4 i
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The Fourth “Bubble Up” did_swap false to_do 4 i
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The Fourth “Bubble Up” did_swap to_do i
true 4 1
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The Fourth “Bubble Up” did_swap to_do i
true 4 1 No Swap 6 0
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The Fourth “Bubble Up” did_swap to_do i
true 4 2
6 0
14 23 33 42 45 67 98 1
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The Fourth “Bubble Up” did_swap to_do i
true 4 2 No Swap 6 0
14 23 33 42 45 67 98 1
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The Fourth “Bubble Up” did_swap to_do i
true 4 3
6 0
14 23 33 42 45 67 98 1
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true 4 3 No Swap 6 0
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After Fourth Pass of Outer Loop did_swap to_do i
true 4 Finished fourth “Bubble Up”
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6 0
14 23 33 42 45 67 98 1
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The Fifth “Bubble Up” did_swap false to_do 3 i
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The Fifth “Bubble Up” did_swap false to_do 3 i
0 No Swap 6 0
14 23 33 42 45 67 98 1
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The Fifth “Bubble Up” did_swap false to_do 3 i
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6 0
14 23 33 42 45 67 98 1
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The Fifth “Bubble Up” did_swap false to_do 3 i
1 No Swap 6 0
14 23 33 42 45 67 98 1
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The Fifth “Bubble Up” did_swap false to_do 3 i
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6 0
14 23 33 42 45 67 98 1
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The Fifth “Bubble Up” did_swap false to_do 3 i
2 No Swap 6 0
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After Fifth Pass of Outer Loop did_swap false to_do 3 i
Finished fifth “Bubble Up”
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Finished “Early” did_swap false to_do 3 i
We didn’t do any swapping, so all of the other elements must be correctly placed.
3
We can “skip” the last two passes of the outer loop.
6 0
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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
LB
Truth in CS Act • NOBODY EVER USES BUBBLE SORT • NOBODY • NOT EVER • BECAUSE IT IS EXTREMELY INEFFICIENT
