Bubble sort

Sorting
• Sorting takes an unordered collection and
makes it an ordered one.
512354277 101
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5 12 35 42 77 101
1 2 3 4 5 6

Exchange/Bubble Sort:
It uses simple algorithm. It sorts by comparing each pair
of adjacent items and swapping them in the order. This
will be repeated until no swaps are needed. The
algorithm got its name from the way smaller elements
"bubble" to the top of the list.
It is not that much efficient, when a list is having more
than a few elements. Among simple sorting algorithms,
algorithms like insertion sort are usually considered as
more efficient.
Bubble sort is little slower compared to other sorting
techniques but it is easy because it deals with only two
elements at a time.

"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
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512354277 101
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Swap42 77

512357742 101
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Swap35 77

512773542 101
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Swap12 77

577123542 101
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No need to swap

577123542 101
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Swap5 101

77123542 5
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101
Largest value correctly placed

Bubble Sort
1. In each pass, we compare adjacent elements and swap them if they are
out of order until the end of the list. By doing so, the 1st
pass ends up
“bubbling up” the largest element to the last position on the list
2. The 2nd pass bubbles up the 2nd
largest, and so on until, after N-1
passes, the list is sorted.
Example:
Pass 1 89 | 45 68 90 29 34 17 Pass 2 45 | 68 89 29 34 17
45 89 | 68 90 29 34 17 45 68 | 89 29 34 17
68 89 | 90 29 34 17 68 89 | 29 34 17
89 90 | 29 34 17 29 89 | 34 17
29 90 | 34 17 34 89 | 17
34 90 | 17 17 89
17 90
45 68 89 29 34 17 90 45 68 29 34 17 89
largest 2nd
largest

The “Bubble Up” Algorithm
index <- 1
last_compare_at <- n – 1
loop
exitif(index > last_compare_at)
if(A[index] > A[index + 1]) then
Swap(A[index], A[index + 1])
endif
index <- index + 1
endloop

No, Swap isn’t built in.
Procedure Swap(a, b isoftype in/out Num)
t isoftype Num
t <- a
a <- b
b <- t
endprocedure // Swap
LB

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
77123542 5
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101
Largest value correctly placed

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
77123542 5
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5421235 77
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101
4253512 77
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101
4235512 77
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101
4235125 77
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101
N-1

Reducing the Number of Comparisons
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5
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5421235 77
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4253512 77
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101
4235512 77
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101

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
– Thus we have 2 comparisons to do
4253512 77
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101

N is … // Size of Array
Arr_Type definesa Array[1..N] of Num
Procedure Swap(n1, n2 isoftype in/out Num)
temp isoftype Num
temp <- n1
n1 <- n2
n2 <- temp
endprocedure // Swap

procedure Bubblesort(A isoftype in/out Arr_Type)
to_do, index isoftype Num
to_do <- N – 1
loop
exitif(to_do = 0)
index <- 1
loop
exitif(index > to_do)
if(A[index] > A[index + 1]) then
Swap(A[index], A[index + 1])
endif
index <- index + 1
endloop
to_do <- to_do - 1
endloop
endprocedure // Bubblesort
Innerloop
Outerloop

Summary
• “Bubble Up” algorithm will move largest
value to its correct location (to the right)
• Repeat “Bubble Up” until all elements are
correctly placed:
– Maximum of N-1 times
• We reduce the number of elements we
compare each time one is correctly placed

Bubble sort

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