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Sorting
Chapter 9
(Spring 2016, CSUS)
Bubble Sort
Chapter 9.1
Often, computers needs to sort a list – to
put it in specific order
Examples:
• sorting scores by highest to lowest
• sorting filenames in alphabetical order
• sorting students by their student-id
This can be done for the benefit of the user
or, most often, for efficiency
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Sorting
The bubble sort is one of the
least efficient algorithms
…but it is easy to understand
Basic approach
• "lighter" elements “bubble up”
to the top of the array
• "heavier" items sink to the
bottom
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Bubble Sort
Consists of two For Loops
Outer loop runs from the first to the last
Inner loop …
• runs from the second element to the last
• it checks every two neighbor elements, if the
they are out of order, it swaps them
• so, the smallest element moves up the array
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How It Works
// How to swap items at indexes i and j
Declare Integer temp
Set temp = array[i]
Set array[i] = array[j]
Set array[j] = temp
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Swap code
2
For outer = 0 to size-1
For inner = 1 to size-1
If A[inner-1] > A[inner]
//swap A[inner-1], A[inner]
End If
End For
End For
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The Bubble Sort
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Bubble Sort Example
0
array
1
2
3
4
73
42
11
58
5
Outer Loop
Inner Loop
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Bubble Sort Example
0
array
1
2
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4
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
3
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
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Bubble Sort Example
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
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Bubble Sort Example
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Outer Loop
Inner Loop
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Bubble Sort Example
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
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Bubble Sort Example
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop
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Bubble Sort Example
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array
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Outer Loop
Inner Loop Heavier items drop rapidly to bottom (like
stones in water)
Lighter items bubble up slowly
The algorithm is hilariously inefficient
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Notice…
7
Selection Sort
Chapter 9.2
The Selection Sort is a similar
to the Bubble Sort
However…
• rather than "bubble up" smaller
items, it scans the entire array
• it finds the smallest element
• only then does it swap the
values
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Selection Sort
Like the Bubble Sort, it consists of two For
Loops – one outer and one inner
Outer loop runs from the first to the last
Inner loop …
• starts at the position of the outer loop
• scans down and finds the smallest value
Then, after the scan, do a single swap
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Selection Sort
For outer = 0 to size-1
Set smallest = outer;
For inner = outer+1 to size-1
If array[inner] < array[smallest]
Set smallest = inner
End If
End For
//swap array[outer] and array[smallest]
End For
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The Selection Sort
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Selection Sort Example
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array
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Outer Loop
Inner Loop
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Selection Sort Example
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Outer Loop
Inner Loop
8
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Selection Sort Example
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array
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Outer Loop
Inner Loop
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Selection Sort Example
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array
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Outer Loop
Inner Loop
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Selection Sort Example
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array
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Outer Loop
Inner Loop
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Selection Sort Example
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Outer Loop
Inner Loop 73
5
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Selection Sort Example
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array
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Outer Loop
Inner Loop
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Selection Sort Example
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array
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Outer Loop
Inner Loop
9
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Selection Sort Example
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array
1
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Outer Loop
Inner Loop
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Selection Sort Example
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array
1
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Outer Loop
Inner Loop
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Selection Sort Example
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array
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73
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Outer Loop
Inner Loop
42
11
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Selection Sort Example
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array
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Outer Loop
Inner Loop
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Selection Sort Example
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array
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Outer Loop
Inner Loop
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Selection Sort Example
0
array
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Outer Loop
Inner Loop
10
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Selection Sort Example
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array
1
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42
58
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Outer Loop
Inner Loop
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Selection Sort Example
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array
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Outer Loop
Inner Loop
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Selection Sort Example
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array
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Outer Loop
Inner Loop Insertion Sort
Chapter 9.3
The Insertion Sort is sorting
algorithm with several
advantages over the Bubble
and Selection
Often, it is compared to
sorting a deck of cards
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Insertion Sort
Let’s say were asked to sort a
row of cards… (and you start
sorting from the left)
You will find a card, move it,
and shift the rest of the cards
to the right
So, you build a sorted list a
bit at a time – on the left side
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Deck of Cards
11
Consists of two loops – inner and outer
A sorted list is constructed above the outer
Outer loop moves down the list
• current array value is temporarily removed
(copied) from the array
• moves down
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How it Works
Inner loop
• moves up from the current outer loop position
• if the cell, being looked at, is larger than the
saved value, it is moved down
• so, the "cards" shift to make room for the saved
cards proper position
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How it Works
For i = 1 to count-1
Set value = array[i]
Set j = i - 1;
While j >= 0 && array[j] > value
array[j + 1] = array[j]
Set j = j - 1
End While
Set array[j + 1] = value
End For
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The Insertion Sort
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Insertion Sort Example
0
array
1
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73
11
58
5
value
42
Outer Loop
Inner Loop
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Insertion Sort Example
0
array
1
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4
73
11
58
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value
42
Outer Loop
Inner Loop
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Insertion Sort Example
0
array
1
2
3
4
73
11
58
5
value
42
Outer Loop
Inner Loop
12
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Insertion Sort Example
0
array
1
2
3
4
73
58
5
value
42
11
Outer Loop
Inner Loop
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Insertion Sort Example
0
array
1
2
3
4
73
11
58
5
value
42
11
Outer Loop
Inner Loop
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Insertion Sort Example
0
array
1
2
3
4
73
11
58
5
value
42
11
Outer Loop
Inner Loop
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Insertion Sort Example
0
array
1
2
3
4
73
11
58
5
value
42
11
Outer Loop
Inner Loop
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Insertion Sort Example
0
array
1
2
3
4
73
5
value
42
11
58
Outer Loop
Inner Loop
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Insertion Sort Example
0
array
1
2
3
4
73
5
value
42
11
58
Outer Loop
Inner Loop
13
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Insertion Sort Example
0
array
1
2
3
4
73
5
value
42
11
58
Outer Loop
Inner Loop
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Insertion Sort Example
0
array
1
2
3
4
73
5
value
42
11
58
Outer Loop
Inner Loop
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Insertion Sort Example
0
array
1
2
3
4
73
Outer Loop
Inner Loop
value
42
11
58
5
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Insertion Sort Example
0
array
1
2
3
4
73value
42
11
58
5
Outer Loop
Inner Loop
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Insertion Sort Example
0
array
1
2
3
4 73
value
42
11
58
5
Outer Loop
Inner Loop
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Insertion Sort Example
0
array
1
2
3
4 73
value
42
11
58
5
Outer Loop
Inner Loop
14
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Insertion Sort Example
0
array
1
2
3
4 73
value
42
11
58
5
Outer Loop
Inner Loop
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Insertion Sort Example
0
array
1
2
3
4 73
value
42
11
58
5
Outer Loop
Inner Loop
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Insertion Sort Example
0
array
1
2
3
4 73
value
42
11
58
5
Outer Loop
Inner Loop
Binary Search
Chapter 9.4
A binary search is an fast and
efficient way to search an
array
Algorithm works like the
classic "secret number game"
Requires that the array is
sorted before the search
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Binary Searching
Starts knowing the max & min values
• in the case of arrays, this is the min and max index
• in the number game, it is the min and max value
Algorithm continues
• it looks at the midpoint between the first and last
• if the value > target, the max is set to the midpoint
• if the value < target, the min is set to the midpoint
• this eliminates half of the numbers each iteration
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How it Works
15
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Binary Example: Find 30
3 85 12 23 30 35 42 47 52 65 77 81
Min Max
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Binary Example: Find 30
3 85 12 23 30 35 42 47 52 65 77 81
Min Max
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Binary Example: Find 30
3 85 12 23 30 35 42 47 52 65 77 81
Min Max
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Binary Example: Find 30
3 85 12 23 30 35 42 47 52 65 77 81
Min Max
The binary search is incredibly efficient
and absolutely necessary for large arrays
Any item can be found only log2(n)
searches!
However, since array must be sorted,
sorting algorithms are equally vital
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Benefits
Array Size Sequential Search Binary Search
10 10 4
100 100 7
1,000 1,000 10
10,000 10,000 14
100,000 100,000 17
1,000,000 1,000,000 20
10,000,000 10,000,000 24
100,000,000 100,000,000 27
1,000,000,000 1,000,000,000 30
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Maximum # of Searches
