sort algorithm

Sorting Algorithm
정보컴퓨터공학과 장권
Content
Sorting algorithm? sorting method sorting example summary reference
Sorting
• In computer science, a sorting algorithm is an algorithm that puts elements of a list in a certain order
• 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
1
77
1 2 3
35
4
12
5 101
6
5
Swap77 42 42 77
77>35
"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
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
1 5
4 42
5 77
6 101
Reducing the Number of Comparisons
1 77 1 42 2 42 2 35 3 35 3 12 4 12 4 77 5 101 5 5 6 5 6 101
1 35
1 12 1 12
2 12
2 35 2 5
3 42
3 5 3 35
4 5
An Animated Example
N 8 did_swap true
to_do
index
7
3 Swap
23 45 14 98
1 2 3 4
6 67 33 42
5 6 7 8
An Animated Example
N 8 did_swap true
to_do
index
7
4
23 45 14 98
1 2 3 4
to_do
index
7
2 Swap
23 98 45 14
1 2 3 4
6 67 33 42
5 6 7 8
An Animated Example
N 8 did_swap true
to_do
index
7
2 Swap
23 45 98 14
1 2 3 4
6 67 33 42
5 6 7 8
An Animated Example
Bubble Sort Selection Sort Insertion Sort Merge Sort Shell Sort Heap Sort
Quick Sort Radix Sort Swap Sort
Bubble Sorting
"Bubbling Up" the Largest Element
1
42
2
3
4
12
5 101
6
5
35 77 Swap77 35
77>12
"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
4 42 4 42
5 77
5 77 5 77
6 101
6 101 6 101
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.”
did_swap isoftype Boolean did_swap <- true loop exitif ((to_do = 0) OR NOT(did_swap)) index <- 1 did_swap <- false loop exitif(index > to_do) if(A[index] > A[index + 1]) then Swap(A[index], A[index + 1]) did_swap <- true endif index <- index + 1 endloop to_do <- to_do - 1 endloop
“Bubbling” All the Elements
1 42 1 35 N-1 2 35 2 12 3 12 3 42 4 77 4 5 5 5 5 77 6 101 6 101
1 12
1 12
2 35 2 5 2 12
3 5 3 35 3 35
4 42
4 42
5 77
5 77
6 101
6 101
7
4 Swap
23 45 14 6
1 2 3 4
98 67 33 42
5 6 7 8
An Animated Example
N 8 did_swap true
to_do
index
7
5
23 45 14 6
1 2 3 4
98 67 33 42
5 6 7 8
An Animated Example
N 8 did_swap true
1 77 2 42 3 35 4 12 5 101 6 5

1 5
2 12
3 35
4 42
5 77
6 101
Types of Sorting Algorithms
There are many, many different types of sorting algorithms, but the primary ones are:
6 67 33 42
5 6 7 8
An Animated Example
N 8 did_swap false
to_do
index
7
1 Swap
98 23 45 14
1 2 3 4
6 67 33 42
5 6 7 8
An Animated Example
N 8 did_swap true
to_do
index
1
42
2
35
3
12
4
77
5 101
6
5
No need to swap
101>5
"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
7
1 Swap
23 98 45 14
1 2 3 4
6 67 33 42
5 6 7 8
An Animated Example
N 8 did_swap true
to_do
index
7
2
23 98 45 14
1 2 3 4
6 67 33 42
5 6 7 8
An Animated Example
N 8 did_swap true
An Animated Example
N 8 did_swap true
to_do
index
7
98 23 45 14
1 2 3 4
6 67 33 42
5 6 7 8
An Animated Example
N 8 did_swap false
to_do
index
7
1
98 23 45 14
1 2 3 4
1
42
2
35
3
12
4
77
5 5
6
101
Largest value correctly placed
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