Sort by Distribution Counting

1
Sort by Distribution Counting

• special case with O(n) performance

2
Distribution Count

• required conditions
• discrete values to sort
• values in small range
• example set
• 8,4,7,5,4,2,8,7,3,7,1,1,6,6,4,6,7,8,7,2,1
• range (1,8)

3
Distribution Count pseudocode

• an array of integers, length n
• tn
• max max(a) min min(a)
• range max min 1
• countrange array of counts
• for (i0 iltn i)
• countai-min
• count0--
• for (j1 jltrange j)
• countj countj-1
• for (in-1 igt0 i--)
• tcountai-min ai
• countai-min--
• for (i0 iltn i)
• ai ti

4
Distribution Count example
14
16
21
21
14
20
17
20
16
19
20
15
16
19
17
14
a
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
8
(21 14 1)
range
counts of each value
3
1
3
2
0
2
3
2
count
0
1
2
3
4
5
6
7
last location of each value in sorted array
2
3
6
8
8
10
13
15
count
0
1
2
3
4
5
6
7
14
14
14
15
16
16
16
17
17
19
19
20
20
20
21
21
t
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
14
14
14
15
16
16
16
17
17
19
19
20
20
20
21
21
a
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
5
Distribution Count performance

• O(max(n,range))
• five for loops
• four based on n
• one based on range
• constant factor is high (number of loops)
• requires space for extra array (t)