Counting sorting and radix ordering of common sorting algorithms

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1. Counting sort

As the name implies, the data in the sorted array is counted and then sorted according to the statistics, for example:

Array to sort:

A[] = {100, 123, 112, 123, 201, 123, 112, 156, 156, 178, 185, 156, 123, 112}

First take the maximum and minimum values in the array (this goes without saying)

Maximum value:201 min:

So the array has a value range of 201-100 + 1 = 102

Open an array of size 102 count[102] and initialize all elements to 0

Iterate over the array again to a[i-100] as the subscript for the array count, adding 1 to the item

The resulting count array should be (here the count element is 0 items will not appear, too many)

count[0] = 1

count[12] = 3

count[23] = 4

count[56] = 3

count[78] = 1

count[85] = 1

count[101] = 1

The rest of the elements are 0.

The count array is traversed, and each element corresponds to a write back to the A array, at which point the array a should be

A = {100,112,112,112,123,123,123,123,156,156,156,178,185,201}

As you can see, the array a is already sorted.

The code is as follows:

void countsort (int* a, size_t n)   //count Sort { ASSERT (a);int min = a[0];int max = a[0];for  (int i = 1;  i < n; ++i) {if  (A[i] > max) max = a[i];else if  (a [I] < min) min = a[i];} int countnum = max - min + 1;int* countarray = new int[ Countnum];memset (countarray, 0, sizeof (int) * (countnum));for  (int i = 0; i  < n; ++i) {++countarray[a[i] - min];} int index = 0;for  (Int i = 0; i < countnum; ++i)   //writeback array {while  (countarray[i]--) {a[index++] = i + min;}} Delete[] countarray;} 

As you can see, the counting sort has a lot of limitations, and it is suitable for sorting data collections in a relatively centralized range of data.

2. Base sorting

Let's look at an example of how the cardinality sort is sorted.

With an initial sequence of: R {0, 123, 543, 187,, 2, one, and

We know that in any Arab number, the cardinality of its various digits is expressed in 0~9.

So we might as well think of 0~9 as 10 barrels.

We classify the number of single digits of a sequence and divide it into a specified bucket. For example: r[0] = 50, single digit is 0, this number is stored in the bucket numbered 0.

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After sorting, we take all the numbers out of each bucket, sequentially, in order from number 0 to number 9.

At this point, the resulting sequence is a sequence of incremental trends on a single digit.

Sort by single digit: {50, 30, 0, 100, 11, 2, 123, 543, 187, 49}

Then follow the 10-bit order ( Note: No 10-bit number is treated as 10-bit 0 )

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Sort by 10-digit number:  {0, 2, one, 123, 543, 187}

Then follow the order of the Hundred ( > Note: There are no hundred numbers according to the Hundred 0 processing )

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follow Number of hundred sorts:  {0, 2, one, a, 123, 187, 543}

Sort complete 650) this.width=650; "src=" Http://img.baidu.com/hi/jx2/j_0058.gif "alt=" J_0058.gif "/>650" this.width=650; " Src= "Http://img.baidu.com/hi/jx2/j_0058.gif" style= "Color:rgb (0,112,192); font-family: ' Microsoft Jas Black ', ' Microsoft Yahei '; Font-size:24px;line-height:24px;white-space:normal, "alt=" J_0058.gif "/>650" this.width=650; "src=" http:/ Img.baidu.com/hi/jx2/j_0058.gif "style=" Color:rgb (0,112,192); font-family: ' Microsoft Jas Black ', ' Microsoft Yahei '; font-size:24px ; line-height:24px;white-space:normal; "alt=" J_0058.gif "/>650) this.width=650; src=" http://img.baidu.com/hi/ Jx2/j_0058.gif "style=" Color:rgb (0,112,192); font-family: ' Microsoft Jas Black ', ' Microsoft Yahei '; font-size:24px;line-height:24px ; white-space:normal; "alt=" J_0058.gif "/>650" this.width=650; "src=" Http://img.baidu.com/hi/jx2/j_0058.gif " Style= "Color:rgb (0,112,192); font-family: ' Microsoft Jas Black ', ' Microsoft Yahei '; Font-size:24px;line-height:24px;white-space: Normal, "alt=" J_0058.gif "/>650" this.width=650; src= "Http://img.baidu.com/hi/jx2/j_0058.gif" style= "COlor:rgb (0,112,192); font-family: ' Microsoft Jas Black ', ' Microsoft Yahei '; font-size:24px;line-height:24px;white-space:normal; " alt= "J_0058.gif"/>

code as follows:

Int getmaxbit (int* a, size_t n)   //gets the most digits in the array {assert (a); int bitnum =  1;int tmpData = 10;for  (Int i = 0; i < n; ++i) {while  (Tmpdata <= a[i]) {++bitnum;tmpdata *= 10;}} Return bitnum;} Void radixsort (int* a, size_t n)   //radix sort {assert (a);int maxbit =  Getmaxbit (a, n); int digit = 1;int* tmp = new int[n];int countbit[ 10];  //count int startbit[10];  //start position for  (int i = 1; i  <= maxbit; ++i) {memset (countbit, 0, sizeof (int) * 10);for  (int i =  0; i < n; ++i) {int bit =  (a[i]/digit)%10;  //first people, in 10 hundred ... ++countbit[bit];} memset (startbit, 0, sizeof (int) * 10);startbit[0] = 0;for  (int i =  1; i&Nbsp;< 10; ++i) {startbit[i] = startbit[i - 1] + countbit[i - &NBSP;1];} for  (int i = 0; i < n; ++i)   //deposit to temporary array {Int index  = startbit[(A[i]/digit)%10]++;tmp[index] = a[i];} for  (int i = 0; i < n; ++i)   //write back to original array {a[i] = tmp [i];} digit *= 10;} Delete[] tmp;}

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Counting sorting and radix ordering of common sorting algorithms