Count sort (counting-sort)

Counting sorting is a stable sorting algorithm, which is not a comparative sorting algorithm. There are restrictions on counting sorting: the number of sorting must be n numbers ranging from 0 to K, so counting sorting is not suitable for sorting letters. Time complexity of counting sorting: O (N + k), space complexity: O (k). When k = N, the time complexity can reach O (n ).

 

Counting sorting: Given A nonordered array, first find the maximum number in the array, and then open up an auxiliary array to map the number in the unordered array to the secondary array, calculate the number of occurrences of each number. Then, we continue to get each position from the auxiliary array. The number of the array to be sorted appears several times, and then the corresponding unordered array is assigned to another array.

 

Sorting Process:

 

A: 2 5 3 0 2 3 0 3 C: 2 0 2 3 0 1

Location: 0 1 2 3 4 5 6 7 Location: 0 1 2 4 5

 

C: 2 2 4 7 7 8

Location: 0 1 2 3 4 5

 

B: 3 C: 2 2 4 6 7 8

Location: 0 1 2 3 4 5 6 7 Location: 0 1 2 4 5

 

B: 0 3 C: 1 2 4 6 7 8

Location: 0 1 2 3 4 5 6 7 Location: 0 1 2 4 5

 

B: 0 3 3 C: 1 2 4 5 7 8

Location: 0 1 2 3 4 5 6 7 Location: 0 1 2 4 5

 

B: 0 0 2 2 3 3 5

Location: 0 1 2 3 4 5 6 7

 

Sample Code:

 

# Include <stdio. h> # include <stdlib. h> # include <string. h> void countingsort (INT arraya [], int arrayb [], int N) // sort the Count {int max = 0; For (INT I = 0; I <N; I ++) // find the maximum number in the array {If (arraya [I]> MAX) max = arraya [I];} int * arrayc = (int *) malloc (sizeof (INT) * (MAX + 1); // open up an array space to store the number of occurrences of each number of memset (arrayc, 0, sizeof (INT) * (MAX + 1); // initialize the opened array to 0 for (INT I = 0; I <n; I ++) // calculate the number of occurrences of each number. arrayc [arraya [I] ++; For (INT I = 1; I <= max; I ++) // accumulate the number of times to know the number, there are several to sort the number of arrayc [I] + = arrayc [I-1]; for (INT I = n-1; i> = 0; I --) // sorts data from high to low, ensuring stability {arrayb [arrayc [arraya [I]-1] = arraya [I]; arrayc [arraya [I] --;} Free (arrayc); // release memory} int main () {int N; int arraya [100], arrayb [100]; printf ("Enter the size of the array to be sorted:"); scanf ("% d", & N); printf ("Enter the numbers in the array :"); for (INT I = 0; I <n; I ++) scanf ("% d", & arraya [I]); countingsort (arraya, arrayb, N ); for (INT I = 0; I <n; I ++) printf ("% d", arrayb [I]);}