What does the cardinality and heap count mean for cardinality sorting

The sorting methods described above are all "comparative" sorting methods, that is, each time you sort, you compare the size of the entire key value to sort.

The "radix sort" introduced here belongs to the "distribution sort", also known as the "bucket sort" or bin sort, as the name suggests, it is through the partial information of the key value, the elements to be sorted are allocated to some "buckets", so as to achieve the role of sorting, the cardinal sorting method is a stable sorting, and its time complexity is o (nlog(r) m), where r is the base number taken and m is the heap number, and in some cases, the cardinal sorting method is more efficient than other comparative sorting methods.

This one is more complicated to say, so let's use the decimal system for n.

For example, I think that n is the number of numbers involved in the sorting, and the cardinal number r is 10 (decimal system, each digit takes the value of 0 9, this is the cardinal sorting.

where the heap number m is the maximum number of digits in these numbers involved in sorting, e.g. , then m=4, which is up to 4 digits.

Cardinal sorting (radix sort) belongs to "distributive sorting", also known as "bucket method" or bin sort, as the name suggests, it is through the key value of the part of the information, the elements to be sorted are allocated to some "buckets", in order to achieve the role of sorting, the cardinal sorting method is a stable sorting, its time complexity is o (nlog(r)m), where r is the cardinality taken, and m is the heap number, at some times, the efficiency of the cardinal sorting method is higher than other stability sorting methods.

Cardinality sorting is suitable for sorting data with unknown overall weights, such as time and strings.

The most significant digit first method, referred to as the msd method: first sort and group according to k1, record the banquet in the same group, the key code k1 is equal, and then divide each group into subgroups according to k2 sorting, and then continue to sort and group the key code after this, until each subgroup is sorted according to the most minor key code kd. The groups are then joined together to obtain an ordered sequence.

As the name suggests, cardinal sorting belongs to the "distributive friend sorting", also known as the "bucket method", which is to assign the elements to be sorted to some "buckets" through the partial information of the key value, so as to achieve the function of sorting.

Cardinality sorting is a stable sorting, and its time complexity is o (nlog(r)m), where r is the cardinality taken, and m is the heap number, and in some cases, the efficiency of the cardinality sorting method is higher than that of other stability sorting methods.

How it works: The invention of cardinal sorting can be traced back to 1887 when Hermann Hollerley contributed to the tabulation machine for punched cards.

It is achieved by unifying all the values to be compared (positive integers) into the same digit length, with zeros in front of the numbers with shorter digits. Then, starting with the lowest bit, sort them one at a time.

In this way, from the lowest bit of sorting all the way to the highest bit of sorting, the sequence becomes an ordered sequence of delays.

Cardinality sorting can be done either lsd (least significant digital) or msd (most significant digital), where lsd is sorted from the rightmost of the key value, while msd, on the other hand, starts from the leftmost of the key.

Scenario: Employees are sorted by salary, and those with the same salary are sorted by age.

Try: Sort by salary (ascending) and then by age (ascending) Try: Sort by age first, then by salary.

Summary: Multi-keyword sorting starts with low keywords first, and all keyword sorting should be guaranteed to be stable ordering.

In ascending order of ten digits, the same ten digits are in ascending order of single digits. YesMulti-keyword sorting, first Tieqing is sorted according to the single digit stability, and then sorted according to the ten digit stability.

Based on the two-digit example, one can be ranked first, then ten, and then hundred.

The maximum number of digits k, the number of digits that need to be sorted n, and the complexity o(kn) are not supported by decimal and string sorting. If you know the file to hold a negative number, you can consider finding the smallest negative number, and then sort the absolute value of all numbers plus the smallest negative number to become a positive number, and then subtract the absolute value of the smallest negative number uniformly when outputing.

Cardinality: Mathematically, cardinal number is a concept in set theory that describes the size of any set. The set of two elements that can be cavified one-to-one is called a mutual equivalence set.

For example, a set of 3 people and a set of 3 horses can establish a one-to-one correspondence, which is two equal sets.

Ordinal number: one of the basic concepts of set theory, which is used in everyday life.

The first and second degrees indicate the generalization of the number of the second touching order. The concept of ordinal numbers is based on the concept of a good order set, and a good order set is a special case of partial order set and full order set.

As the name suggests, it is through the partial information of the key value, the elements to be sorted are allocated to some "buckets", so as to achieve the role of sorting, the cardinal sorting method is a stable sorting, and its time complexity is o (nlog(r)m), where r is the cardinality taken, m is the number of heaps, and in some cases, the cardinal sorting method is more efficient than other stability sorting methods.

Cardinality sorting is to sort the data by cardinality.

You give a decimal number, and the base number is 10.

They are grouped by the values of the cardinal bits.

Group from 0 to 9 from "single digit".

Transcription: 51, 31, 23, 45, 16, 38, 18, 9 and then 0-9 on the "ten".

89 is transcribed in order to 9, 16, 18, 23, 31, 38, 45, 51.

Sorting with bubbles is the easiest, eg. Input example:

Output example: include

int main()

for(i=0;ia[j+1])

for(i=0;iprintf("%d ",a[i]);

printf("%d ",a[n-1]);

return 0;}