Internal sorting-directly insert sorting

A sorting middleware has been developed recently, so we need to study sorting.AlgorithmAnd focuses on implementation.

The algorithm language is C language, and the Environment is vs2010 integrated environment.

Data type to be record:

 //  Data  # Define Maxsize 20 Typedef  Int  Keytype; typedef  Int  Infotype; typedef  Struct  {Keytype key;  // Keyword Infotype otherinfo; //  Other data items } Redtype; //  Record type Typedef Struct  {Redtype R [maxsize + 1 ]; //  R [0] idle or used as a sentry Unit      Int Length; //  Sequence table length } Sqlist;//  Sequence Table type 

 

 

Simplest insert sorting

Sort by insert directly:Insert a record to an ordered table that has already been sorted to obtain a new ordered table with the number of records increasing by 1..

The theory of direct insertion sorting is relatively simple, and the algorithm is also relatively simple.

 //  Insert sort  Void Insertsort (sqlist & L ){  //  Directly insert and sort the sequence table L      For ( Int I = 2 ; I <= L. length; I ++ ){  If (LT (L. R [I]. Key, L. R [I- 1  ]. Key) {L. R [  0 ] = L. R [I]; L. R [I] = L. R [I- 1  ];}  Int J = I- 2  ;  For (; LT (L. R [ 0 ]. Key, L. R [J]. Key); j -- ) {L. R [J + 1 ] = L. R [J];} l. R [J + 1 ] = L. R [ 0  ] ;}} 

Function LT (INT, INT) is the content of comparison. Here is an example of integer size comparison based on data types.

BoolLT (IntX,IntY ){If(X <Y)Return True;ElseReturn False;}
 

Test

In order to be tested, the following is a complete testCode

Insert Sorting Algorithm instance

 // Testinsersort. cpp: defines console applications.Program.  //  # Include  "  Stdafx. h  "  # Include  "  Stdio. h  "  //  Data  # Define Maxsize 20 Typedef  Int  Keytype; typedef Int  Infotype; typedef  Struct  {Keytype key;  //  Keyword Infotype otherinfo; //  Other data items } Redtype; //  Record type Typedef Struct  {Redtype R [maxsize + 1 ]; // R [0] idle or used as a sentry Unit      Int Length; //  Sequence table length } Sqlist; //  Sequence Table type  Bool LT ( Int X, Int  Y ){  If (X < Y)  Return   True  ; Else          Return   False  ;}  //  Insert sort  Void Insertsort (sqlist & L ){  //  Directly insert and sort the sequence table L      For ( Int I = 2 ; I <= L. length; I ++ ){  If (LT (L. R [I]. Key, L. R [I-1  ]. Key) {L. R [  0 ] = L. R [I]; L. R [I] = L. R [I- 1  ];}  Int J = I- 2  ;  For (; LT (L. R [ 0 ]. Key, L. R [J]. Key); j -- ) {L. R [J + 1 ] =L. R [J];} l. R [J + 1 ] = L. R [ 0  ] ;}}  Int _ Tmain ( Int Argc, _ tchar * Argv []) {sqlist L; scanf (  "  % D  " ,& L. Length );  For ( Int I = 1 ; I <= L. length; I ++) {Scanf (  "  % D  " ,& L. R [I]. Key);} insertsort (L );  For ( Int I = 1 ; I <= L. length; I ++ ) {Printf (  "  % D \ t  "  , L. R [I]. Key );}  Return   0 ;} 

Efficiency of insert sorting

Space:S (1)Insert and sort directly requires only one auxiliary space.

Time: the basic job of sorting, 1. Compare the size of the keyword; 2. Move the record

Best case: when the record is already ordered and the sequence is the desired order, the second for loop will not be run, and the overall space complexity is O (n)

Worst case: when the record is the opposite of the sequence to be obtained, the second for loop is executed most frequently, compared to (2, 3 ,..., n) times, that is, (n + 2) (n-1)/2. The number of moves is (2, 3 ,..., n, N + 1), that is, (n + 4) (n-1)/2.

The average number of times is about N2/4, that is, the time complexity isO (n2)

 

 

References[1] Yan Weimin Wu Weimin data structure (C Language) Beijing: Tsinghua University Press, 1997.4