Two-point insertion sort

Two-point insertion sorting algorithm

　　first, the basic idea: derived from the binary search, assuming that the table elements are in ascending order, the keyword to be inserted and the middle position of the table record keywords and comparison. If it is less than the keyword, the element is inserted into the subsequent child table, and conversely, if it is greater than the keyword, the element is inserted in the preceding child table. Iterate until all the keywords are inserted into the table.

　　

　　

　　Second, C language code:

　　

1#include <stdio.h>2#include <stdlib.h>3 4 //Direct Insert ordering for r[0...n-1] ascending order5 voidBinaryinsertsort (RecType r[],intN)6 {7     inti;8     intJ;9     intLow ;Ten     intHigh ; One     intmid; A RecType tmp; -      -      for(i =1; I < n; i++) { theTMP =R[i]; -Low =0;  -High = i-1;  -          +         //find the position of an orderly insert in R[low...high] -          while(Low <=High ) { +Mid = (low + high)/2; A             if(Tmp.key <R[mid].key) { atHigh = mid-1;//left half area -}Else { -Low = mid +1;//Right Half area -             } -         } -          in         //record backward, high means that each time it is compared from right to left in an ordered interval -          for(j = i-1; J >= High +1; j--) { tor[j+1] =R[j]; +         }  -r[high+1] = tmp;//Inserting Records the     } *} 

Three, algorithm analysis

　　　　Time complexity: By the algorithm code is known, the binary insertion sort consists of two loops, for n sort records, the outer layer must undergo n-1 cycles, in each order to find the position of the insertion point <= high when the number of cycles of the tree Logi, wherein the 0≦i≦n-1, while the record of the movement of the second The number aspect is the same as the direct insertion sort, so for the binary insertion sort:

The minimum number of times the keyword comparison and record movement is (n-1) Σlogi, where 0≦i≦n-1 the time complexity of the algorithm is O (n).

The maximum number of keyword comparisons and records moved is (n-1) Σ (I+logi), where 0≦i≦n-1, the algorithm's time complexity is O (n²).

The average comparison of keywords and the number of records moved is [(n-1) Σ (I+logi)]/2, where 0≦i≦n-1, the time complexity of the algorithm is O (n²).

Spatial complexity: The algorithm code shows that the extra space required is only one TMP variable, so the spatial complexity of the direct insertion sorting algorithm is O (1).

Iv. thinking

Binary insertion sort does the number of records move the same as the direct insert sort after a traversal of the insert sort?

Two-point insertion sort