Insert and Merge sort

Introduction to the algorithm: The main concern is the performance of the program, speed is very eager!!!

The sorting algorithm is the classical algorithm

1. Insert Sort

(1), Algorithm model

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(2), code implementation

#include <stdio.h>void insertsort (Int *a, int count); Void showarray (Int *a,  int count); Void showarray (int *a, int count) {    int i ;         for (i = 0; i < count; i++) {         printf ("%d ",  a[i]);    }     printf ("\ n");  }void insertsort (Int *a, int count) {     int i;    int j;    int n;     int tmp;    for (i = 1; i < count; i++) {         tmp = a[i];         for (j = 0; a[i]>a[j] && j<i; j++) {             ;        }         if (i != j) {            for (n  = i; n > j; n--) {                 a[n] = a[n-1];        &NBSP;&NBSP;&NBSP;&NBSP;&NBSP;}&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;A[J]  = tmp;        }    }}void main ( void) {    int a[] = {2, 5, 7, 1, 11, 0, 6,  9};    int count = sizeof (a)/sizeof (int);     printf ("Output the following:  before sorting");     showarray (A, count);     insertsort (A ,  count);     printf ("Sort output as follows: ");     showarray (A, count);} 

(3), results

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(4), algorithm analysis

Insert Sort worst case: all elements in the array are in reverse order;

Time complexity:O (n^2);

2. Merge sort

(1), the algorithm thought:

I, if n = 1; Done

II, recursive sequencing, divided into 2 parts, in [0, N/2] and [N/2, N]

III. Sort the 2-part merge

(2), Core code implementation

#include <stdio.h> #include <malloc.h>void mergersort (int *a1, int *a2, int &NBSP;**A3,&NBSP;INT&NBSP;COUNT1,&NBSP;INT&NBSP;COUNT2,&NBSP;INT&NBSP;*COUNT3); Void showArray (int * A3, int count); Void showarray (int *a3, int count) {    int  i;    for (i = 0; i < count; i++) {         printf ("%d ",  a3[i]);    }     printf ("\ n");} Void mergersort (int *a1, int *a2, int **a3, int count1, int  COUNT2,&NBSP;INT&NBSP;*COUNT3) {    int count;    int i  = 0;    int j = 0;    int n = 0;     count = *count3 = count1 + count2;     *a3 =  (int *) malloc (sizeof (int)  * count);     //below are < Because the length of the array is passed over;     while (I < count1 && j < count2 ) {        if (a1[i] < a2[j]) {              (*A3) [n++] = a1[i];             i++;        }else if (A1 [I] == a2[j]) {             (*A3) [n++]  = a1[i];             (*A3) [n++] =  a2[j];            i++;             j++;        } else{       //just wrote program else (A1[i] > a2[j]), and later found that the Else statement is not conditional!!!              (*A3) [n++] = a2[j];             j++;         }    }    while (I&NBSP;&LT;&NBSP;COUNT1) {          (*A3) [n++] = a1[i];         i++;    }    while (J < count2) {          (*A3) [n++] = a2[j];        j++ ;    }}/*  Merge Sort core algorithm is: the order of the 2 arrays have been sorted into the final sorting process; */void main (void) {     int a1[] = {1, 3, 5, 7};    int a2[] =  {0,&NBSP;2,&NBSP;4,&NBSP;6,&NBSP;8,&NBSP;9,&NBSP;10};&NBSP;&NBSP;&NBSP;&NBsp;int count1 = sizeof (A1)/sizeof (int);    int count2 =  sizeof (A2)/sizeof (int);    int *a3 = null;    int  Count3 = 0;    mergersort (A1, a2, &a3, count1, count2, &NBSP;&AMP;COUNT3);     showarray (A3,&NBSP;COUNT3);     free (A3);}

(3), results

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(4), complete code implementation

#include <stdio.h> #include <malloc.h>void mergesort (int *a, int low, int  high); Void merge (Int *a, int low, int mid, int high);void  Merge (Int *a, int low, int mid, int high) {    int  I = low;    int j = mid+1;    int n  = 0;    int *a2;    a2 =  (int *) malloc ( sizeof (int)  *  (high-low+1))     if (a2 == null) {         return;    }    //The following are <=, because all the passing is subscript;     while (I <= mid && j <= high) {         if (A[i] < a[j]) {             a2[n++] = a[i];            i++;         }else if (A[i] == a[j]) {             a2[n++] = a[i];             i++;            j++;         }else{             a2[n++] = a[j];             j++;        }    }     while (I <= mid) {        a2[n++] = a[i];         i++;    }    while (j  <= high) {        a2[n++] = a[j];         j++;    }    for (n = 0, i = low; i  <= high; n++, i++) {  //copies the elements in A2 back to a;         a[i] = a2[n];    }    free (A2);} Void mergesort (Int *a, int low, int high) {    int mid;     if (Low < high) {        mid =   (Low + high)  / 2;        mergesort (a,  LOW,&NBSP;MID);         mergesort (A, mid+1, high);         merge (A, low, mid, high);     }} Void main (void) {    int a[] = {2, 4, 1, 7, 5, 6, 9, 10};     int count = sizeof (a)/sizeof (int);    int i;     mergesort (a, 0, count-1);     for (i = 0; i <  count; i++) {        printf ("%d ",  a[i]);     }    printf ("\ n");}

(5), results

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(6), algorithm analysis

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Merge sort time complexity: Tree height log (n), a total of n elements to be sorted, so is:O (Nlogn);

Within 30 elements, insert sort performance is better, after more than 30 elements, the performance of the merge sort is more excellent;

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Insert and Merge sort