插入排序

算法导论课后练习题，本人非科班出生，也未有人指导，纯属自学，难免有错误，恳请指导！
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INSERTION-SORT(A)
for j = 2 to A.length
     key = A[j]
     i = j-1
     while i > 0 and A[i] > key
           A[i+1] = A[i]
           i = i - 1
      A[i + 1] = key


---------insertion_sort.h------------------------




void insertion_sort(double array[], int length)
{
    int i, j;
    int tmp;
    if (length < 2)
        return;


    for (j = 1; j < length; j++)
    {
        tmp = array[j];
        i = j-1;
        while(i >= 0 && array[i] > tmp)
        {
            array[i + 1] = array[i];
            i--;
        }   


        array[i + 1] = tmp;
    }
}


---------------main.c-------------------------------




#include
#include "insertion_sort.h"




int main(void)
{
    printf("插入排序测试\n");
    double arr[6] = {
        31, 41, 59, 26, 41, 58};
    printf("array=");
    for (int i = 0; i < 6; i++)
    {
        printf("%lf ", arr[i]);
    }   
    printf("\nsorted array=");
    insertion_sort(arr, 6);
    for (int i = 0; i < 6; i++)
    {
        printf("%lf ", arr[i]);
    }       
    printf("\n........................................\n");
   
    return 0;   
}


------------------------------------------------------------------------------------
重写过程INSERTION_SORT,使之按非升序排序
INSERTION_SORT_DOWN(A)
    for j = 1 to A.length
        key = A[j]
        i = j - 1
        while i > 0 and A[i] < key
            A[i + 1] = A[i]
            i = i - 1
        A[i + 1] = key
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LINEAR_SEARCH(A, *v)
    for i = 1 to A.length
        if *v = A[i]
            return i;
    *v = NIL
证明-
初始化：第一次循环迭代之前，即j=1时，如果找到v的值，则返回该值在序列A中的索引，循环结束
保持：每次迭代未找到该值，索引向后推进一个单位
终止：当找到该值，立即返回该值在序列中的索引，终止。若未找到该值，for结束，该值置为NIL
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BINARY_ADD(A, B, C)
tmp = 0
for i = 1 to A.length
    if A[i] != B[i]
        C[i] = 1 + tmp
        tmp = 0
    else if A[i] == 1 && B[i] == 1
        C[i] = 0 + tmp
        tmp = 1
    else
        C[i] = 0 + tmp
         tmp = 0
C[i+1] = tmp