折半插入排序

辅助

#include<time.h>
#include<iostream>
using namespace std;
void show(int a[], int length) {
  for (int i = 1; i <= length; i++) {
    cout << a[i] << " ";
  }
  cout << endl;
}

算法重点

//2.折半插入法
//需要经过[log2i]+1次比较,时间复杂度o(n^2)，移动次数与直接插入算法差不多，比较次数较少
/*
特点：稳定排序，只能顺序结构，初始记录无序，n比较大
1.设待排序的记录保存在数组r[1,n]中，r[1]有序序列
2.循环（n-1)次，每次使用折半插入法，查找r[i]在已排好序的序列中的位置，直接插入，最后得到表长为n的序列
*/


void BInsertSort(int a[], int length) {
  int changeTime = 0, compareTime = 0;
  for (int i = 2; i <= length; i++) {
    a[0] = a[i];//哨兵保存数值
    changeTime++;
    int low = 1, high = i - 1;//设置区间
    while (low <= high) {
      int meidan = (low + high) / 2;//折半
      if (a[0] < a[meidan]) {
        high = meidan - 1;//插入点在左区域
      }
      else low = meidan + 1;//插入点在右区域
      compareTime++;
    }
    for (int j = i - 1; j >= high + 1; --j) {//记录后移
      a[j + 1] = a[j]; changeTime++;
    }
    a[high + 1] = a[0]; changeTime++;
    printf("Thr %2d time sort:\t",(i-1));
    show(a, length);
  }
  cout << "Key word ComareTime2=" << compareTime << endl;
  cout << "Key word ChangeTime2=" << changeTime << endl;
}

测试

int main() {
  int *a = new int[17];
  int length = 16;
  srand(unsigned(time(NULL)));
  for (int i = 1; i <= 16; i++) {
    a[i]=rand()% 90 + 10;
  }
  cout << "============ ==" << endl;
  cout << " 折半插入排序: " << endl;
  cout << "== ============" << endl;
  cout << "before sort：" << ends;
  for (int i = 1; i <= 16; i++) {
    cout<<a[i]<<" ";
  }
  cout << endl;
  BInsertSort(a, length);
  cout << "after sort：" << ends;
  for (int i = 1; i <= 16; i++) {
    cout << a[i] << " ";
  }
  cout << endl;
  delete a;
  a = NULL;
}