有序表查找_插值查找

为什么一定要二查找，而不是四分之一或者更多呢？

插值查找(Interpolation Search)是根据要查找的关键字key与查找表中最大最小记录的关键字比较后的查找方法，其核心就在于插值的计算公式。

插值查找时间复杂度O(logn)。

对于表长较大，而关键字分布又比较均匀的查找表来说，插值查找算法的平均性能比折半查找要好得多。

反之，数组中如果分布极端不均匀，用插值查找则未必合适。

代码：

#include <iostream>
using namespace std;

int Interpolation_Search(int *a, int n, int key)
{
  int mid = 0;
  int high = n-1;
  int low = 0;
  while (low <= high)
  {
	  mid = low + (high - low)*(key - a[low])/(a[high] - a[low]);//与二分查找区别
	  if(key < a[mid])
	  {
		  high = mid-1;
	  }
	  else if (key > a[mid])
	  {
		  low = mid+1;
	  }
	  else if (key == a[mid])
	  {
		  return mid;
	  }
  }
  return -1;//查找失败
}

int main()
{
	int a[10] = {1,2,3,4,5,6,7,8,9,10};
	int key = 2;
	cout<<Interpolation_Search(a, 10, key)<<endl;
	key = 99;
	cout<<Interpolation_Search(a, 10, key)<<endl;//如果返回-1，则查找失败
	getchar();
	return 0;
}

结果：

加一个round标识来比较两种算法的查找次数。

#include <iostream>
using namespace std;

int Interpolation_Search(int *a, int n, int key)
{
  int mid = 0;
  int high = n-1;
  int low = 0;
  int round = 0;//round标识，用于记录查找次数
  while (low <= high)
  {
	  round ++;
	  mid = low + (high - low)*(key - a[low])/(a[high] - a[low]);//与二分查找区别
	  if(key < a[mid])
	  {
		  high = mid-1;
	  }
	  else if (key > a[mid])
	  {
		  low = mid+1;
	  }
	  else if (key == a[mid])
	  {
		  cout<<"Round: "<<round<<endl;
		  return mid;
	  }
	  
  }
  return -1;//查找失败
}

int main()
{
	int a[10] = {1,2,3,4,5,6,7,8,9,10};
	int key = 2;
	cout<<Interpolation_Search(a, 10, key)<<endl;
	key = 99;
	cout<<Interpolation_Search(a, 10, key)<<endl;//如果返回-1，则查找失败
	getchar();
	return 0;
}

#include <iostream>
using namespace std;

int Binery_Search(int *a, int n, int key)
{
  int mid = 0;
  int high = n-1;
  int low = 0;
  int round = 0;//round标识，用于记录查找次数
  while (low <= high)
  {
	  round ++;
	  mid = (low+high)/2;//二分查找
	  if(key < a[mid])
	  {
		  high = mid-1;
	  }
	  else if (key > a[mid])
	  {
		  low = mid+1;
	  }
	  else if (key == a[mid])
	  {
		  cout<<"Round: "<<round<<endl;
		  return mid;
	  }
	  
  }
  return -1;//查找失败
}

int main()
{
	int a[10] = {1,2,3,4,5,6,7,8,9,10};
	int key = 2;
	cout<<Binery_Search(a, 10, key)<<endl;
	key = 99;
	cout<<Binery_Search(a, 10, key)<<endl;//如果返回-1，则查找失败
	getchar();
	return 0;
}

说明插值查找第1次就找到了，而二分查找在第2次才找到。