二分查找法与拉格朗日插值查找法

#define _CRT_SECURE_NO_WARNINGS
#include<stdio.h>
#include<stdlib.h>
#define N 1024
 
void search1(int a[N], int num)//二分法插值查找
{
	int tou = 0;
	int wei = N - 1;
	int zhong;
	int flag = -1;//假定一开始找不到
	int ci = 0;
	while (tou <= wei)
	{
		zhong = (tou + wei) / 2;
		//zhong=tou+(wei-tou)*(1/2)
		printf("
%d %d %d %d", tou, wei, zhong, ++ci);
		if (num == a[zhong])
		{
			printf("Find! a[%d]=%d", zhong, num);
			flag = 1;
			break;
		}
		else if (num > a[zhong])
		{
			tou = zhong + 1;
 
		}
		else
		{
			wei = zhong - 1;
		}
	}
	if (flag == -1)
	{
 
		printf("Not Find!");
	}
 
}
 
void search2(int a[N], int num)//拉格朗日查找
{
	int tou = 0;
	int wei = N - 1;
	int zhong;
	int flag = -1;//假定一开始找不到
	int ci = 0;
	while (tou <= wei)
	{
		//zhong = (tou + wei) / 2;
		zhong = tou + (wei - tou)*1.0*(num-a[tou])/(a[wei]-a[tou]);//*1.0 乘以一个实数 避免产生误差
		printf("
%d %d %d %d", tou, wei, zhong, ++ci);
		if (num == a[zhong])
		{
			printf("Find! a[%d]=%d", zhong, num);
			flag = 1;
			break;
		}
		else if (num > a[zhong])
		{
			tou = zhong + 1;
 
		}
		else
		{
			wei = zhong - 1;
		}
	}
	if (flag == -1)
	{
 
		printf("Not Find!");
	}
 
}
 
 
void main()
{
	int a[N];
	for (int i = 0; i < 1024; i++)
	{
		a[i] = i;
		//printf("%d  ", a[i]);
	}
	int num;
	scanf("%d", &num);
	search2(a, num);//调用函数查找
	system("pause");
}

　　

将插值比例1/2换成其他值实现拉格朗日插值查找

由来：拉格朗日插值公式

数据均匀排布的情况下 一次找到

数据不均匀排布的情况下 找到的次数在一次和二分查找法之间