顺序表查找和有序表查找

查找里面顺比表查找和有序表查找（包括二分查找，插值查找，斐波那契查找）比较简单，直接贴代码，代码里面有详细注释。

#include <iostream>
using namespace std;

//顺序表查找（线性查找、静态表查找）  时间复杂度为O(n)
int Seq_Search(int *s,int n,int key)
{
    s[0] = key;   //设置了一个哨兵，避免了每次比较一次过后都要判断查找位置是否越界
    int i = n;
    while (s[i] != key)
    {
        --i;
    }
    return i;
}

//二分查找（折半查找） 前提条件：记录的关键码必须有序，必须是顺序存储   时间复杂度为O(logn)
int Binary_Search(int *s,int n,int key)
{
    int low,mid,high;
    low = 1;
    high = n;
    while (low <= high)
    {
        mid = (low + high)/2;
        if (s[mid] > key)
        {
            high = mid - 1;
        }else if (s[mid] < key)
        {
            low = mid + 1;
        }else
            return mid;
    }
    return 0;
}

//插值查找(对于表长较大，关键字分布比较均匀的查找表来说，插值查找算法的平均性能要比二分查找算法的性能高)
int B_Search(int *s,int n,int key)
{
    int low,mid,high;
    low = 1;
    high = n;
    while (low <= high)
    {
        mid = low + (high - low)*(key - s[low])/(s[high] - s[low]);
        if (s[mid] > key)
        {
            high = mid - 1;
        }else if (s[mid] < key)
        {
            low = mid + 1;
        }else
            return mid;
    }
    return 0;
}

//计算斐波那契数列
void Fibonacci(int *F)
{
    F[0]=0;
    F[1]=1;
    for(int i =2;i<10;i++)  
    { 
        F[i] = F[i-1] + F[i-2];  
    } 
}

//斐波那契查找(时间复杂度是O(logn))
int Fibonacci_Search(int *s,int n,int key,int *F)
{
    int low,high,mid,i,k;
    low = 1;
    high = n;
    k = 0;  //k为斐波那契数列的下标
    while (n > F[k] - 1)  //计算n位于斐波那契数列的位置
    {
        k++;
    }
    for (i = n;i < F[k] -1;i++)  //将不满的数值补全
    {
        s[i] = s[n];
    }
    //开始查找
    while (low <= high)
    {
        mid = low + F[k] - 1;
        if (key < s[mid])
        {
            high = mid - 1;
            k = k - 1;   //斐波那契数列下标减一位
        }else if (key > s[mid])
        {
            low = mid + 1;
            k = k - 2;   //斐波那契数列下标减两位
        }else
        {
            if (mid <= n)
            {
                return mid;
            }else
                return n;   //若mid>n，说明是补全的数值，返回n
        }
    }
    return 0;
}

void main()
{
    int s[] = {0,1,16,24,35,47,59,62,73,88,99};
    int n = 11;
    int m,a;
    int Fbi[10];
    Fibonacci(Fbi);

    cout << "输入顺序表查找要查找的数字: ";
    cin >> m;
    a = Seq_Search(s,n,m);
    cout << "顺序表查找" << m <<"的位置在："<< a << endl << endl;

    cout << "输入二分查找要查找的数字: ";
    cin >> m;
    a = Binary_Search(s,n,m);
    cout << "二分查找" << m <<"的位置在："<< a << endl << endl;

    cout << "输入插值查找要查找的数字: ";
    cin >> m;
    a = B_Search(s,n,m);
    cout << "插值查找" << m <<"的位置在："<< a << endl << endl;

    cout << "输入斐波那契查找要查找的数字: ";
    cin >> m;
    a = Fibonacci_Search(s,n,m,Fbi);
    cout << "斐波那契查找" << m <<"的位置在："<< a << endl << endl;

    system("pause");
}

运行结果：