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和题目一样，这个算法是按照黄金分割法作为原理的

黄金分割就是0.618:1

 

先看下菲波那切数列

 

代码实现：

#include <stdio.h>

#define MAXSIZE 20

void fibonacci(int *f)
{
    int i;

    f[0] = 1;
    f[1] = 1;
    
    for(i=2; i < MAXSIZE; ++i)
    {
        f[i] = f[i-2] + f[i-1];

    }
}

int fibonacci_search(int *a,int key,int n)
{
    int low = 0;
    int high = n - 1;
    int mid = 0;
    int k = 0;
    int F[MAXSIZE];
    int i;

    fibonacci(F);
    
    while( n > F[k]-1 ) 
    {
        ++k;
    }

    for( i=n; i < F[k]-1; ++i)
    {
        a[i] = a[high];
    }

    while( low <= high )
    {
        mid = low + F[k-1] - 1;

        if( a[mid] > key )
        {
            high = mid - 1;
            k = k - 1;
        }
        else if( a[mid] < key )
        {
            low = mid + 1;
            k = k - 2;
        }
        else
        {
            if( mid <= high ) 
            {
                return mid;
            }
            else
            {
                return high;
            }
        }
    }

    return -1;
}

int main()
{
    
    int a[MAXSIZE] = {1, 5, 15, 22, 25, 31, 39, 42, 47, 49, 59, 68, 88};
    int key;
    int pos;

    printf("请输入要查找的数字:");
    scanf("%d", &key);
    
    pos = fibonacci_search(a, key, 13);
    
    if( pos != -1 )
    {
        printf("\n查找成功，关键字 %d 所在的位置是: %d\n\n", key, pos);
    }
    else
    {
        printf("未在数组中找到元素:%d\n\n", key);
    }
        
    return 0;
}