Python写出斐波那契二分检索，即使用斐波那契数列二分有序序列，查找某给定元素，找到返回下标，找不到返回-1

以下是一个基于斐波那契数列的二分查找程序的实现：

def fibonacci_search(arr, x):
    n = len(arr)
    fib2 = 0
    fib1 = 1
    fib = fib2 + fib1
    
    # Find the smallest Fibonacci number greater than or equal to n
    while fib < n:
        fib2 = fib1
        fib1 = fib
        fib = fib2 + fib1
    
    # Marks the eliminated range from front
    offset = -1
    
    # While there are elements to be inspected
    while fib > 1:
        # Check if fib2 is a valid location
        i = min(offset + fib2, n - 1)
        
        # If x is greater than the value at index fib2, cut the subarray array from offset to i
        if arr[i] < x:
            fib = fib1
            fib1 = fib2
            fib2 = fib - fib1
            offset = i
        
        # If x is less than the value at index fib2, cut the subarray after i+1
        elif arr[i] > x:
            fib = fib2
            fib1 = fib1 - fib2
            fib2 = fib - fib1
        
        # If x is equal to the value at index fib2, return the index
        else:
            return i
    
    # Compare the last element with x
    if fib1 and offset < n-1 and arr[offset+1] == x:
        return offset + 1
    
    # If the element was not found, return -1
    return -1

该函数接受一个数组和一个要查找的值x作为参数，并返回x在数组中的下标，如果x不存在于数组中，则返回-1。

该算法的时间复杂度为 O(log n)。虽然它比传统的二分查找稍微慢一些，但它的优点是可以在没有指针引用的情况下进行搜索，因此它可以用于非随机存取的数据结构（例如磁盘存储）。此外，该算法还具有与二分查找相同的优点，即时间复杂度为 O(log n)。