The Simpipo series of interesting deeds

The first to study this sequence is, of course, Fibonacci. He was to describe the number of rabbits growing as follows.

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Later, it is widely used in various occasions, this is the definition of the following columns:

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First of all, when we look at this sequence, we think of the recursive method of realizing it first:

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can also be implemented using the three-mesh operator:

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Analysis:

Recursive time complexity: number of recursion times * per recursive count.

Recursive spatial complexity: recursive depth * the size of each recursive.

Using recursion to implement Fibonacci sequences is very inefficient.

The time complexity is O (2^n), and the spatial complexity is O (n).

Optimization of the Fibonacci sequence:

Fibonacci Sequence: 0,1,1,2,3,5,8 ...

The law can be drawn: Starting with the third number, each number is the sum of the first two numbers.

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Note: The time complexity is O (n), the space complexity is O (1)

It can also be implemented by using arrays:

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Note: The time is complex O (n) and the spatial complexity is O (n).

Attention:

(1) in the Fibonacci sequence, be sure to note that when n=0, the result is 0.

(2) Apply a long long to prevent cross-border.

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The Simpipo series of interesting deeds