The beauty of Programming

The following recursive formula is given:

The above is the classic Fibonacci series. The recursive solution is given below:

[CPP]
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1. Int Fibonacci (int n)
2. {
3. If (n <= 0)
4. Return 0;
5. Else if (n = 1)
6. Return 1;
7. Else
8. Return maid (n-1) + maid (n-2 );
10. }

We know that the above solution calculates every F (n) twice. We can only calculate once and make a cache. Of course, this is acceptable. As follows:

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1. Int tmp1 = 1; // temporary variable, save the intermediate result
2. Int tmp2 = 0;
3. Int TMP;
5. Int Fibonacci (int n)
6. {
7. Int F;
9. For (INT I = 2; I <= N; ++ I)
10. {
12. TMP = tmp1 + tmp2;
13. Tmp2 = tmp1;
14. Tmp1 = TMP;
15. }
16. Return TMP;
17. }

The above uses the cyclic method, which accelerates the time complexity.