Suppose there are n steps in a stair. Each time you can only take one or two steps. The relationship between n and the number of ways to go upstairs is shown in the following table. Calculate how many ways to go upstairs by using by writing:

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Suppose there are n steps in a stair. Each time you can only take one or two steps. The relationship
between n and the number of ways to go upstairs is shown in the following table. Calculate how
many ways to go upstairs by using by writing:
(1) a recursion program: int JUMP_R(int n);
(2) a dynamic programming program: int JUMP_DP (int n).
Steps: n
1
2
3
4
n
Formula
F(1)=1
F(2)=2
F(3)=F(1)+F(2)
F(3)=F(2)+F(3)
F(n)=F(n-2)+F(n-1)
Number
1
2
3
5
Transcribed Image Text:Suppose there are n steps in a stair. Each time you can only take one or two steps. The relationship between n and the number of ways to go upstairs is shown in the following table. Calculate how many ways to go upstairs by using by writing: (1) a recursion program: int JUMP_R(int n); (2) a dynamic programming program: int JUMP_DP (int n). Steps: n 1 2 3 4 n Formula F(1)=1 F(2)=2 F(3)=F(1)+F(2) F(3)=F(2)+F(3) F(n)=F(n-2)+F(n-1) Number 1 2 3 5
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