Implemented in C ++: Sine Dance

Problem Description

　　FJ recently opened a mathematical analysis course for his cows, FJ know to learn this course, it must have a good basic trigonometric functions. So he was ready and cows do a "Sine Dance" game, entertaining, raise cows computing power.
　　May assume
　　An SiN = (. 1-SiN (SiN 2 + (. 3-SiN (SiN. 4 + ... (n-)) ...)
　　of Sn = (... (n-A1 +). 1-n-A2 +) A3 + 2 + ...) an + 1
　　FJ want cows to calculate the value of Sn, please FJ help you print out the full expression of Sn to facilitate cows do problems.

Input Format

　　Only a few: N <201.

Output Format

　　Please output the corresponding expression Sn, with a newline character. Output must not contain extra space or line feed, carriage return.

Sample input

3

Sample Output

((Sin (1) +3) sin (1-sin (2)) + 2) sin (1-sin (2 + sin (3))) + 1

 

Ideas: first calculate An, An and substituting the Sn into the can. An recursive use to solve and Sn.

 1 #include<iostream>
 2 using namespace std;
 3 
 4 class dance
 5 {
 6 public:
 7     int get_n()
 8     {
 9         cin>>n;
10         return n;
11     }
12 
13     void dance_an(int i,int n)
14     {
15         if(i==n)
16         {
17             cout<<"sin(";
18             cout<<n;
19             cout<<")";
20         }
21         else
22         {
23             cout<<"sin(";
24             cout<<i;
25             if(i<n)
26             {
27                 if (i % 2 == 1)
28                 {
29                     cout << "-";
30                 }
31                 else
32                 {
33                     cout << "+";
34                 }
35             }
36             dance_an(i+1,n);
37             cout<<")";
38         }
39     }
40 
41     void dance_sn(int i,int n)
42     {
43         if(i==1)
44         {
45             dance_an(1,i);
46             cout<<"+";
47             cout<<n;
48         }
49         else
50         {
51             cout<<"(";
52             dance_sn(i-1,n);
53             cout<<")";
54             dance_an(1,i);
55             cout<<"+";
56             cout<<n-i+1;
57         }
58     }
59 private:
60     int n;
61 };
62 
63 int main(void)
64 {
65     dance cow;
66     int n=cow.get_n();
67     cow.dance_sn(n,n);
68     return 0;
69 }