Exam questions basic practice Sine Dance

1. Title

Title link

　　http://lx.lanqiao.cn/problem.page?gpid=T62

Problem Description

　　Recently, FJ has set up a mathematical analysis course for his cows. FJ knows that to learn this course, he must have a good basic function of trigonometric functions. So he is going to make a "Sine Dance" game with the cows, to be entertaining and to improve the cows' computing power.
　　Let's set
　　An = sin (1–sin (2 + sin (3–sin (4 + ... sin (n)) ...)
　　Sn = (... (A1 + n) A2 + n-1) A3 + ... + 2) An + 1
　　FJ wants the cows to calculate the value of Sn. Please help FJ print out the complete expression of Sn, so that the cows can easily solve the problem.

Input format

　　There is only one number: N <201.

Output format

　　Please output the corresponding expression Sn, ending with a newline character. The output must not contain extra spaces or line feeds or carriage returns.

Sample input

3

Sample output

((sin (1) +3) sin (1 – sin (2)) + 2) sin (1 – sin (2 + sin (3))) + 1

2. Solve

Idea: List the strings according to the two expressions given in the question

A[i]="A" + "sin(" + "i" + "i个)"

s is initially set to "n-1 '('"

s="s" + "A[i]" + "+" + "n-i+1" + "1个)"

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 int main(){
 4     int N;
 5     char t;
 6     cin>>N;
 7     string s="";
 8     string A="",T="",H=""; 
 9     for(int i=0;i<N-1;i++){
10         //s初始设为"n-1个'('"
11         s+='(';  
12     }
13     
14     for(int i=1;i<=N;i++){
15         //A[i]="A" + "sin(" + "i" + "i个)" 
16         T+=')';//T是')'的叠加体 
17         A+="sin(";
18         t='0'+i;
19         A+=t;//A是A[i]的叠加体 
20         H=A+T;  //H表示A[i] 
21         
22         //s="s" + "H" + "+" + "n-i+1" + "1个)" 
23         s+=H;
24         s+='+';
25         t='0'+(N-i+1);
26         s+=t;
27         if(i!=N) s+=')';
28         
29         //Prepare for the next A [i] plus plus or minus sign 
30          if (i% 2 == 1) A + = '-' ;
 31          else A + = '+' ;
 32      }
 33      
34      cout << s << endl;
 35 }