My program worked correctly on N in 1 to 9, and incorrectly on numbers greater than 9 (error in string concatenation). I kept getting an error on test 2 until I fixed the error. Apparently, in test 2, the input is a number greater than 10.
Try this test:
in:
11
out:
((((((((((sin(1)+11)sin(1-sin(2))+10)sin(1-sin(2+sin(3)))+9)sin(1-sin(2+sin(3-sin(4))))+8)sin(1-sin(2+sin(3-sin(4+sin(5)))))+7)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6))))))+6)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6+sin(7)))))))+5)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6+sin(7-sin(8))))))))+4)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6+sin(7-sin(8+sin(9)))))))))+3)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6+sin(7-sin(8+sin(9-sin(10))))))))))+2)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6+sin(7-sin(8+sin(9-sin(10+sin(11)))))))))))+1

I have written the code the using user defined function thats why it has become much bigger.

#include<Stdio.h>
#include<math.h>
int Sn(int n);
int An(int a);
int main()
{
    int x;
    scanf("%d",&x);
    Sn(x);
}
int Sn(int n)
{
    int j;
    if(n==1) {An(1); printf("+1");}
    else { for(j=1;j<n;j++) printf("(");
        for(j=1;j<=n;j++)
       {if(j==1)
        {An(j);printf("+%d)",n);}
        else if(j!=n) {An(j);printf("+%d)",n-j+1);}
        else {An(j);printf("+1");}}}

}

 int An(int a)
{ int i,p;
    if(a==1)
   printf("sin(%d)",a);
   else
   {for(i=1;i<=a;i++)
       { p= pow(-1,i+1);
          if(i==1) printf("sin(%d",i);
          else if(p==1) printf("+sin(%d",i);
         else printf("-sin(%d",i);}
          for(i=0;i<a;i++) printf(")"); }
}

Edited by author 29.10.2020 21:19

/***************************************************************************************************
                         Anzmaul Haque Akash
                    DIU, Daffodil International University
                    E-mail: anzamul15-2297@diu.edu.bd
 Youtube:https://www.youtube.com/channel/UCXvXHUkxyLYKeQkIg_RyMBw
******************************************************************************************************/
#include<bits/stdc++.h>

#define ln     (int)1e6
#define pi     acos(-1.0)
#define pb     push_back
#define pf     push_front 1
#define mp     make_pair
#define F      first
#define S      second
#define INF    1000000000000000000
#define LES    -1000000000000000000
#define intlim 2147483648
#define ll     long long
#define ull    unsigned long long
#define str    string
#define in     insert

#define all(akash)       akash.begin(),akash.end()
#define ms(arr)          memset(arr,0,sizeof(arr))
#define msbooltrue(arr)  memset(arr,true,sizeof(arr))
#define msboolfalse(arr) memset(arr,false,sizeof(arr))
#define msINF(arr)       memset(arr,INF,sizeof(arr))
#define case1(cs)        cout<<"Case "<<cs<<": "
#define case2(cs)        cout<<"Case "<<cs<<":\n"
#define lb               cout<<"\n";

#define vec vector
#define qu  queue
#define li  list
#define pq  priority_queue
#define em  empty

#define fori(i,a,b) for(int i=0;i<b;i++)
#define ford(i,a,b) for(int i=b-1;i>=0;i--)
#define forc(ch);   for(char ch:str)

#define sc1(a)         scanf("%lld",&a)
#define sc2(a,b)       scanf("%lld %lld",&a,&b)
#define sc3(a,b,c)     scanf("%lld %lld %lld",&a,&b,&c)
#define sc4(a,b,c,d)   scanf("%lld %lld %lld %lld",&a,&b,&c,&d)
#define sc5(a,b,c,d,e) scanf("%lld %lld %lld %lld %lld",&a,&b,&c,&d,&e)

using namespace std;

void solve(ll n){

    ll temp_n=n;

    temp_n--;

    for(ll i=0; i<n-1; i++){
        cout<<"(";
    }
    cout<<"sin(1)+"<<n<<")"; //Segment 1.

    str s="sin(1-sin("; // if n>1 this one is using for the template.


    for(ll i=2;i<=n;i++){ //main loop.

        str temp;
        temp.clear();
        temp=s;


        for(ll x=2; x<i;x++){ //This one creat middle of Every part.

            if(x%2==0){ //' + ' for even ' - ' for odd.
                temp+=to_string(x);
                temp+="+sin(";
            }
            else{
                temp+=to_string(x);
                temp+="-sin(";
            }

        }

        temp+=to_string(i);

        for(ll y=1;y<=i;y++){ //for closing ' ) ' every equation.
            temp+=")";
        }

        cout<<temp; //print each segment.

        if(temp_n > 1){
            cout<<"+"<<temp_n<<")"; //Printing every segment last digit with out 1.
        }
        temp_n--;
    }

    cout<<"+1";lb//This one for end.
}

int main()
{
    ll n;
    sc1(n);

    if(n>1){
        solve(n); //solve function.
    }
    else if(n==1){
        cout<<"sin(1)+1";lb //for 1.
    }

    return 0;
}

#include<bits/stdc++.h>
using namespace std;
void prin ( int i)
{
    int j;
    for ( j =1 ; j <= i ;j++)
    {
        cout << "sin(" << j;
        if ( j == i){
        for (j = 0 ; j<i ; j ++)
            cout <<")";
        break;}
        else {
        if (j%2)
            cout << "-";
        else cout << "+";
        }
    }
}
int main()
{
    int i,j,n;
    cin >> n;
    int k = n;
    for (i = 1; i < n ;i++)
    cout << "(";
    for ( i = 1 ; i <= n ; i++,k--)
    {
        prin(i);
        if (i!= n)
            cout << "+"<<k<<")";
    }
    cout << "+1\n";
    return 0;
}

Don't forget to make an endline in your pretty code....

#include <bits/stdc++.h>

int main()
{
    int n,i,j,k;

    scanf("%d",&n);

    for(i=1; i<=n; i++){
            if(i==1 && n!=1){
                printf("(");
            }
        for(j=1; j<=i; j++){
            if(i==1 && n==i){
                printf("(sin(1))+%d",n);
            }
            else if(i==1){
                printf("(sin(1)+%d)",n);
            }
            else {
                if(j%2==0){
                    printf("-sin(%d",j);
                }
                else if(j==1){
                    printf("sin(%d",j);
                }
                else {
                    printf("+sin(%d",j);
                }
                if(j==i){
                    //printf(")");
                    for(k=1; k<=i; k++){
                        printf(")");
                    }
                }
            }
        }
        //if(i==n){
          //  printf(")");
       // }
       if(i!=1 && i!=n){
        printf("+%d)",n+1-i);
       }
       else if(i!=1 && i==n){
        printf("+%d",n+1-i);
       }

    }
    return 0;
}

using System;

class Test
{
    public static void Main()
    {
        String strB = "";
        String strA = "";

        int num = Convert.ToInt32(Console.ReadLine());
        int b = 1;

        for (int a = num; a > 0; a--)
        {
            strA = StrAMaker(a);

            strB = ')' + strA + '+' + b + strB;
            b++;
        }
        string s3 = new string('(', --num);
        strB = s3 + strB.TrimStart(')');
        Console.WriteLine(strB);
    }

    public static string StrAMaker (int a)
    {
        string s1 = new string(')', a);
        String s2 = "";

        for (int i = 1; i <= a; i++)
        {
            if (i % 2 == 0)
            {
                s2 = s2 + "sin(" + i + "+";
                if (i == a) s2 = s2.TrimEnd('+') + s1;
            }
            else
            {
                s2 = s2 + "sin(" + i + "-";
                if (i == a) s2 = s2.TrimEnd('-') + s1;
            }
        }

        return s2;
    }
}

my code:
#include<bits/stdc++.h>
using namespace std;

typedef long long                   ll;
typedef pair<int,int>               pii;
typedef pair<ll,ll>                 pll;
typedef pair<string , string>       pss;

#define all(x)                      (x).begin(),(x).end()
#define Sort(x)                     sort(all((x)))
#define F                           first
#define S                           second
#define sep                         ' '
#define file_io                     freopen("input.txt" , "r+" , stdin) ; freopen("output.txt" , "w+" , stdout);
#define fast_io                     ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define error(x)                    cerr << "$$$ " << x << '\n';
#define error2(x,y)                 cerr << "#F : " << x << "      #S : " << y << '\n';
#define pb                          push_back

const ll MX5 = 3*1e5+3;
const ll MX6 = 2*1e6+3;
const ll INF = 8e18;
const ll MOD = 1e9 + 7;
const ll MOD2= 998244353;

ll power(ll a, ll b, ll md) {
    return (!b ? 1 : (b & 1 ? a * power(a * a % md, b / 2, md) % md : power(a * a % md, b / 2, md) % md));
}
ll bmm(ll a,ll b){
    return (a%b==0 ? b : bmm(b,a%b));
}

ll A[MX5];


string num(ll n){
    string ans="";
    while(n){
        ans=(char)(n%10+'0')+ans;
        n/=10;
    }
    return ans;
}

string An(ll t,ll n){
    string a=num(t);
    if(t==n){
        return "sin("+a+")";
    }
    if(t%2==1){
        return "sin("+a+"-"+An(t+1,n)+")";
    }
    return "sin("+a+"+"+An(t+1,n)+")";
}
string Sn(ll t,ll n){
    string a=num(n-t+1);
    if(t==1){
        return An(1,1)+"+"+a;
    }
    return "("+Sn(t-1,n)+")"+An(1,t)+"+"+a;
}
int main(){
    fast_io
    //file_io
    ll n;
    cin >> n;
    string answer=Sn(n,n);
    cout << answer;
    return 0;
}

Edited by author 12.08.2019 13:01

#include<iostream>
using namespace std;
void sin (int n,int i)
{
    if(i==n+1)
      return ;
    else
    {
      if(i==1)
        {
          cout<<"sin("<<i;
          sin(n,i+1);
        }
      else if(i%2==1)
        {
          cout<<"+sin("<<i;
          sin(n,i+1);
        }
      else
        {
          cout<<"-sin("<<i;
          sin(n,i+1);
        }
       cout<<")";
    }

}
void sol( int n,int i)
{
  if(i==n)
    return;
  if(i==1)
    for(int i=1;i<n;i++)
      cout<<'(';
  sin(i,1);
  cout<<'+'<<n-i+1<<')';
  sol(n,i+1);

  if(i==1)
  {
    sin(n,1);
    cout<<"+1";
  }
}
int main ()
{
  int n;
  cin>>n;
  sol(n,1);
}

i have some problems with (), please give answers for some other cases

I thought i'll never get AC at this problem, but after some time i wrote that very nice (as for me ^___^) functions doing the work.

void a( int n, int k )
{
-printf("sin(%d",k);
-if ( k < n )
-{
--if ( k % 2 )
---printf("-");
--else
---printf("+");
--a( n, k + 1 );
-}
-printf(")");
}

void s( int n, int k )
{
-if ( k < n )
-{
--printf("(");
--s( n, k + 1 );
--printf(")");
-}
-a( n - k + 1, 1 );
-printf("+%d",k);
}

For answer just need to call s( n, 1 ).
Good luck!

Edited by author 20.03.2010 18:23

Here is my code:
# include <bits/stdc++.h>

using namespace std;

string s[300];

string conv(int x) {
    string str;
    while(x) {
        str.push_back(x % 10 + '0');
        x /= 20;
    }
    reverse(str.begin(), str.end());
    return str;
}

int main() {
    int n;
    cin >> n;
    for(int i = 1; i <= n; i++) {
        for(int j = 1; j <= i; j++) {
            s[i] += "sin(" + conv(j);
            if(j != i) {
                if(j % 2)
                    s[i].push_back('-');
                else
                    s[i].push_back('+');
            }
        }
        for(int j = 1; j <= i; j++)
            s[i].push_back(')');
    }

    for(int i = 1; i < n; i++) cout << '(';
    for(int i = 1; i <= n; i++) {
        cout << s[i] << '+' << n - i + 1;
        if(i != n)
            cout << ')';
    }
    cout << endl;
    return 0;
}

Edited by author 13.11.2015 09:37

Edited by author 13.11.2015 09:37

At first I thought I was getting WA's because of the wrong minus sign.
Actual reason was printing integers.
I was trying to print integers using just PUTCHAR.
Of course it worked fine for 0-9. And was failing for other numbers.

Maybe correct name for that problem is "SINE dance"?
"Sinus" is something about anathomy.

#include <iostream>
#include <cstdlib>
#include <string>
using namespace std;

string S, A;
unsigned short An = 1;
bool negative     = true;

void get_next_A();
void get_S(unsigned short);

int main()
{
    unsigned short input_n;

    cin >> input_n;

    get_S(input_n);

    cout << S << endl;

    return 0;
}

void get_next_A()
{
    if(An == 1)
        A = "sin(1)";
    else
    {
        A.erase(A.size() - An + 1, An);

        if(negative)
            A += "-sin(";
        else
            A += "+sin(";

        char buffer[5];

        itoa(An, buffer, 10);
        A += buffer;

        for(unsigned short j = 0; j < An; ++j)
            A += ")";

        negative = !negative;

    }

    ++An;
    return;
}

void get_S(unsigned short n)
{
    char _buffer[10];

    for(unsigned short i = 0; i < n - 1; ++i)
        S += '(';

    for(unsigned short i = n; i > 0; --i)
    {
        get_next_A();

        itoa(i, _buffer, 10);

        S += A;
        S += '+';
        S += _buffer;
        if(i != 1)
            S += ')';

    }

    return;
}

((((((((((sin(1)+11)sin(1-sin(2))+10)sin(1-sin(2+sin(3)))+9)sin(1-sin(2+sin(3-si
n(4))))+8)sin(1-sin(2+sin(3-sin(4+sin(5)))))+7)sin(1-sin(2+sin(3-sin(4+sin(5-sin
(6))))))+6)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6+sin(7)))))))+5)sin(1-sin(2+sin(3-
sin(4+sin(5-sin(6+sin(7-sin(8))))))))+4)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6+sin(
7-sin(8+sin(9)))))))))+3)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6+sin(7-sin(8+sin(9-s
in(10))))))))))+2)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6+sin(7-sin(8+sin(9-sin(10+s
in(11)))))))))))+1

When N = 11

Программа почему-то постоянно дает сбой на 2-ом тесте, но так как явные ошибки в коде не обнаружены, может просто я не понял условие?
0
1
sin(1)+1
2
(sin(1)+2)sin(1-sin(2))+1
3
((sin(1)+3)sin(1-sin(2))+2)sin(1-sin(2+sin(3)))+1
4
(((sin(1)+4)sin(1-sin(2))+3)sin(1-sin(2+sin(3)))+2)sin(1-sin(2+sin(3-sin(4))))+1
5
((((sin(1)+5)sin(1-sin(2))+4)sin(1-sin(2+sin(3)))+3)sin(1-sin(2+sin(3-sin(4))))+2)sin(1-sin(2+sin(3-sin(4+sin(5)))))+1
6
(((((sin(1)+6)sin(1-sin(2))+5)sin(1-sin(2+sin(3)))+4)sin(1-sin(2+sin(3-sin(4))))+3)sin(1-sin(2+sin(3-sin(4+sin(5)))))+2)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6))))))+1
7
((((((sin(1)+7)sin(1-sin(2))+6)sin(1-sin(2+sin(3)))+5)sin(1-sin(2+sin(3-sin(4))))+4)sin(1-sin(2+sin(3-sin(4+sin(5)))))+3)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6))))))+2)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6+sin(7)))))))+1
8
(((((((sin(1)+8)sin(1-sin(2))+7)sin(1-sin(2+sin(3)))+6)sin(1-sin(2+sin(3-sin(4))))+5)sin(1-sin(2+sin(3-sin(4+sin(5)))))+4)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6))))))+3)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6+sin(7)))))))+2)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6+sin(7-sin(8))))))))+1
9
((((((((sin(1)+9)sin(1-sin(2))+8)sin(1-sin(2+sin(3)))+7)sin(1-sin(2+sin(3-sin(4))))+6)sin(1-sin(2+sin(3-sin(4+sin(5)))))+5)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6))))))+4)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6+sin(7)))))))+3)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6+sin(7-sin(8))))))))+2)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6+sin(7-sin(8+sin(9)))))))))+1
10
(((((((((sin(1)+10)sin(1-sin(2))+9)sin(1-sin(2+sin(3)))+8)sin(1-sin(2+sin(3-sin(4))))+7)sin(1-sin(2+sin(3-sin(4+sin(5)))))+6)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6))))))+5)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6+sin(7)))))))+4)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6+sin(7-sin(8))))))))+3)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6+sin(7-sin(8+sin(9)))))))))+2)sin(1-sin(2+sin(3-sin(4+sin(5-sin(6+sin(7-sin(8+sin(9-sin(10))))))))))+1

Found the mistake :)

Edited by author 09.07.2015 01:22

#include<stdio.h>
main()
{
    int n,i,j;
    scanf("%i",&n);
    for(i=1;i<n;i++) printf("(");
    for(i=1;i<=n;i++)
    {
      for(j=1;j<=i;j++)
      {
         if(j>1)
           printf((j&1)?"+":"-");
         printf("sin(%i",j);
      }
      for(j=1;j<=i;j++)printf(")");
      printf("+%i",n+1-i);
      if(i!=n)printf(")");
    }
}