boolean parenthesization

 #include<iostream>
 using namespace std;

 /* wrong code written by me
 int countParenth(char sym[],char op[],int n){
   int total[n][n],F[n][n];
   for(int i=0;i<n;i++)
     total[i][i]=sym[i]=='T'?1:0;
    for(int i=0;i<n;i++)
     F[i][i]=sym[i]=='F'?1:0;
   for(int gap=1;gap<n;gap++){
     for(int i=0,j=gap;j<n;i++,j++){
       int valT=0,valF=0;
       for(int k=i;k<j;k++){
           int first=total[i][k],sec=total[k+1][j];
           int res=0;
           if(op[k]=='|')
             res=first||sec;
            if(op[k]=='&')
             res=first&&sec;
            if(op[k]=='^')
             res=first^sec;
            if(res){
              int a=first==0?1:first;
              int b=sec==0?1:sec;
              valT+=a*b;
              }
            else{
              int a=first==0?1:first;
              int b=sec==0?1:sec;
              valF+=a*b;
              }
           }
         total[i][j]=total[j][i]=valT;
         F[i][j]=F[j][i]=valF;
       }
     }
   return total[0][n-1];
   }
  */

  int countParenth(char sym[],char ope[],int n){  //TT |
    int T[n][n],F[n][n];
    for(int i=0;i<n;i++){
       T[i][i]=sym[i]=='T'?1:0;
       F[i][i]=sym[i]=='F'?1:0;
      }
    for(int gap=1;gap<n;gap++){
      for(int i=0,j=gap;j<n;i++,j++){
        T[i][j]=0,F[i][j]=0;
        for(int k=i;k<j;k++){
          int tik=T[i][k]+F[i][k];
          int tkj=T[k+1][j]+F[k+1][j];
          if(ope[k]=='|'){
            F[i][j]+=F[i][k]*F[k+1][j];
            T[i][j]+=tik*tkj-F[i][k]*F[k+1][j];
            }
          if(ope[k]=='&'){
            T[i][j]+=T[i][k]*T[k+1][j];
            F[i][j]+=tik*tkj-T[i][k]*T[k+1][j];
            }
          if(ope[k]=='^'){
            T[i][j]+=F[i][k]*T[k+1][j]+T[i][k]*F[k+1][j];
            F[i][j]+=F[i][k]*F[k+1][j]+T[i][k]*T[k+1][j];
            }
          }
        }
      }
      return T[0][n-1];
    }

 int main(){
    char symbols[] = "TTFT";
    char operators[] = "|&^";
    int n = 4;
    cout << countParenth(symbols,operators,n);
    return 0;
    }