Problem: Count the maximum number of ways we can parenthesize of a given boolean expression so that the value of expression evaluates to true or false as asked.
Boolean expression will be given with following symbols.
Symbols
‘T’ —> true
‘F’ —> false
And the Operators
& —> boolean AND
| —> boolean OR
^ —> boolean XOR
The appears as Interview question in Microsoft & Amazon.
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#include <iostream> #include <string> using namespace std; int T[105][105]; int F[105][105]; int main() { //code int t,n; string s,str,op; cin>>t; while(t--) { cin>>n; cin>>str; s=""; op=""; for(int i=0;i<str.size();i++) { if(i%2==0) s+=str[i]; else op+=str[i]; } for(int i=0;i<105;i++) { for(int j=0;j<105;j++) { T[i][j]=0; F[i][j]=0; } } for(int i=0;i<s.size();i++) { if(s[i]=='T') T[i][1]=1; else F[i][1]=1; } for(int len=2;len<=s.size();len++) { for(int i=0;i+len-1<s.size();i++) { for(int k=1;k<=len;k++) { if(op[i+k-1]=='&') { T[i][len]= (T[i][len] + T[i][k]*T[i+k][len-k])%1003; F[i][len]= (F[i][len] + F[i][k]*F[i+k][len-k])%1003; F[i][len]= (F[i][len] + F[i][k]*T[i+k][len-k])%1003; F[i][len]= (F[i][len] + T[i][k]*F[i+k][len-k])%1003; } if(op[i+k-1]=='^') { T[i][len]= (T[i][len] + F[i][k]*T[i+k][len-k])%1003; T[i][len]= (T[i][len] + T[i][k]*F[i+k][len-k])%1003; F[i][len]= (F[i][len] + F[i][k]*F[i+k][len-k])%1003; F[i][len]= (F[i][len] + T[i][k]*T[i+k][len-k])%1003; } if(op[i+k-1]=='|') { F[i][len]= (F[i][len] + F[i][k]*F[i+k][len-k])%1003; T[i][len]= (T[i][len] + T[i][k]*T[i+k][len-k])%1003; T[i][len]= (T[i][len] + F[i][k]*T[i+k][len-k])%1003; T[i][len]= (T[i][len] + T[i][k]*F[i+k][len-k])%1003; } } } } //cout<<s<<" "<<op<<endl; cout<<T[0][s.size()]<<endl; } return 0; } |