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Copy pathBoolean Parenthesization.cpp
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Boolean Parenthesization.cpp
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//{ Driver Code Starts
// Initial Template for C++
#include <bits/stdc++.h>
using namespace std;
// } Driver Code Ends
// User function Template for C++
#define ll long long int
ll mod = 1003;
class Solution{
public:
int helper(int i, int j, string& s, int isTrue,vector<vector<vector<int>>>& dp)
{
if(i > j)
return 0;
if(i == j)
{
if(isTrue == 1)
return s[i] == 'T';
else
return s[i] == 'F';
}
if(dp[i][j][isTrue] != -1)
return dp[i][j][isTrue];
ll ways = 0;
for(int idx = i+1; idx <= j-1; idx += 2)
{
ll LT = helper(i, idx-1, s, 1, dp);
ll LF = helper(i, idx-1, s, 0, dp);
ll RT = helper(idx+1, j, s, 1, dp);
ll RF = helper(idx+1, j, s, 0, dp);
if(s[idx] == '&')
{
if(isTrue)
ways = ( ways + (LT * RT) % mod) % mod;
else
ways = (ways + (LT * RF) % mod + (LF * RT) % mod + (LF * RF) % mod) % mod;
}
else if(s[idx] == '|')
{
if(isTrue)
ways = (ways + (LT * RT) % mod + (LT * RF) % mod + (LF * RT) % mod) % mod;
else
ways = (ways + (LF * RF) % mod)% mod;
}
else
{
if(isTrue)
ways = (ways + (LT * RF) % mod + (LF * RT) % mod) % mod;
else
ways = (ways + (LT * RT) % mod + (LF * RF) % mod) % mod;
}
}
return dp[i][j][isTrue] = ways;
}
int countWays(int N, string S){
// code here
// vector<vector<vector<int>>> dp(N,vector<vector<int>>(N,vector<int>(2,-1)));
// return helper(0, N-1, S, 1, dp);
vector<vector<vector<int>>> dp(N,vector<vector<int>>(N,vector<int>(2,0)));
for(int i=0; i<N; i++)
{
dp[i][i][1] = S[i] == 'T';
dp[i][i][0] = S[i] == 'F';
}
for(int i = N-1; i>= 0; --i)
{
for(int j = i+1; j<N; ++j)
{
for(int isTrue = 0; isTrue <= 1; ++isTrue)
{
ll ways = 0;
for(int idx = i+1; idx <= j-1; idx += 2)
{
ll LT = dp[i][idx-1][1];
ll LF = dp[i][idx-1][0];
ll RT = dp[idx+1][j][1];
ll RF = dp[idx+1][j][0];
if(S[idx] == '&')
{
if(isTrue)
ways = ( ways + (LT * RT) % mod) % mod;
else
ways = (ways + (LT * RF) % mod + (LF * RT) % mod + (LF * RF) % mod) % mod;
}
else if(S[idx] == '|')
{
if(isTrue)
ways = (ways + (LT * RT) % mod + (LT * RF) % mod + (LF * RT) % mod) % mod;
else
ways = (ways + (LF * RF) % mod)% mod;
}
else
{
if(isTrue)
ways = (ways + (LT * RF) % mod + (LF * RT) % mod) % mod;
else
ways = (ways + (LT * RT) % mod + (LF * RF) % mod) % mod;
}
}
dp[i][j][isTrue] = ways;
}
}
}
return dp[0][N-1][1];
}
};
//{ Driver Code Starts.
int main(){
int t;
cin>>t;
while(t--){
int N;
cin>>N;
string S;
cin>>S;
Solution ob;
cout<<ob.countWays(N, S)<<"\n";
}
return 0;
}
// } Driver Code Ends