Hacktober/Boolean_Parenthesis.cpp at main · Prathamvv13/Hacktober · GitHub

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

int dp[101][101][2];
int parenthesis_count(string s,
                      int i,
                      int j,
                      int isTrue)
{
    // Base Condition
    if (i > j)
        return false;
    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];
    int ans = 0;
    for (int k = i + 1
         ; k <= j - 1; k = k + 2)
    {
        int leftF, leftT, rightT, rightF;
        if (dp[i][k - 1][1] == -1)
        {
            leftT = parenthesis_count(s, i, k - 1, 1);
        } // Count no. of T in left partition
        else {
            leftT = dp[i][k - 1][1];
        }

        if (dp[k + 1][j][1] == -1)
        {
            rightT = parenthesis_count(s, k + 1, j, 1);
        } // Count no. of T in right partition
        else
        {
            rightT = dp[k + 1][j][1];
        }

        if (dp[i][k - 1][0] == -1)
        {
            // Count no. of F in left partition
            leftF = parenthesis_count(s, i, k - 1, 0);
        }
        else
        {
            leftF = dp[i][k - 1][0];
        }

        if (dp[k + 1][j][0] == -1)
        {
            // Count no. of F in right partition
            rightF = parenthesis_count(s, k + 1, j, 0);
        }
        else
        {
            rightF = dp[k + 1][j][0];
        }

        if (s[k] == '&')
        {
            if (isTrue == 1)
                ans += leftT * rightT;
            else
                ans += leftF * rightF + leftT * rightF
                       + leftF * rightT;
        }
        else if (s[k] == '|')
        {
            if (isTrue == 1)
                ans += leftT * rightT + leftT * rightF
                       + leftF * rightT;
            else
                ans = ans + leftF * rightF;
        }
        else if (s[k] == '^')
        {
            if (isTrue == 1)
                ans = ans + leftF * rightT + leftT * rightF;
            else
                ans = ans + leftT * rightT + leftF * rightF;
        }
        dp[i][j][isTrue] = ans;
    }
    return ans;
}

// Driver Code
int main()
{
    string symbols = "TTFT";
    string operators = "|&^";
    string s;
    int j = 0;

    for (int i = 0; i < symbols.length(); i++)
    {
        s.push_back(symbols[i]);
        if (j < operators.length())
            s.push_back(operators[j++]);
    }

    // We obtain the string  T|T&F^T
    int n = s.length();

    // There are 4 ways
    // ((T|T)&(F^T)), (T|(T&(F^T))), (((T|T)&F)^T) and
    // (T|((T&F)^T))
    memset(dp, -1, sizeof(dp));
    cout << parenthesis_count(s, 0, n - 1, 1);
    return 0;
}