Matrix Chain Multiplication [Parenthesization Evaluation]

// Matrix Chain Multiplication, Parenthesization Evaluation
// Given the dimensions of "N" number of matrices and the Parenthesization (Multiplication Procedure), have to find the number of multiplications operations required for these "N" matrices using the given procedure.
/* Sample Input: 10 20 30 40 50
                ( 1 ( 2 3 ) 4 ) [Spaces are mandatory]
*/


#include <iostream>
#include <string>
#include <sstream>
#define SIZE 100

using namespace std;

struct matrix {
    int row;
    int col;
};


class stack {
private:
    struct matrix M;
    class stack *next;
public:
    stack(): next(NULL) {}
    ~stack() {}

    class stack *push (struct matrix m) {
        class stack *temp = new stack;
        temp -> M = m;
        temp -> next = this;
        return temp;
    }

    class stack *pop() {
        if (this != NULL) {
            class stack *temp = this -> next;
            delete this;
            return temp;
        }
        else
            return this;
    }

    struct matrix top() {
        if (this != NULL)
            return this -> M;
        else {
            struct matrix X;
            X.row = 0;
            X.col = 0;
            return X;
        }
    }
};

int main() {
    string line;
    cout << "Enter the P Values: ";
    getline(cin, line);

    istringstream Pv(line);
    int N = -1;
    int P[SIZE];
    while (Pv >> line)
        stringstream(line) >> P[++N];


    struct matrix M[SIZE];
    for (int i = 0; i < N; i++) {
        M[i].row = P[i];
        M[i].col = P[i + 1];
    }

    cout << "Enter the Expression: ";
    getline(cin, line);
    istringstream Exp(line);

    struct matrix a, b, c;
    class stack *S = NULL;

    int x, sum = 0;
    while (Exp >> line) {
        if (line == ")") {
            a = S -> top();
            S = S -> pop();
            b = S -> top();
            S = S -> pop();
            sum += b.row * a.row * a.col;
            c.row = b.row;
            c.col = a.col;
            S = S -> push(c);
        }
        else if (line != "(") {
            stringstream(line) >> x;
            S = S -> push (M[x - 1]);
        }
    }

    cout << "Number of Multiplication Required: " << sum << endl;

    return 0;
}