UVa442 Matrix Chain Multiplication

// UVa442 Matrix Chain Multiplication
// 题意：输入n个矩阵的维度和一些矩阵链乘表达式，输出乘法的次数。假定A和m*n的，B是n*p的，那么AB是m*p的，乘法次数为m*n*p
// 算法：用一个栈。遇到字母时入栈，右括号时出栈并计算，然后结果入栈。因为输入保证合法，括号无序入栈

 

#include<cstdio>
#include<stack>
#include<iostream>
#include<string>
using namespace std;

struct Matrix {
  int a, b;
  Matrix(int a=0, int b=0):a(a),b(b) {}
} m[26];

stack<Matrix> s;

int main() {
  int n;
  cin >> n;
  for(int i = 0; i < n; i++) {
    string name;
    cin >> name;
    int k = name[0] - 'A';
    cin >> m[k].a >> m[k].b;
  }
  string expr;
  while(cin >> expr) {
    int len = expr.length();
    bool error = false;
    int ans = 0;
    for(int i = 0; i < len; i++) {
      if(isalpha(expr[i])) s.push(m[expr[i] - 'A']);
      else if(expr[i] == ')') {
        Matrix m2 = s.top(); s.pop();
        Matrix m1 = s.top(); s.pop();
        if(m1.b != m2.a) { error = true; break; }
        ans += m1.a * m1.b * m2.b;
        s.push(Matrix(m1.a, m2.b));
      }
    }
    if(error) printf("error\n"); else printf("%d\n", ans);
  }

  return 0;
}