zoj1094 Matrix Chain Multiplication 模拟

Matrix Chain Multiplication

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Time Limit: 2 Seconds       Memory Limit: 65536 KB

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Matrix multiplication problem is a typical example of dynamical programming.

Suppose you have to evaluate an expression like A*B*C*D*E where A,B,C,D and E are matrices. Since matrix multiplication is associative, the order in which multiplications are performed is arbitrary. However, the number of elementary multiplications needed strongly depends on the evaluation order you choose. For example, let A be a 50*10 matrix, B a 10*20 matrix and C a 20*5 matrix. There are two different strategies to compute A*B*C, namely (A*B)*C and A*(B*C). The first one takes 15000 elementary multiplications, but the second one only 3500.

Your job is to write a program that determines the number of elementary multiplications needed for a given evaluation strategy.

Input Specification

Input consists of two parts: a list of matrices and a list of expressions. The first line of the input file contains one integer  n  (1 <=  n  <= 26), representing the number of matrices in the first part. The next  n  lines each contain one capital letter, specifying the name of the matrix, and two integers, specifying the number of rows and columns of the matrix.  The second part of the input file strictly adheres to the following syntax (given in EBNF):

SecondPart = Line { Line } <EOF> Line = Expression <CR> Expression = Matrix | "(" Expression Expression ")" Matrix = "A" | "B" | "C" | ... | "X" | "Y" | "Z"

Output Specification

For each expression found in the second part of the input file, print one line containing the word "error" if evaluation of the expression leads to an error due to non-matching matrices. Otherwise print one line containing the number of elementary multiplications needed to evaluate the expression in the way specified by the parentheses.

Sample Input

9 A 50 10 B 10 20 C 20 5 D 30 35 E 35 15 F 15 5 G 5 10 H 10 20 I 20 25 A B C (AA) (AB) (AC) (A(BC)) ((AB)C) (((((DE)F)G)H)I) (D(E(F(G(HI))))) ((D(EF))((GH)I))

Sample Output

0 0 0 error 10000 error 3500 15000 40500 47500

15125

import java.io.BufferedInputStream; import java.io.PrintWriter; import java.util.HashMap; import java.util.Map; import java.util.Scanner; import java.util.Stack; public class Main { public static void main(String[] args) { new Task().solve(); } } class Task { Scanner in = new Scanner(new BufferedInputStream(System.in)) ; PrintWriter out = new PrintWriter(System.out); class Node{ long row , col ; Node(long row , long col){ this.row = row ; this.col = col ; } } Map<Character , Node> hash = new HashMap<Character, Task.Node>() ; String calc(String expre){ Stack<Node> stk = new Stack<Node>() ; long sum = 0 ; for(char c : expre.toCharArray()){ if(')' == c){ if(stk.size() < 3){ return "error" ; } Node right = stk.pop() ; Node left = stk.pop() ; if(left.row == -1 || right.row == -1 || left.col != right.row){ return "error" ; } sum += left.row * left.col * right.col ; if(stk.pop().row != -1){ return "error" ; } stk.push(new Node(left.row , right.col)) ; } else{ Node node = hash.get(c) ; if(node == null){ return "error" ; } stk.push(node) ; } } if(stk.size() == 1 && stk.pop().row != -1){ return String.valueOf(sum) ; } return "error" ; } void solve() { hash.clear() ; hash.put('(' , new Node(-1, -1)) ; int n = in.nextInt() ; while(n-- > 0){ hash.put(in.next().charAt(0), new Node(in.nextLong(), in.nextLong())) ; } while(in.hasNext()){ out.println(calc(in.next())) ; //out.flush(); } out.flush(); } }