uva442-Matrix Chain Multiplication

最新推荐文章于 2021-01-27 17:18:44 发布

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最新推荐文章于 2021-01-27 17:18:44 发布

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本文探讨了矩阵链乘法问题，通过分析不同计算顺序对基本乘法操作次数的影响，提出了一个程序来确定给定计算策略所需的最小基本乘法次数。通过实例展示了如何通过正确的顺序减少乘法操作数量。

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Matrix Chain Multiplication

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 ( ), 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

这题的解题思路类似于加减乘除运算

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

struct mat{
	int row;
	int column;
};
stack<char> st1;
stack<mat> st2;
map<char, int> rows, columns;
int main(void){
	string s;
	char c;
	int r, l;
	int num;

#ifndef ONLINE_JUDGE
	freopen("f:\\infile.txt","r",stdin);
#endif

	cin >> num;
	while(num--){
		cin >> c >> r >> l;
		rows[c] = r;
		columns[c] = l;
	}

	cin.ignore(10, '\n');
	while(getline(cin, s)){
		int flag = 0;
		int mulTime = 0;
		while(st2.size())
			st2.pop();
		for(int i = 0; i < s.size(); i++){
			if(s[i] == '('){
				st1.push(s[i]);
			}
			else if(s[i] == ')'){
				mat x, y;
				y = st2.top();
				st2.pop();
				x = st2.top();
				st2.pop();
				if(x.column != y.row){
					cout << "error" << endl;
					flag = 1;
					break;
				}
				mat temp;
				temp.row = x.row;
				temp.column = y.column;
				st2.push(temp);
				mulTime += (x.row*x.column*y.column);
			}
			else{
				mat temp;
				temp.row = rows[s[i]];
				temp.column = columns[s[i]];
				st2.push(temp);
			}
		}
		if(flag == 0)
			cout << mulTime << endl;
	}
	return 0;
}