uva442-Matrix Chain Multiplication
2014-07-13 15:29
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Matrix Chain Multiplication |
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 (
![](http://uva.onlinejudge.org/external/4/442img1.gif)
), 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 printone 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
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;
}
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