Zoj 1094 Poj 2246 矩阵链乘法如何用堆栈实现？
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本文共计701个文字，预计阅读时间需要3分钟。
题目：矩阵链乘时间限制：1000MS 内存限制：65536K 总提交：1695 接受：1090
描述：假设你需要评估一个表达式，如 A*AB*AC*AD*AE，其中 A、B、C、D 和 E 是矩阵。由于矩阵乘法是 i×j×k 的操作，所以矩阵链乘问题旨在找到一种最优的乘法顺序，以最小化总操作次数。
Matrix Chain Multiplication
Time Limit: 1000MS
Memory Limit: 65536K
Total Submissions: 1695
Accepted: 1090
Description
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
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 } Line = Expression Expression = Matrix | "(" Expression Expression ")"Matrix = "A" | "B" | "C" | ... | "X" | "Y" | "Z"
Output
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
9A 50 10B 10 20C 20 5D 30 35E 35 15F 15 5G 5 10H 10 20I 20 25ABC(AA)(AB)(AC)(A(BC))((AB)C)(((((DE)F)G)H)I)(D(E(F(G(HI)))))((D(EF))((GH)I))
Sample Output
000error10000error350015000405004750015125
Source
Ulm Local 1996
Source CodeProblem: 2246 User: nealgavin Memory: 252K Time: 0MS Language: C++ Result: Accepted Source Code #include<iostream>#include<cstring>#include<stack>#include<map>using namespace std;class node{ public:int row,col;};map<char,node>matri;stack<node>array;int main(){ int n; char name; cin>>n; for(int i=0;i<n;i++) { cin>>name;cin>>matri[name].row>>matri[name].col; } char css[123]; while(cin>>css) { int len=strlen(css); int count=0;bool flag=0; for(int i=0;i<len;i++) { if(css[i]=='(')continue; else if(css[i]==')') { node a=array.top();array.pop(); node b=array.top();array.pop(); if(b.col!=a.row){flag=1;cout<<"error\n";break;} else {count+=b.row*b.col*a.col;b.col=a.col;array.push(b);} } else array.push(matri[css[i]]); } if(!flag) cout<<count<<"\n"; }}
本文共计701个文字，预计阅读时间需要3分钟。
题目：矩阵链乘时间限制：1000MS 内存限制：65536K 总提交：1695 接受：1090
描述：假设你需要评估一个表达式，如 A*AB*AC*AD*AE，其中 A、B、C、D 和 E 是矩阵。由于矩阵乘法是 i×j×k 的操作，所以矩阵链乘问题旨在找到一种最优的乘法顺序，以最小化总操作次数。
Matrix Chain Multiplication
Time Limit: 1000MS
Memory Limit: 65536K
Total Submissions: 1695
Accepted: 1090
Description
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
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 } Line = Expression Expression = Matrix | "(" Expression Expression ")"Matrix = "A" | "B" | "C" | ... | "X" | "Y" | "Z"
Output
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
9A 50 10B 10 20C 20 5D 30 35E 35 15F 15 5G 5 10H 10 20I 20 25ABC(AA)(AB)(AC)(A(BC))((AB)C)(((((DE)F)G)H)I)(D(E(F(G(HI)))))((D(EF))((GH)I))
Sample Output
000error10000error350015000405004750015125
Source
Ulm Local 1996
Source CodeProblem: 2246 User: nealgavin Memory: 252K Time: 0MS Language: C++ Result: Accepted Source Code #include<iostream>#include<cstring>#include<stack>#include<map>using namespace std;class node{ public:int row,col;};map<char,node>matri;stack<node>array;int main(){ int n; char name; cin>>n; for(int i=0;i<n;i++) { cin>>name;cin>>matri[name].row>>matri[name].col; } char css[123]; while(cin>>css) { int len=strlen(css); int count=0;bool flag=0; for(int i=0;i<len;i++) { if(css[i]=='(')continue; else if(css[i]==')') { node a=array.top();array.pop(); node b=array.top();array.pop(); if(b.col!=a.row){flag=1;cout<<"error\n";break;} else {count+=b.row*b.col*a.col;b.col=a.col;array.push(b);} } else array.push(matri[css[i]]); } if(!flag) cout<<count<<"\n"; }}