uva442

maksyuki 发表于 oj 分类，标签: 数据结构-栈/单调

28 1月 2018

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

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

error

10000

error

3500

15000

40500

47500

15125

题目类型：表达式计算(栈模拟)

算法分析：使用栈来模拟计算矩阵表达式

/**************************************************
filename       :m.cpp
author         :maksyuki
created time   :2018/1/28 10:26:00
last modified  :2018/1/28 10:48:24
file location  :C:\Users\abcd\Desktop\TheEternalPoet
***************************************************/

#pragma comment(linker, "/STACK:102400000,102400000")
#include <set>
#include <bitset>
#include <list>
#include <map>
#include <stack>
#include <queue>
#include <deque>
#include <string>
#include <vector>
#include <ios>
#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <algorithm>
#include <utility>
#include <complex>
#include <numeric>
#include <functional>
#include <cmath>
#include <ctime>
#include <climits>
#include <cstdarg>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cctype>
#include <cassert>
using namespace std;

#define CFF freopen ("in", "r", stdin)
#define CFO freopen ("out", "w", stdout)
#define CPPFF ifstream cin ("in")
#define CPPFO ofstream cout ("out")
#define	DB(ccc)	cout << #ccc << " = " << ccc << endl
#define	DBT printf("time used: %.2lfs\n", (double) clock() / CLOCKS_PER_SEC)
#define PB push_back
#define MP(A, B) make_pair(A, B)

typedef long long LL;
typedef unsigned long long ULL;
typedef double DB;
typedef pair <int, int> PII;
typedef pair <int, bool> PIB;

const int INF = 0x7F7F7F7F;
const int MOD = 1e9 + 7;
const double EPS = 1e-10;
const double PI = 2 * acos (0.0);
const int maxn = 1e5 + 6666;

PII aa[maxn];

int main()
{
#ifdef LOCAL
    CFF;
    //CFO;
#endif
    
    int n;
    cin >> n;
        
    string s;
    int va, vb; 
    for(int i = 1; i <= n; i++) {
        cin >> s >> va >> vb;
        aa[s[0]-'A'].first = va;
        aa[s[0]-'A'].second = vb;
    }

    while(cin >> s) {
        bool is_valid = true;
        stack<int> sta;
        LL ans = 0;
        for(int i = 0; s[i]; i++) {
            if(s[i] == ')') {
                int ta = sta.top(); sta.pop();
                int tb = sta.top(); sta.pop();
                sta.pop();
                int ra = aa[tb-'A'].first, ca = aa[tb-'A'].second;
                int rb = aa[ta-'A'].first, cb = aa[ta-'A'].second;
                if(ca == rb) {
                    ans += ra * ca * cb;
                    aa[36+i].first = ra; 
                    aa[36+i].second = cb; 
                    sta.push(36+i+'A');
                }
                else {
                    is_valid = false;
                    break;
                }
            }
            else sta.push(s[i]);
        }

        if(is_valid) cout << ans << endl;
        else cout << "error" << endl;
    }
    return 0;
}

100

101

102

103

104

105

106

107

108

109

110

/**************************************************

filename :m.cpp

author :maksyuki

created time :2018/1/28 10:26:00

last modified :2018/1/28 10:48:24

file location :C:\Users\abcd\Desktop\TheEternalPoet

***************************************************/

#pragma comment(linker, "/STACK:102400000,102400000")

#include <set>

#include <bitset>

#include <list>

#include <map>

#include <stack>

#include <queue>

#include <deque>

#include <string>

#include <vector>

#include <ios>

#include <iostream>

#include <fstream>

#include <sstream>

#include <iomanip>

#include <algorithm>

#include <utility>

#include <complex>

#include <numeric>

#include <functional>

#include <cmath>

#include <ctime>

#include <climits>

#include <cstdarg>

#include <cstdio>

#include <cstdlib>

#include <cstring>

#include <cctype>

#include <cassert>

using namespace std;

#define CFF freopen ("in", "r", stdin)

#define CFO freopen ("out", "w", stdout)

#define CPPFF ifstream cin ("in")

#define CPPFO ofstream cout ("out")

#define DB(ccc) cout << #ccc << " = " << ccc << endl

#define DBT printf("time used: %.2lfs\n", (double) clock() / CLOCKS_PER_SEC)

#define PB push_back

#define MP(A, B) make_pair(A, B)

typedef long long LL;

typedef unsigned long long ULL;

typedef double DB;

typedef pair <int, int> PII;

typedef pair <int, bool> PIB;

const int INF = 0x7F7F7F7F;

const int MOD = 1e9 + 7;

const double EPS = 1e-10;

const double PI = 2 * acos (0.0);

const int maxn = 1e5 + 6666;

PII aa[maxn];

int main()

{

#ifdef LOCAL

CFF;

//CFO;

#endif

int n;

cin >> n;

string s;

int va, vb;

for(int i = 1; i <= n; i++) {

cin >> s >> va >> vb;

aa[s[0]-'A'].first = va;

aa[s[0]-'A'].second = vb;

}

while(cin >> s) {

bool is_valid = true;

stack<int> sta;

LL ans = 0;

for(int i = 0; s[i]; i++) {

if(s[i] == ')') {

int ta = sta.top(); sta.pop();

int tb = sta.top(); sta.pop();

sta.pop();

int ra = aa[tb-'A'].first, ca = aa[tb-'A'].second;

int rb = aa[ta-'A'].first, cb = aa[ta-'A'].second;

if(ca == rb) {

ans += ra * ca * cb;

aa[36+i].first = ra;

aa[36+i].second = cb;

sta.push(36+i+'A');

}

else {

is_valid = false;

break;

}

else sta.push(s[i]);

}

if(is_valid) cout << ans << endl;

else cout << "error" << endl;

}

return 0;

}

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