UVA 442 Matrix Chain Multiplication

题目链接：https://vjudge.net/problem/UVA-442

题目大意

　　给定 n 个矩阵， 计算只包含这 n 个矩阵的一个矩阵表达式进行矩阵乘法运算所需要的乘法次数，表达式不合法就输出“error”。

分析

　　栈结构模板题。

代码如下

#include <bits/stdc++.h>
using namespace std;
 
#define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define Rep(i,n) for (int i = 0; i < (n); ++i)
#define For(i,s,t) for (int i = (s); i <= (t); ++i)
#define rFor(i,t,s) for (int i = (t); i >= (s); --i)
#define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)
#define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)
#define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)
#define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)
 
#define pr(x) cout << #x << " = " << x << "  "
#define prln(x) cout << #x << " = " << x << endl
 
#define LOWBIT(x) ((x)&(-x))
 
#define ALL(x) x.begin(),x.end()
#define INS(x) inserter(x,x.begin())
 
#define ms0(a) memset(a,0,sizeof(a))
#define msI(a) memset(a,inf,sizeof(a))
#define msM(a) memset(a,-1,sizeof(a))

#define MP make_pair
#define PB push_back
#define ft first
#define sd second
 
template<typename T1, typename T2>
istream &operator>>(istream &in, pair<T1, T2> &p) {
    in >> p.first >> p.second;
    return in;
}
 
template<typename T>
istream &operator>>(istream &in, vector<T> &v) {
    for (auto &x: v)
        in >> x;
    return in;
}
 
template<typename T1, typename T2>
ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
    out << "[" << p.first << ", " << p.second << "]" << "
";
    return out;
}

inline int gc(){
    static const int BUF = 1e7;
    static char buf[BUF], *bg = buf + BUF, *ed = bg;
    
    if(bg == ed) fread(bg = buf, 1, BUF, stdin);
    return *bg++;
} 

inline int ri(){
    int x = 0, f = 1, c = gc();
    for(; c<48||c>57; f = c=='-'?-1:f, c=gc());
    for(; c>47&&c<58; x = x*10 + c - 48, c=gc());
    return x*f;
}
 
typedef long long LL;
typedef unsigned long long uLL;
typedef pair< double, double > PDD;
typedef pair< int, int > PII;
typedef pair< int, PII > PIPII;
typedef pair< string, int > PSI;
typedef pair< int, PSI > PIPSI;
typedef set< int > SI;
typedef vector< int > VI;
typedef vector< VI > VVI;
typedef vector< PII > VPII;
typedef map< int, int > MII;
typedef map< int, PII > MIPII;
typedef map< string, int > MSI;
typedef multimap< int, int > MMII;
typedef unordered_map< int, int > uMII;
typedef pair< LL, LL > PLL;
typedef vector< LL > VL;
typedef vector< VL > VVL;
typedef priority_queue< int > PQIMax;
typedef priority_queue< int, VI, greater< int > > PQIMin;
const double EPS = 1e-10;
const LL inf = 0x7fffffff;
const LL infLL = 0x7fffffffffffffffLL;
const LL mod = 1e9 + 7;
const int maxN = 1e5 + 7;
const LL ONE = 1;
const LL evenBits = 0xaaaaaaaaaaaaaaaa;
const LL oddBits = 0x5555555555555555;

int n, ans;

struct Matrix{
    int r, c;
    
    Matrix() {}
    Matrix(int row, int col) : r(row), c(col) {}
    
    Matrix operator* (const Matrix &x) const {
        if(r == -2) return x;
        if(x.r == -2) return *this;
        if(c != x.r) {
            ans = -1;
            return Matrix(-1, -1);
        }
        ans += r * c * x.c;
        return Matrix(r, x.c);
    }
};

map< int, Matrix > id_mat;
string expr; // 表达式 
int lbra; // 左括号数量计数器 
stack< Matrix > sm; // 手动压栈(结果栈) 

int main(){
    //freopen("MyOutput.txt","w",stdout);
    INIT();
    cin >> n;
    Rep(i, n) {
        string tmp;
        int x, y;
        cin >> tmp >> x >> y;
        id_mat[tmp[0]] = Matrix(x, y);
    }
    
    while(cin >> expr) {
        expr = "(" + expr + ")";
        ans = 0;
        lbra = 0;
        
        Matrix tmp(-2, -2);
        Rep(pos, expr.size()) {
            if(-1 == ans) break;
            if(expr[pos] == '(') {
                ++lbra;
                sm.push(tmp);
                tmp = Matrix(-2, -2);
            }
            else if(expr[pos] == ')'){
                --lbra;
                tmp = sm.top() * tmp;
                sm.pop();
            }
            else tmp = tmp * id_mat[expr[pos]];
        }
        
        if(-1 == ans || lbra) cout << "error" << endl;
        else cout << ans << endl;
    }
    return 0;
}