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

  1 #include <bits/stdc++.h>
  2 using namespace std;
  3  
  4 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
  5 #define Rep(i,n) for (int i = 0; i < (n); ++i)
  6 #define For(i,s,t) for (int i = (s); i <= (t); ++i)
  7 #define rFor(i,t,s) for (int i = (t); i >= (s); --i)
  8 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)
  9 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)
 10 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)
 11 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)
 12  
 13 #define pr(x) cout << #x << " = " << x << "  "
 14 #define prln(x) cout << #x << " = " << x << endl
 15  
 16 #define LOWBIT(x) ((x)&(-x))
 17  
 18 #define ALL(x) x.begin(),x.end()
 19 #define INS(x) inserter(x,x.begin())
 20  
 21 #define ms0(a) memset(a,0,sizeof(a))
 22 #define msI(a) memset(a,inf,sizeof(a))
 23 #define msM(a) memset(a,-1,sizeof(a))
 24 
 25 #define MP make_pair
 26 #define PB push_back
 27 #define ft first
 28 #define sd second
 29  
 30 template<typename T1, typename T2>
 31 istream &operator>>(istream &in, pair<T1, T2> &p) {
 32     in >> p.first >> p.second;
 33     return in;
 34 }
 35  
 36 template<typename T>
 37 istream &operator>>(istream &in, vector<T> &v) {
 38     for (auto &x: v)
 39         in >> x;
 40     return in;
 41 }
 42  
 43 template<typename T1, typename T2>
 44 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
 45     out << "[" << p.first << ", " << p.second << "]" << "\n";
 46     return out;
 47 }
 48 
 49 inline int gc(){
 50     static const int BUF = 1e7;
 51     static char buf[BUF], *bg = buf + BUF, *ed = bg;
 52     
 53     if(bg == ed) fread(bg = buf, 1, BUF, stdin);
 54     return *bg++;
 55 } 
 56 
 57 inline int ri(){
 58     int x = 0, f = 1, c = gc();
 59     for(; c<48||c>57; f = c=='-'?-1:f, c=gc());
 60     for(; c>47&&c<58; x = x*10 + c - 48, c=gc());
 61     return x*f;
 62 }
 63  
 64 typedef long long LL;
 65 typedef unsigned long long uLL;
 66 typedef pair< double, double > PDD;
 67 typedef pair< int, int > PII;
 68 typedef pair< int, PII > PIPII;
 69 typedef pair< string, int > PSI;
 70 typedef pair< int, PSI > PIPSI;
 71 typedef set< int > SI;
 72 typedef vector< int > VI;
 73 typedef vector< VI > VVI;
 74 typedef vector< PII > VPII;
 75 typedef map< int, int > MII;
 76 typedef map< int, PII > MIPII;
 77 typedef map< string, int > MSI;
 78 typedef multimap< int, int > MMII;
 79 typedef unordered_map< int, int > uMII;
 80 typedef pair< LL, LL > PLL;
 81 typedef vector< LL > VL;
 82 typedef vector< VL > VVL;
 83 typedef priority_queue< int > PQIMax;
 84 typedef priority_queue< int, VI, greater< int > > PQIMin;
 85 const double EPS = 1e-10;
 86 const LL inf = 0x7fffffff;
 87 const LL infLL = 0x7fffffffffffffffLL;
 88 const LL mod = 1e9 + 7;
 89 const int maxN = 1e5 + 7;
 90 const LL ONE = 1;
 91 const LL evenBits = 0xaaaaaaaaaaaaaaaa;
 92 const LL oddBits = 0x5555555555555555;
 93 
 94 int n, ans;
 95 
 96 struct Matrix{
 97     int r, c;
 98     
 99     Matrix() {}
100     Matrix(int row, int col) : r(row), c(col) {}
101     
102     Matrix operator* (const Matrix &x) const {
103         if(r == -2) return x;
104         if(x.r == -2) return *this;
105         if(c != x.r) {
106             ans = -1;
107             return Matrix(-1, -1);
108         }
109         ans += r * c * x.c;
110         return Matrix(r, x.c);
111     }
112 };
113 
114 map< int, Matrix > id_mat;
115 string expr; // 表达式 
116 int lbra; // 左括号数量计数器 
117 stack< Matrix > sm; // 手动压栈(结果栈) 
118 
119 int main(){
120     //freopen("MyOutput.txt","w",stdout);
121     INIT();
122     cin >> n;
123     Rep(i, n) {
124         string tmp;
125         int x, y;
126         cin >> tmp >> x >> y;
127         id_mat[tmp[0]] = Matrix(x, y);
128     }
129     
130     while(cin >> expr) {
131         expr = "(" + expr + ")";
132         ans = 0;
133         lbra = 0;
134         
135         Matrix tmp(-2, -2);
136         Rep(pos, expr.size()) {
137             if(-1 == ans) break;
138             if(expr[pos] == '(') {
139                 ++lbra;
140                 sm.push(tmp);
141                 tmp = Matrix(-2, -2);
142             }
143             else if(expr[pos] == ')'){
144                 --lbra;
145                 tmp = sm.top() * tmp;
146                 sm.pop();
147             }
148             else tmp = tmp * id_mat[expr[pos]];
149         }
150         
151         if(-1 == ans || lbra) cout << "error" << endl;
152         else cout << ans << endl;
153     }
154     return 0;
155 }

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