SDUTOJ 2498 数据结构实验之图论十一：AOE网上的关键路径

题目链接：http://acm.sdut.edu.cn/onlinejudge2/index.php/Home/Index/problemdetail/pid/2498.html

题目大意

　　略。

分析

　　注意！！！，此题只有一个源点，但有多个汇点。

　　这题本质上是求源点到汇点字典序的带权最长路，从前往后求比较麻烦，我们可以考虑从后往前求，求每个节点到某个汇点的最长距离和字典序最小的后继节点。

　　为此可先求拓扑序列，然后从后往前遍历拓扑序列，并进行松弛操作（同时也可以解决多汇点问题，SPFA则不行）。

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 < (int)(n); ++i)
 #define For(i,s,t) for (int i = (int)(s); i <= (int)(t); ++i)
 #define rFor(i,t,s) for (int i = (int)(t); i >= (int)(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 UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end())
 #define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end()); // 删去 x 中所有 c
 #define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower);
 #define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper);

 #define ms0(a) memset(a,0,sizeof(a))
 #define msI(a) memset(a,0x3f,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 T>
 ostream &operator<<(ostream &out, vector<T> &v) {
     Rep(i, v.size()) out << v[i] << " \n"[i == v.size()];
     return out;
 }

 template<typename T1, typename T2>
 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
     out << "[" << p.first << ", " << p.second << "]" << "\n";
     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, , BUF, stdin);
     return *bg++;
 } 

 inline int ri(){
     int x = , f = , c = gc();
     for(; c<||c>; f = c=='-'?-:f, c=gc());
     for(; c>&&c<; x = x* + c - , c=gc());
     return x*f;
 }

 template<class T>
 inline string toString(T x) {
     ostringstream sout;
     sout << x;
     return sout.str();
 }

 inline int toInt(string s) {
     int v;
     istringstream sin(s);
     sin >> v;
     return v;
 }

 //min <= aim <= max
 template<typename T>
 inline bool BETWEEN(const T aim, const T min, const T max) {
     return min <= aim && aim <= max;
 }

 typedef long long LL;
 typedef unsigned long long uLL;
 typedef vector< int > VI;
 typedef vector< bool > VB;
 typedef vector< char > VC;
 typedef vector< double > VD;
 typedef vector< string > VS;
 typedef vector< LL > VL;
 typedef vector< VI > VVI;
 typedef vector< VB > VVB;
 typedef vector< VS > VVS;
 typedef vector< VL > VVL;
 typedef vector< VVI > VVVI;
 typedef vector< VVL > VVVL;
 typedef pair< int, int > PII;
 typedef pair< LL, LL > PLL;
 typedef pair< int, string > PIS;
 typedef pair< string, int > PSI;
 typedef pair< string, string > PSS;
 typedef pair< double, double > PDD;
 typedef vector< PII > VPII;
 typedef vector< PLL > VPLL;
 typedef vector< VPII > VVPII;
 typedef vector< VPLL > VVPLL;
 typedef vector< VS > VVS;
 typedef map< int, int > MII;
 typedef unordered_map< int, int > uMII;
 typedef map< LL, LL > MLL;
 typedef map< string, int > MSI;
 typedef map< int, string > MIS;
 typedef set< int > SI;
 typedef stack< int > SKI;
 typedef queue< int > QI;
 typedef priority_queue< int > PQIMax;
 typedef priority_queue< int, VI, greater< int > > PQIMin;
 const double EPS = 1e-;
 const LL inf = 0x7fffffff;
 const LL infLL = 0x7fffffffffffffffLL;
 const LL mod = 1e9 + ;
 const int maxN = 1e4 + ;
 const LL ONE = ;
 const LL evenBits = 0xaaaaaaaaaaaaaaaa;
 const LL oddBits = 0x5555555555555555;

 struct Edge{
     int from, to, w;
     int et, lt;
 };

 istream& operator>> (istream& in, Edge &x) {
     in >> x.from >> x.to >> x.w;
     return in;
 }

 struct Vertex{
     int in, out, value, nxt;
     VI next, prev;
     int et, lt;

     void clear() {
         value = in = out = ;
         nxt = inf;
         next.clear();
         prev.clear();
         et = ;
         lt = inf;
     }
 };

 int N, M, S, T;
 Vertex V[maxN];
 vector< Edge > E;
 VI topo, ans;

 void addEdge(Edge &x) {
     V[x.from].next.PB(E.size());
     V[x.to].prev.PB(E.size());
     ++V[x.to].in;
     ++V[x.from].out;
     E.PB(x);
 }

 void init() {
     For(i, , N) V[i].clear();
     E.clear();
     topo.clear();
     ans.clear();
 }

 void TopoSort() {
     SKI sk;
     For(i, , N) if(!V[i].in) sk.push(i);

     while(!sk.empty()) {
         int tmp = sk.top(); sk.pop();

         topo.PB(tmp);
         Rep(i, V[tmp].next.size()) {
             Edge &e = E[V[tmp].next[i]];
             if(!--V[e.to].in) sk.push(e.to);
         }
     }
 }

 // 在拓扑排序的基础上松弛
 inline void relax() {
     rFor(i, topo.size() - , ) {
         Rep(j, V[topo[i]].prev.size()) {
             Edge &e = E[V[topo[i]].prev[j]];
             if(V[e.from].value < V[e.to].value + e.w || V[e.from].value == V[e.to].value + e.w && e.to < V[e.from].nxt) {
                 V[e.from].value = V[e.to].value + e.w;
                 V[e.from].nxt = e.to;
             }
         }
     }
 }

 int main(){
     //freopen("MyOutput.txt","w",stdout);
     //freopen("input.txt","r",stdin);
     INIT();
     while(cin >> N >> M) {
         init();
         For(i, , M) {
             Edge t;
             cin >> t;
             addEdge(t);
         }

         TopoSort();
         S = topo.front();
         T = topo.back();

         relax();

         int t = S;
         while(t != inf) {
             ans.PB(t);
             t = V[t].nxt;
         }

         cout << V[S].value << endl;
         Rep(i, ans.size() - ) cout << ans[i] << " " << ans[i + ] << endl;
     }
     return ;
 }