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, 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;
}

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-8;
const LL inf = 0x7fffffff;
const LL infLL = 0x7fffffffffffffffLL;
const LL mod = 1e9 + 7;
const int maxN = 1e4 + 7;
const LL ONE = 1;
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 = 0;
        nxt = inf;
        next.clear();
        prev.clear();
        et = 0;
        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, 1, N) V[i].clear();
    E.clear();
    topo.clear();
    ans.clear();
}

void TopoSort() {
    SKI sk;
    For(i, 1, 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() - 1, 0) {
        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, 1, 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() - 1) cout << ans[i] << " " << ans[i + 1] << endl;
    } 
    return 0;
}