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  • 网络流二·最大流最小割定理 HihoCoder

    网络流二·最大流最小割定理

     HihoCoder - 1378

      1 #include <bits/stdc++.h>
      2 using namespace std;
      3 const int maxv = 1010;
      4 const int maxe = 20010;
      5 const int inf = 0x3f3f3f3f;
      6 struct Edge{
      7     int u, v, nex;
      8     int cap, flow;
      9     Edge(int u=0, int v=0, int nex=0, int cap=0, int flow=0):
     10         u(u), v(v), nex(nex), cap(cap), flow(flow){}
     11 }e[maxe<<1];
     12 int head[maxv];
     13 int cnt;
     14 void init(){
     15     memset(head, -1, sizeof(head));
     16     cnt = 0;
     17 }
     18 
     19 void add(int u, int v, int cap){
     20     e[cnt] = Edge(u, v, head[u], cap, 0);
     21     head[u] = cnt++;
     22     e[cnt] = Edge(v, u, head[v], 0, 0);
     23     head[v] = cnt++;
     24 }
     25 
     26 int d[maxv], num[maxv], cur[maxv], p[maxv];
     27 int vis[maxv];
     28 int S, T;
     29 int N;
     30 
     31 void bfs(){
     32     memset(d, -1, sizeof(d));
     33     memset(vis, 0, sizeof(vis));
     34     queue<int> q;
     35     q.push(T);
     36     vis[T] = 1;
     37     d[T] = 0;
     38     while(!q.empty()){
     39         int u = q.front();
     40         q.pop();
     41         for(int i = head[u]; ~i; i = e[i].nex){
     42             int id = i&(-2);  //正边
     43             int v = e[id].u;
     44             if(!vis[v] && e[id].cap > e[id].flow){
     45                 vis[v] = 1;
     46                 d[v] = d[u] + 1;
     47                 q.push(v);
     48             }
     49         }
     50     }
     51 }
     52 
     53 int augment(){
     54     int u = T;
     55     int a = inf;
     56     while(u!=S){
     57         int id = p[u];
     58         a = min(a, e[id].cap - e[id].flow);
     59         u = e[id].u;
     60     }
     61     u = T;
     62     while(u!=S){
     63         int id = p[u];
     64         e[id].flow += a;
     65         e[id^1].flow -= a;
     66         u = e[id].u;
     67     }
     68     return a;
     69 }
     70 
     71 int ISAP(){
     72     bfs();
     73     int flow = 0;
     74     memset(num, 0, sizeof(num));
     75     for(int i = 0; i < N; i++){
     76         cur [i] = head[i];
     77         if(~d[i]) num[d[i]]++;
     78     }
     79     int u = S;
     80     while(d[S] < N){
     81         if(u == T){
     82             flow += augment();
     83             u = S;
     84         }
     85         int ok = 0;
     86         for(int i = cur[u]; ~i; i = e[i].nex){
     87             int v = e[i].v;
     88             if(d[u] == d[v]+1 && e[i].cap > e[i].flow){
     89                 p[v] = i;
     90                 ok = 1;
     91                 cur[u] = i;
     92                 u = v;
     93                 break;
     94             }
     95         }
     96         if(!ok){
     97             int m = N-1;
     98             for(int i = head[u]; ~i; i = e[i].nex){
     99                 if(e[i].cap > e[i].flow && ~d[e[i].v]) m = min(m, d[e[i].v]);
    100             }
    101             if(--num[d[u]] == 0) break;
    102             num[d[u]=m+1]++;
    103             cur[u] = head[u];
    104             if(u != S) u = e[p[u]].u;
    105         }
    106     }
    107     return flow;
    108 }
    109 vector<int> V;
    110 void dfs(int u){
    111     for(int i = head[u]; ~i; i = e[i].nex){
    112         int v = e[i].v;
    113         if(!vis[v]&&e[i].flow < e[i].cap){
    114             V.push_back(v);
    115             vis[v] = 1;
    116             dfs(v);
    117         }
    118     }
    119 }
    120 int main(){
    121     init();
    122     int n, m;
    123     scanf("%d %d", &n, &m);
    124     int u, v, cap;
    125     for(int i = 0; i < m; i++){
    126         scanf("%d %d %d", &u, &v, &cap);
    127         u--;v--;
    128         add(u, v, cap);
    129     }
    130     S = 0;
    131     T = n-1;
    132     N = n;
    133     int ans = ISAP();
    134     V.push_back(S);
    135     memset(vis, 0, sizeof(vis));
    136     vis[S] = 1;
    137     dfs(S);
    138     printf("%d %d
    %d",ans, V.size(), V[0]+1);
    139     for(int i = 1; i < V.size(); i++){
    140         printf(" %d", V[i]+1);
    141     }
    142     puts("");
    143 }
    View Code
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  • 原文地址:https://www.cnblogs.com/yijiull/p/7630978.html
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