HDU 3549 Flow Problem (dinic模版 && isap模版)

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=3549

题意：

给你一个有向图，问你1到n的最大流。

dinic模版 (n*n*m)

 #include <iostream>
 #include <cstdio>
 #include <cstring>
 using namespace std;
 const int N = ; //点个数
 const int M = ; //边个数
 const int inf = 0x3f3f3f3f;
 struct Edge {
     int to, next, cap, flow;
 }edge[M];
 int tot, head[N];
 void init() {
     tot = 0;
     memset(head, -, sizeof(head));
 }
 inline void add(int u, int v, int w, int rw = ) {
     edge[tot].to = v; edge[tot].cap = w; edge[tot].flow = ;
     edge[tot].next = head[u]; head[u] = tot++;
     edge[tot].to = u; edge[tot].cap = rw; edge[tot].flow = ;
     edge[tot].next = head[v]; head[v] = tot++;
 }
 int Q[N];
 int dep[N], cur[N], sta[N];
 bool bfs(int s, int t, int n) {
     int front = , tail = ;
     memset(dep, -, sizeof(dep[])*(n + ));
     dep[s] = ;
     Q[tail++] = s;
     while(front < tail) {
         int u = Q[front++];
         for(int i = head[u]; ~i; i = edge[i].next) {
             int v = edge[i].to;
             if(edge[i].cap > edge[i].flow && dep[v] == -) {
                 dep[v] = dep[u] + ;
                 if(v == t)
                     return true;
                 Q[tail++] = v;
             }
         }
     }
     return false;
 }

 int dinic(int s, int t, int n) {
     int maxflow = ;
     while(bfs(s, t, n)) {
         for(int i = ; i < n; ++i)
             cur[i] = head[i];
         int u = s, tail = ;
         while(cur[s] != -) {
             if(u == t) {
                 int tp = inf;
                 for(int i = tail - ; i >= ; --i) {
                     tp = min(tp, edge[sta[i]].cap - edge[sta[i]].flow);
                 }
                 maxflow += tp;
                 for(int i = tail - ; i >= ; --i) {
                     edge[sta[i]].flow += tp;
                     edge[sta[i] ^ ].flow -= tp;
                     if(edge[sta[i]].cap - edge[sta[i]].flow == )
                         tail = i;
                 }
                 u = edge[sta[tail] ^ ].to;
             } else if(cur[u] != - && edge[cur[u]].cap > edge[cur[u]].flow && dep[u] +  == dep[edge[cur[u]].to]) {
                 sta[tail++] = cur[u];
                 u = edge[cur[u]].to;
             } else {
                 while(u != s && cur[u] == -) {
                     u = edge[sta[--tail] ^ ].to;
                 }
                 cur[u] = edge[cur[u]].next;
             }
         }
     }
     return maxflow;
 }

 int main()
 {
     int t, n, m, u, v, c;
     scanf("%d", &t);
     for(int ca = ; ca <= t; ++ca) {
         scanf("%d %d", &n, &m);
         init();
         for(int i = ; i <= m; ++i) {
             scanf("%d %d %d", &u, &v, &c);
             add(u, v, c);
         }
         printf("Case %d: %d\n", ca, dinic(, n, n));
     }
     return ;
 }

貌似一般比dinic更优一点

 #include <iostream>
 #include <cstdio>
 #include <cstring>
 using namespace std;
 const int N = 1e3 + ;
 const int M = 1e4 + ;
 const int inf = 0x3f3f3f3f;
 struct Edge {
     int to, next, cap, flow;
 }edge[M];
 int tot, head[N], gap[N], dep[N], cur[N];
 void init() {
     tot = ;
     memset(head, -, sizeof(head));
 }
 void addedge(int u, int v, int w, int rw = ) {
     edge[tot].next = head[u]; edge[tot].to = v; edge[tot].cap = w; edge[tot].flow = ; head[u] = tot++;
     edge[tot].next = head[v]; edge[tot].to = u; edge[tot].cap = rw; edge[tot].flow = ; head[v] = tot++;
 }
 int Q[N];
 void bfs(int start, int end) {
     memset(dep, -, sizeof(dep));
     memset(gap, , sizeof(gap));
     gap[] = ;
     int front = , rear = ;
     dep[end] = ;
     Q[rear++] = end;
     while(front != rear) {
         int u = Q[front++];
         for(int i = head[u]; ~i; i = edge[i].next) {
             int v = edge[i].to;
             if(dep[v] != -)
                 continue;
             Q[rear++] = v;
             dep[v] = dep[u] + ;
             gap[dep[v]]++;
         }
     }
 }
 int S[N];
 int sap(int start, int end, int N) {
     bfs(start, end);
     memcpy(cur, head, sizeof(head));
     int top = ;
     int u = start;
     int ans = ;
     while(dep[start] < N) {
         if(u == end) {
             int Min = inf;
             int inser;
             for(int i = ; i < top; ++i) {
                 if(Min > edge[S[i]].cap - edge[S[i]].flow) {
                     Min = edge[S[i]].cap - edge[S[i]].flow;
                     inser = i;
                 }
             }
             for(int i = ; i < top; ++i) {
                 edge[S[i]].flow += Min;
                 edge[S[i] ^ ].flow -= Min;
             }
             ans += Min;
             top = inser;
             u = edge[S[top] ^ ].to;
             continue;
         }
         bool flag = false;
         int v;
         for(int i = cur[u]; ~i; i = edge[i].next) {
             v = edge[i].to;
             if(edge[i].cap - edge[i].flow && dep[v] +  == dep[u]) {
                 flag = true;
                 cur[u] = i;
                 break;
             }
         }
         if(flag) {
             S[top++] = cur[u];
             u = v;
             continue;
         }
         int Min = N;
         for(int i = head[u]; ~i; i = edge[i].next) {
             if(edge[i].cap - edge[i].flow && dep[edge[i].to] < Min) {
                 Min = dep[edge[i].to];
                 cur[u] = i;
             }
         }
         gap[dep[u]]--;
         if(!gap[dep[u]])
             return ans;
         dep[u] = Min + ;
         gap[dep[u]]++;
         if(u != start)
             u = edge[S[--top] ^ ].to;
     }
     return ans;
 }

 int main()
 {
     int t, n, m, u, v, c;
     scanf("%d", &t);
     for(int ca = ; ca <= t; ++ca) {
         scanf("%d %d", &n, &m);
         init();
         for(int i = ; i < m; ++i) {
             scanf("%d %d %d", &u, &v, &c);
             addedge(u, v, c);
         }
         printf("Case %d: %d\n", ca, sap(, n, n));
     }
     return ;
 }