网络流模板 NetworkFlow

时间：2016-12-27 22:25:52 阅读：277 评论：0 收藏：0 [点我收藏+]

身边的小伙伴们都在愉快地刷网络流，我也来写一发模板好了。

Network Flow - Maximum Flow

Time Limit : 1 sec, Memory Limit : 65536 KB
Japanese version is here

Maximum Flow

A flow network is a directed graph which has a

Input

A flow network is given in the following format.

Output

Print the maximum flow.

Constraints

Sample Input 1

Sample Output 1

  1 #include <bits/stdc++.h>
  2 
  3 #define fread_siz 1024
  4 
  5 inline int get_c(void)
  6 {
  7     static char buf[fread_siz];
  8     static char *head = buf + fread_siz;
  9     static char *tail = buf + fread_siz;
 10 
 11     if (head == tail)
 12         fread(head = buf, 1, fread_siz, stdin);
 13 
 14     return *head++;
 15 }
 16 
 17 inline int get_i(void)
 18 {
 19     register int ret = 0;
 20     register int neg = false;
 21     register int bit = get_c();
 22 
 23     for (; bit < 48; bit = get_c())
 24         if (bit == ‘-‘)neg ^= true;
 25 
 26     for (; bit > 47; bit = get_c())
 27         ret = ret * 10 + bit - 48;
 28 
 29     return neg ? -ret : ret;
 30 }
 31 
 32 template <class T>
 33 inline T min(T a, T b)
 34 {
 35     return a < b ? a : b;
 36 }
 37 
 38 const int inf = 2e9;
 39 const int maxn = 20005;
 40 
 41 int n, m;
 42 int s, t;
 43 
 44 int edges;
 45 int hd[maxn];
 46 int to[maxn];
 47 int nt[maxn];
 48 int fl[maxn];
 49 
 50 inline void add(int u, int v, int f)
 51 {
 52     nt[edges] = hd[u]; to[edges] = v; fl[edges] = f; hd[u] = edges++;
 53     nt[edges] = hd[v]; to[edges] = u; fl[edges] = 0; hd[v] = edges++;
 54 }
 55 
 56 int dep[maxn];
 57 
 58 inline bool bfs(void)
 59 {
 60     static int que[maxn];
 61     static int head, tail;
 62     
 63     memset(dep, 0, sizeof(dep));
 64     head = 0, tail = 0;
 65     que[tail++] = s;
 66     dep[s] = 1;
 67     
 68     while (head != tail)
 69     {
 70         int u = que[head++], v;
 71         for (int i = hd[u]; ~i; i = nt[i])
 72             if (!dep[v = to[i]] && fl[i])
 73                 dep[v] = dep[u] + 1, que[tail++] = v;
 74     }
 75     
 76     return dep[t];
 77 }
 78 
 79 inline int dfs(int u, int f)
 80 {
 81     if (u == t || !f)
 82         return f;
 83     
 84     int used = 0, flow, v;
 85     
 86     for (int i = hd[u]; ~i; i = nt[i])
 87         if (dep[v = to[i]] == dep[u] + 1 && fl[i])
 88         {
 89             flow = dfs(v, min(f - used, fl[i]));
 90             
 91             used += flow;
 92             fl[i] -= flow;
 93             fl[i^1] += flow;
 94             
 95             if (used == f)
 96                 return f;
 97         }
 98         
 99     if (!used)
100         dep[u] = 0;
101         
102     return used;
103 }
104 
105 inline int dinic(void)
106 {
107     int maxFlow = 0, newFlow;
108     
109     while (bfs())
110         while (newFlow = dfs(s, inf))
111             maxFlow += newFlow;
112             
113     return maxFlow;
114 }
115 
116 signed main(void)
117 {
118     n = get_i();
119     m = get_i();
120     
121     memset(hd, -1, sizeof(hd));
122     
123     for (int i = 1; i <= m; ++i)
124     {
125         int u = get_i();
126         int v = get_i();
127         int f = get_i();
128         add(u, v, f);
129     }
130     
131     s = 0, t = n - 1;
132     
133     printf("%d\n", dinic());
134 }

Network Flow - Minimum Cost Flow

Time Limit : 1 sec, Memory Limit : 65536 KB

最小費用流

各辺にコストが設定されたフローネットワークにおいて、始点 $s$

フローネットワークの各辺 $e$

入力

フローネットワーク $G (V, E)$

$| V | | E | F$

$| V |$

$u_{i}$

出力

最小費用流を１行に出力する。ただし、始点 $s$

制約

2 ≤ $| V |$
1 ≤ $| E |$
0 ≤ $F$
0 ≤ $c_{i}$
$u_{i}$
頂点 $x$

入力例

出力例

  1 #include <bits/stdc++.h>
  2 
  3 #define fread_siz 1024
  4 
  5 inline int get_c(void)
  6 {
  7     static char buf[fread_siz];
  8     static char *head = buf + fread_siz;
  9     static char *tail = buf + fread_siz;
 10 
 11     if (head == tail)
 12         fread(head = buf, 1, fread_siz, stdin);
 13 
 14     return *head++;
 15 }
 16 
 17 inline int get_i(void)
 18 {
 19     register int ret = 0;
 20     register int neg = false;
 21     register int bit = get_c();
 22 
 23     for (; bit < 48; bit = get_c())
 24         if (bit == ‘-‘)neg ^= true;
 25 
 26     for (; bit > 47; bit = get_c())
 27         ret = ret * 10 + bit - 48;
 28 
 29     return neg ? -ret : ret;
 30 }
 31 
 32 template <class T>
 33 inline T min(T a, T b)
 34 {
 35     return a < b ? a : b;
 36 }
 37 
 38 const int inf = 2e9;
 39 const int maxn = 2005;
 40 
 41 int n, m;
 42 int s, t;
 43 int flow;
 44 
 45 int edges;
 46 int hd[maxn];
 47 int nt[maxn];
 48 int to[maxn];
 49 int vl[maxn];
 50 int fl[maxn];
 51 
 52 inline void add(int u, int v, int f, int w)
 53 {
 54     nt[edges] = hd[u]; to[edges] = v; fl[edges] = f; vl[edges] = +w; hd[u] = edges++;
 55     nt[edges] = hd[v]; to[edges] = u; fl[edges] = 0; vl[edges] = -w; hd[v] = edges++;
 56 }
 57 
 58 int dis[maxn];
 59 int pre[maxn];
 60 
 61 inline bool spfa(void)
 62 {
 63     static int que[maxn];
 64     static int inq[maxn];
 65     static int head, tail;
 66     
 67     memset(dis, 0x3f, sizeof(dis));
 68     head = 0, tail = 0;
 69     que[tail++] = s;
 70     pre[s] = -1;
 71     inq[s] = 1;
 72     dis[s] = 0;
 73     
 74     while (head != tail)
 75     {
 76         int u = que[head++], v; inq[u] = 0;
 77         
 78         for (int i = hd[u]; ~i; i = nt[i])
 79             if (dis[v = to[i]] > dis[u] + vl[i] && fl[i])
 80             {
 81                 dis[v] = dis[u] + vl[i];
 82                 pre[v] = i ^ 1;
 83                 if (!inq[v])
 84                     inq[v] = 1, que[tail++] = v;
 85             }
 86     }
 87     
 88     return dis[t] < 0x3f3f3f3f;
 89 }
 90 
 91 inline int expend(void)
 92 {
 93     int newFlow = inf;
 94     
 95     for (int i = pre[t]; ~i; i = pre[to[i]])
 96         newFlow = min(newFlow, fl[i ^ 1]);
 97         
 98     for (int i = pre[t]; ~i; i = pre[to[i]])
 99         fl[i] += newFlow, fl[i^1] -= newFlow;
100         
101     return flow -= newFlow, newFlow * dis[t];
102 }
103 
104 inline int mcmf(void)
105 {
106     int ret = 0;
107     
108     while (spfa())
109         ret += expend();
110         
111     return flow ? -1 : ret;
112 }
113 
114 signed main(void)
115 {
116     n = get_i();
117     m = get_i();
118     
119     flow = get_i();
120     
121     memset(hd, -1, sizeof(hd));
122     
123     for (int i = 1; i <= m; ++i)
124     {
125         int u = get_i();
126         int v = get_i();
127         int f = get_i();
128         int w = get_i();
129         add(u, v, f, w);
130     }
131     
132     s = n, t = n - 1;
133     
134     add(s, 0, flow, 0);
135     
136     printf("%d\n", mcmf());
137 }

@Author: YouSiki

网络流模板 NetworkFlow

原文：http://www.cnblogs.com/yousiki/p/6227524.html

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