原理： 传送门
无源汇有上下界限制的网络流
题意：给n个点，及m根pipe，每根pipe用来流躺液体的，单向的，每时每刻每根pipe流进来的物质要等于流出去的物质，要使得m条pipe组成一个循环体，里面流躺物质。并且满足每根pipe一定的流量限制，范围为[Li,Ri].即要满足每时刻流进来的不能超过Ri，同时最小不能低于Li。 如果可以输出yes，并且输出每条管道的流量。否则输出no。
代码：
1 #include<bits/stdc++.h> 2 using namespace std; 3 #define Fopen freopen("_in.txt","r",stdin); freopen("_out.txt","w",stdout); 4 #define LL long long 5 #define ULL unsigned LL 6 #define fi first 7 #define se second 8 #define pb push_back 9 #define lson l,m,rt<<1 10 #define rson m+1,r,rt<<1|1 11 #define max3(a,b,c) max(a,max(b,c)) 12 #define min3(a,b,c) min(a,min(b,c)) 13 #define _S(X) cout << x << ' '; 14 #define __S(x) cout << x << endl; 15 typedef pair<int,int> pll; 16 const int INF = 0x3f3f3f3f; 17 const LL mod = (int)1e9+7; 18 const int N = 20100; 19 const int _M = 500100; 20 int head[N]; 21 int M[N]; 22 int w[_M], to[_M], nx[_M], id[_M]; 23 int B[_M]; 24 int n, m, _u, _v, _w; 25 int tot, s, t, ss, tt; 26 int deep[N], cur[N]; 27 void add(int u, int v, int val){ 28 w[tot] = val; 29 to[tot] = v; 30 nx[tot] = head[u]; 31 head[u] = tot++; 32 } 33 34 void init(){ 35 memset(head, -1, sizeof(int)*(n+3)); 36 memset(M, 0, sizeof(int)*(n+3)); 37 tot = 0; 38 s = 1; 39 t = n; 40 ss = n + 1; 41 tt = n + 2; 42 } 43 44 int bfs(int s, int t){ 45 queue<int> q; 46 memset(deep, 0, sizeof(int)*(n+3)); 47 q.push(s); 48 deep[s] = 1; 49 while(!q.empty()){ 50 int u = q.front(); 51 q.pop(); 52 for(int i = head[u]; ~i; i = nx[i]){ 53 if(w[i] > 0 && deep[to[i]] == 0){ 54 deep[to[i]] = deep[u] + 1; 55 q.push(to[i]); 56 } 57 } 58 } 59 if(deep[t] > 0) return 1; 60 return 0; 61 } 62 int Dfs(int u, int t, int flow){ 63 if(u == t) return flow; 64 for(int &i = cur[u]; ~i; i = nx[i]){ 65 if(deep[u]+1 == deep[to[i]] && w[i] > 0){ 66 int di = Dfs(to[i], t, min(w[i], flow)); 67 if(di > 0){ 68 w[i] -= di, w[i^1] += di; 69 return di; 70 } 71 } 72 } 73 return 0; 74 } 75 int Dinic(int s, int t){ 76 int ans = 0, tmp; 77 while(bfs(s, t)){ 78 for(int i = 1; i <= n+2; i++) cur[i] = head[i]; 79 while(tmp = Dfs(s, t, INF)) ans += tmp; 80 } 81 return ans; 82 } 83 int main(){ 84 while(~scanf("%d%d", &n, &m)){ 85 init(); 86 int b, c; 87 for(int i = 1; i <= m; i++){ 88 scanf("%d%d%d%d", &_u, &_v, &b, &c); 89 id[i] = tot; B[i] = b; 90 add(_u,_v,c-b); add(_v,_u,0); 91 M[_u] -= b; M[_v] += b; 92 } 93 int sum = 0; 94 for(int i = 1; i <= n; i++){ 95 if(M[i] > 0) add(ss, i, M[i]), add(i, ss, 0), sum += M[i]; 96 if(M[i] < 0) add(i, tt, -M[i]), add(tt, i, 0); 97 } 98 int ans = Dinic(ss, tt); 99 if(ans == sum){ 100 puts("YES"); 101 for(int i = 1; i <= m; i++) 102 printf("%d ",w[id[i]^1] + B[i]); 103 } 104 else puts("NO"); 105 } 106 return 0; 107 }
有源汇有上下界最大流
代码：
1 #include<bits/stdc++.h> 2 using namespace std; 3 #define Fopen freopen("_in.txt","r",stdin); freopen("_out.txt","w",stdout); 4 #define LL long long 5 #define ULL unsigned LL 6 #define fi first 7 #define se second 8 #define pb push_back 9 #define lson l,m,rt<<1 10 #define rson m+1,r,rt<<1|1 11 #define max3(a,b,c) max(a,max(b,c)) 12 #define min3(a,b,c) min(a,min(b,c)) 13 #define _S(X) cout << x << ' '; 14 #define __S(x) cout << x << endl; 15 typedef pair<int,int> pll; 16 const int INF = 0x3f3f3f3f; 17 const LL mod = (int)1e9+7; 18 const int N = 1000; 19 const int _M = 50010; 20 int head[N]; 21 int M[N]; 22 int w[_M], to[_M], nx[_M]; 23 int n, m, _u, _v, _w; 24 int tot, s, t, ss, tt; 25 int deep[N], cur[N]; 26 void add(int u, int v, int val){ 27 w[tot] = val; 28 to[tot] = v; 29 nx[tot] = head[u]; 30 head[u] = tot++; 31 } 32 33 void init(){ 34 memset(head, -1, sizeof(int)*(n+3)); 35 memset(M, 0, sizeof(int)*(n+3)); 36 tot = 0; 37 ss = n + 1; 38 tt = n + 2; 39 } 40 41 int bfs(int s, int t){ 42 queue<int> q; 43 memset(deep, 0, sizeof(int)*(n+3)); 44 q.push(s); 45 deep[s] = 1; 46 while(!q.empty()){ 47 int u = q.front(); 48 q.pop(); 49 for(int i = head[u]; ~i; i = nx[i]){ 50 if(w[i] > 0 && deep[to[i]] == 0){ 51 deep[to[i]] = deep[u] + 1; 52 q.push(to[i]); 53 } 54 } 55 } 56 if(deep[t] > 0) return 1; 57 return 0; 58 } 59 int Dfs(int u, int t, int flow){ 60 if(u == t) return flow; 61 for(int &i = cur[u]; ~i; i = nx[i]){ 62 if(deep[u]+1 == deep[to[i]] && w[i] > 0){ 63 int di = Dfs(to[i], t, min(w[i], flow)); 64 if(di > 0){ 65 w[i] -= di, w[i^1] += di; 66 return di; 67 } 68 } 69 } 70 return 0; 71 } 72 int Dinic(int s, int t){ 73 int ans = 0, tmp; 74 while(bfs(s,t)){ 75 for(int i = 1; i <= n+2; i++) cur[i] = head[i]; 76 while(tmp = Dfs(s, t, INF)) ans += tmp; 77 } 78 return ans; 79 } 80 int main(){ 81 while(~scanf("%d%d", &n, &m)){ 82 init(); 83 scanf("%d%d", &s, &t); 84 int b, c; 85 for(int i = 1; i <= m; i++){ 86 scanf("%d%d%d%d", &_u, &_v, &b, &c); 87 add(_u,_v,c-b); add(_v,_u,0); 88 M[_u] -= b; M[_v] += b; 89 } 90 int sum = 0; 91 for(int i = 1; i <= n; i++){ 92 if(M[i] > 0) add(ss, i, M[i]), add(i, ss, 0), sum += M[i]; 93 if(M[i] < 0) add(i, tt, -M[i]), add(tt, i, 0); 94 } 95 add(t,s,INF); 96 add(s,t,0); 97 int ans = Dinic(ss, tt); 98 if(ans == sum){ 99 ans = w[--tot]; 100 w[tot] = 0; w[--tot] = 0; 101 ans += Dinic(s, t); 102 printf("%d ", ans); 103 } 104 else puts("please go home to sleep"); 105 } 106 return 0; 107 }
有源汇有上下界最小流
代码：
1 #include<bits/stdc++.h> 2 using namespace std; 3 #define Fopen freopen("_in.txt","r",stdin); freopen("_out.txt","w",stdout); 4 #define LL long long 5 #define ULL unsigned LL 6 #define fi first 7 #define se second 8 #define pb push_back 9 #define lson l,m,rt<<1 10 #define rson m+1,r,rt<<1|1 11 #define max3(a,b,c) max(a,max(b,c)) 12 #define min3(a,b,c) min(a,min(b,c)) 13 #define _S(X) cout << x << ' '; 14 #define __S(x) cout << x << endl; 15 typedef pair<int,int> pll; 16 const int INF = 0x3f3f3f3f; 17 const LL mod = (int)1e9+7; 18 const int N = 50100; 19 const int _M = 350010; 20 int head[N]; 21 int M[N]; 22 int w[_M], to[_M], nx[_M]; 23 int n, m, _u, _v, _w; 24 int tot, s, t, ss, tt; 25 int deep[N], cur[N]; 26 void add(int u, int v, int val){ 27 w[tot] = val; 28 to[tot] = v; 29 nx[tot] = head[u]; 30 head[u] = tot++; 31 } 32 33 void init(){ 34 memset(head, -1, sizeof(int)*(n+3)); 35 memset(M, 0, sizeof(int)*(n+3)); 36 tot = 0; 37 ss = n + 1; 38 tt = n + 2; 39 } 40 41 int bfs(int s, int t){ 42 queue<int> q; 43 memset(deep, 0, sizeof(int)*(n+3)); 44 q.push(s); 45 deep[s] = 1; 46 47 while(!q.empty()){ 48 int u = q.front(); 49 q.pop(); 50 for(int i = head[u]; ~i; i = nx[i]){ 51 if(w[i] > 0 && deep[to[i]] == 0){ 52 deep[to[i]] = deep[u] + 1; 53 q.push(to[i]); 54 } 55 } 56 } 57 if(deep[t] > 0) return 1; 58 return 0; 59 } 60 int Dfs(int u, int t, int flow){ 61 if(u == t) return flow; 62 for(int &i = cur[u]; ~i; i = nx[i]){ 63 if(deep[u]+1 == deep[to[i]] && w[i] > 0){ 64 int di = Dfs(to[i], t, min(w[i], flow)); 65 if(di > 0){ 66 w[i] -= di, w[i^1] += di; 67 return di; 68 } 69 } 70 } 71 return 0; 72 } 73 int Dinic(int s, int t){ 74 int ans = 0, tmp; 75 while(bfs(s,t)){ 76 for(int i = 1; i <= n+2; i++) cur[i] = head[i]; 77 while(tmp = Dfs(s, t, INF)) ans += tmp; 78 } 79 return ans; 80 } 81 int main(){ 82 while(~scanf("%d%d", &n, &m)){ 83 init(); 84 scanf("%d%d", &s, &t); 85 int b, c; 86 for(int i = 1; i <= m; i++){ 87 scanf("%d%d%d%d", &_u, &_v, &b, &c); 88 add(_u,_v,c-b); add(_v,_u,0); 89 M[_u] -= b; M[_v] += b; 90 } 91 int sum = 0; 92 for(int i = 1; i <= n; i++){ 93 if(M[i] > 0) add(ss, i, M[i]), add(i, ss, 0), sum += M[i]; 94 if(M[i] < 0) add(i, tt, -M[i]), add(tt, i, 0); 95 } 96 add(t,s,INF); 97 add(s,t,0); 98 int ans = Dinic(ss, tt); 99 if(ans == sum){ 100 ans = w[--tot]; 101 w[tot] = 0; w[--tot] = 0; 102 ans -= Dinic(t, s); 103 printf("%d ", ans); 104 } 105 else puts("please go home to sleep"); 106 } 107 return 0; 108 }