上下界网络流模板

1、#115. 无源汇有上下界可行流

#include <algorithm>
#include  <iterator>
#include  <iostream>
#include   <cstring>
#include   <cstdlib>
#include   <iomanip>
#include    <bitset>
#include    <cctype>
#include    <cstdio>
#include    <string>
#include    <vector>
#include     <stack>
#include     <cmath>
#include     <queue>
#include      <list>
#include       <map>
#include       <set>
#include   <cassert>

/*

⊂_ヽ
　 ＼＼ Λ＿Λ  来了老弟
　　 ＼('ㅅ')
　　　 >　⌒ヽ
　　　/ 　 へ＼
　　 /　　/　＼＼
　　 ﾚ　ノ　　 ヽ_つ
　　/　/
　 /　/|
　(　(ヽ
　|　|、＼
　| 丿 ＼ ⌒)
　| |　　) /
'ノ )　　Lﾉ

*/

using namespace std;
#define lson (l , mid , rt << 1)
#define rson (mid + 1 , r , rt << 1 | 1)
#define debug(x) cerr << #x << " = " << x << "\n";
#define pb push_back
#define pq priority_queue



typedef long long ll;
typedef unsigned long long ull;
//typedef __int128 bll;
typedef pair<ll ,ll > pll;
typedef pair<int ,int > pii;
typedef pair<int,pii> p3;

//priority_queue<int> q;//这是一个大根堆q
//priority_queue<int,vector<int>,greater<int> >q;//这是一个小根堆q
#define fi first
#define se second
//#define endl '\n'

#define boost ios::sync_with_stdio(false);cin.tie(0)
#define rep(a, b, c) for(int a = (b); a <= (c); ++ a)
#define max3(a,b,c) max(max(a,b), c);
#define min3(a,b,c) min(min(a,b), c);


const ll oo = 1ll<<17;
const ll mos = 0x7FFFFFFF;  //2147483647
const ll nmos = 0x80000000;  //-2147483648
const int inf = 0x3f3f3f3f;
const ll inff = 0x3f3f3f3f3f3f3f3f; //18
const int mod = 1e9+7;
const double esp = 1e-8;
const double PI=acos(-1.0);
const double PHI=0.61803399;    //黄金分割点
const double tPHI=0.38196601;


template<typename T>
inline T read(T&x){
    x=0;int f=0;char ch=getchar();
    while (ch<'0'||ch>'9') f|=(ch=='-'),ch=getchar();
    while (ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
    return x=f?-x:x;
}

inline void cmax(int &x,int y){if(x<y)x=y;}
inline void cmax(ll &x,ll y){if(x<y)x=y;}
inline void cmin(int &x,int y){if(x>y)x=y;}
inline void cmin(ll &x,ll y){if(x>y)x=y;}

/*-----------------------showtime----------------------*/

            const int maxn = 1e5+9;
            struct E{
                int v,val,id;
                int nxt;
            }edge[maxn];
            int head[maxn],gtot=0;
            void addedge(int u,int v,int val,int id){
                edge[gtot].v = v;
                edge[gtot].val = val;
                edge[gtot].nxt = head[u];
                edge[gtot].id = -1;
                head[u] = gtot++;

                edge[gtot].v = u;
                edge[gtot].val = 0;
                edge[gtot].nxt = head[v];
                edge[gtot].id = id;
                head[v] = gtot++;
            }
            int dis[maxn],cur[maxn];
            bool bfs(int s,int t){
                memset(dis, inf, sizeof(dis));
                queue<int>que;
                que.push(s);
                dis[s] = 0;
                for(int i=s; i<=t; i++) cur[i] = head[i];
                while(!que.empty()){
                    int u = que.front(); que.pop();
                    for(int i=head[u]; ~i; i=edge[i].nxt){
                        int v = edge[i].v, val = edge[i].val;
                        if(val > 0 && dis[v] > dis[u]+1) {
                            dis[v] = dis[u] + 1;
                            que.push(v);
                        }
                    }
                }
                return dis[t] < inf;
            }


            int dfs(int u, int t, int maxflow){
                if(u == t || maxflow == 0) return maxflow;
                for(int i=cur[u]; ~i; i = edge[i].nxt){
                       cur[u] = i;
                       int v = edge[i].v,val = edge[i].val;
                       if(val > 0 && dis[v] == dis[u] + 1){
                            int f = dfs(v, t, min(maxflow, val));
                            if(f > 0){
                                edge[i].val -= f;
                                edge[i ^ 1].val += f;
                                return f;
                            }
                       }
                }
                return 0;
            }


            int dinic(int s,int t){
                int flow = 0;
                while(bfs(s, t)){
                    while(int f = dfs(s,t,inf)) flow += f;
                }
                return flow;
            }

            int ans[maxn],du[maxn],liu[maxn];
int main(){
            memset(head, -1, sizeof(head));
            int n,m;
            scanf("%d%d", &n, &m);
            int s = 0, t = n+1;
            for(int i=1; i<=m; i++)
            {
                int u,v,l,r;
                scanf("%d%d%d%d", &u, &v, &l, &r);
                ans[i] = l;
                du[u] -= l; du[v] += l;
                liu[i] = r - l;
                addedge(u, v, r - l, i);
            }
            int sum = 0;
            for(int i=1; i<=n; i++) {
                if(du[i] > 0) addedge(s, i, du[i], -1), sum += du[i];
                if(du[i] < 0) addedge(i, t, -du[i], -1);
            }
            int tmp = dinic(s, t);
            if(sum == tmp) {
                puts("YES");
                for(int i=1; i<=n; i++) {
                    for(int j=head[i]; ~j; j= edge[j].nxt){
                        if(edge[j].id == -1) continue;
                        int id = edge[j].id;
                        ans[id] += (edge[j].val);
                       // cout<< i << "," << edge[j].v << " = " << (edge[j].val) << endl;;
                    }
                }
                for(int i=1; i<=m; i++) printf("%d\n", ans[i]);
            }
            else puts("NO");
            return 0;
}

 2、#116. 有源汇有上下界最大流

#include <algorithm>
#include  <iterator>
#include  <iostream>
#include   <cstring>
#include   <cstdlib>
#include   <iomanip>
#include    <bitset>
#include    <cctype>
#include    <cstdio>
#include    <string>
#include    <vector>
#include     <stack>
#include     <cmath>
#include     <queue>
#include      <list>
#include       <map>
#include       <set>
#include   <cassert>

/*

⊂_ヽ
　 ＼＼ Λ＿Λ  来了老弟
　　 ＼('ㅅ')
　　　 >　⌒ヽ
　　　/ 　 へ＼
　　 /　　/　＼＼
　　 ﾚ　ノ　　 ヽ_つ
　　/　/
　 /　/|
　(　(ヽ
　|　|、＼
　| 丿 ＼ ⌒)
　| |　　) /
'ノ )　　Lﾉ

*/

using namespace std;
#define lson (l , mid , rt << 1)
#define rson (mid + 1 , r , rt << 1 | 1)
#define debug(x) cerr << #x << " = " << x << "\n";
#define pb push_back
#define pq priority_queue



typedef long long ll;
typedef unsigned long long ull;
//typedef __int128 bll;
typedef pair<ll ,ll > pll;
typedef pair<int ,int > pii;
typedef pair<int,pii> p3;

//priority_queue<int> q;//这是一个大根堆q
//priority_queue<int,vector<int>,greater<int> >q;//这是一个小根堆q
#define fi first
#define se second
//#define endl '\n'

#define boost ios::sync_with_stdio(false);cin.tie(0)
#define rep(a, b, c) for(int a = (b); a <= (c); ++ a)
#define max3(a,b,c) max(max(a,b), c);
#define min3(a,b,c) min(min(a,b), c);


const ll oo = 1ll<<17;
const ll mos = 0x7FFFFFFF;  //2147483647
const ll nmos = 0x80000000;  //-2147483648
const int inf = 0x3f3f3f3f;
const ll inff = 0x3f3f3f3f3f3f3f3f; //18
const int mod = 1e9+7;
const double esp = 1e-8;
const double PI=acos(-1.0);
const double PHI=0.61803399;    //黄金分割点
const double tPHI=0.38196601;


template<typename T>
inline T read(T&x){
    x=0;int f=0;char ch=getchar();
    while (ch<'0'||ch>'9') f|=(ch=='-'),ch=getchar();
    while (ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
    return x=f?-x:x;
}

inline void cmax(int &x,int y){if(x<y)x=y;}
inline void cmax(ll &x,ll y){if(x<y)x=y;}
inline void cmin(int &x,int y){if(x>y)x=y;}
inline void cmin(ll &x,ll y){if(x>y)x=y;}

/*-----------------------showtime----------------------*/

            const int maxn = 1e5+9;
            struct E{
                int v,val;
                int nxt;
            } edge[maxn];
            int head[maxn],gtot=0;
            void addedge(int u,int v,int val){
                edge[gtot].v = v;
                edge[gtot].val = val;
                edge[gtot].nxt = head[u];
                head[u] = gtot++;

                edge[gtot].v = u;
                edge[gtot].val = 0;
                edge[gtot].nxt = head[v];
                head[v] = gtot++;
            }
            int dis[maxn],cur[maxn];
            int n,m;
            bool bfs(int s,int t){
                memset(dis, inf, sizeof(dis));
                queue<int>que;
                que.push(s);
                dis[s] = 0;
                for(int i=0; i<=n+1; i++) cur[i] = head[i];   //注意这里不再是s到t。
                while(!que.empty()){
                    int u = que.front(); que.pop();
                    for(int i=head[u]; ~i; i=edge[i].nxt){
                        int v = edge[i].v, val = edge[i].val;
                        if(val > 0 && dis[v] > dis[u]+1) {
                            dis[v] = dis[u] + 1;
                            que.push(v);
                        }
                    }
                }
                return dis[t] < inf;
            }


            int dfs(int u, int t, int maxflow){
                if(u == t || maxflow == 0) return maxflow;
                for(int i=cur[u]; ~i; i = edge[i].nxt){
                       cur[u] = i;
                       int v = edge[i].v,val = edge[i].val;
                       if(val > 0 && dis[v] == dis[u] + 1){
                            int f = dfs(v, t, min(maxflow, val));
                            if(f > 0){
                                edge[i].val -= f;
                                edge[i ^ 1].val += f;
                                return f;
                            }
                       }
                }
                return 0;
            }


            int dinic(int s,int t){
                int flow = 0;
                while(bfs(s, t)){
                    while(int f = dfs(s,t,inf)) flow += f;
                }
                return flow;
            }

            int ans[maxn],du[maxn];
int main(){
            memset(head, -1, sizeof(head));
            int s,t;
            scanf("%d%d%d%d", &n, &m, &s, &t);
            int S = 0, T = n+1;
            for(int i=1; i<=m; i++)
            {
                int u,v,l,r;
                scanf("%d%d%d%d", &u, &v, &l, &r);
                ans[i] = l;
                du[u] -= l; du[v] += l;
                addedge(u, v, r - l);
            }
            addedge(t, s, inf);
            int sum = 0;
            for(int i=1; i<=n; i++) {
                if(du[i] >= 0) addedge(S, i, du[i]), sum += du[i];
                else  addedge(i, T, -du[i]);
            }

            int tmp = dinic(S, T);
            if(sum == tmp) {
                printf("%d\n", dinic(s, t));
            }
            else puts("please go home to sleep");
            return 0;
}

 3、#117. 有源汇有上下界最小流

#include <algorithm>
#include  <iterator>
#include  <iostream>
#include   <cstring>
#include   <cstdlib>
#include   <iomanip>
#include    <bitset>
#include    <cctype>
#include    <cstdio>
#include    <string>
#include    <vector>
#include     <stack>
#include     <cmath>
#include     <queue>
#include      <list>
#include       <map>
#include       <set>
#include   <cassert>

/*

⊂_ヽ
　 ＼＼ Λ＿Λ  来了老弟
　　 ＼('ㅅ')
　　　 >　⌒ヽ
　　　/ 　 へ＼
　　 /　　/　＼＼
　　 ﾚ　ノ　　 ヽ_つ
　　/　/
　 /　/|
　(　(ヽ
　|　|、＼
　| 丿 ＼ ⌒)
　| |　　) /
'ノ )　　Lﾉ

*/

using namespace std;
#define lson (l , mid , rt << 1)
#define rson (mid + 1 , r , rt << 1 | 1)
#define debug(x) cerr << #x << " = " << x << "\n";
#define pb push_back
#define pq priority_queue



typedef long long ll;
typedef unsigned long long ull;
//typedef __int128 bll;
typedef pair<ll ,ll > pll;
typedef pair<int ,int > pii;
typedef pair<int,pii> p3;

//priority_queue<int> q;//这是一个大根堆q
//priority_queue<int,vector<int>,greater<int> >q;//这是一个小根堆q
#define fi first
#define se second
//#define endl '\n'

#define boost ios::sync_with_stdio(false);cin.tie(0)
#define rep(a, b, c) for(int a = (b); a <= (c); ++ a)
#define max3(a,b,c) max(max(a,b), c);
#define min3(a,b,c) min(min(a,b), c);


const ll oo = 1ll<<17;
const ll mos = 0x7FFFFFFF;  //2147483647
const ll nmos = 0x80000000;  //-2147483648
const int inf = 0x3f3f3f3f;
const ll inff = 0x3f3f3f3f3f3f3f3f; //18
const int mod = 1e9+7;
const double esp = 1e-8;
const double PI=acos(-1.0);
const double PHI=0.61803399;    //黄金分割点
const double tPHI=0.38196601;


template<typename T>
inline T read(T&x){
    x=0;int f=0;char ch=getchar();
    while (ch<'0'||ch>'9') f|=(ch=='-'),ch=getchar();
    while (ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
    return x=f?-x:x;
}

inline void cmax(int &x,int y){if(x<y)x=y;}
inline void cmax(ll &x,ll y){if(x<y)x=y;}
inline void cmin(int &x,int y){if(x>y)x=y;}
inline void cmin(ll &x,ll y){if(x>y)x=y;}

/*-----------------------showtime----------------------*/

            const int maxn = 4e5+9;
            struct E{
                int v,val;
                int nxt;
            } edge[maxn];
            int head[maxn],gtot=0;
            void addedge(int u,int v,int val){
                edge[gtot].v = v;
                edge[gtot].val = val;
                edge[gtot].nxt = head[u];
                head[u] = gtot++;

                edge[gtot].v = u;
                edge[gtot].val = 0;
                edge[gtot].nxt = head[v];
                head[v] = gtot++;
            }
            int dis[maxn],cur[maxn];
            int n,m;
            bool bfs(int s,int t){
                memset(dis, inf, sizeof(dis));
                queue<int>que;
                que.push(s);
                dis[s] = 0;
                for(int i=0; i<=n+1; i++) cur[i] = head[i];   //注意这里不再是s到t。
                while(!que.empty()){
                    int u = que.front(); que.pop();
                    for(int i=head[u]; ~i; i=edge[i].nxt){
                        int v = edge[i].v, val = edge[i].val;
                        if(val > 0 && dis[v] > dis[u]+1) {
                            dis[v] = dis[u] + 1;
                            que.push(v);
                        }
                    }
                }
                return dis[t] < inf;
            }


            int dfs(int u, int t, int maxflow){
                if(u == t || maxflow == 0) return maxflow;
                for(int i=cur[u]; ~i; i = edge[i].nxt){
                       cur[u] = i;
                       int v = edge[i].v,val = edge[i].val;
                       if(val > 0 && dis[v] == dis[u] + 1){
                            int f = dfs(v, t, min(maxflow, val));
                            if(f > 0){
                                edge[i].val -= f;
                                edge[i ^ 1].val += f;
                                return f;
                            }
                       }
                }
                return 0;
            }


            int dinic(int s,int t){
                int flow = 0;
                while(bfs(s, t)){
                    while(int f = dfs(s,t,inf)) flow += f;
                }
                return flow;
            }

            int ans[maxn],du[maxn];
int main(){
            memset(head, -1, sizeof(head));
            int s,t;
            scanf("%d%d%d%d", &n, &m, &s, &t);
            int S = 0, T = n+1;
            for(int i=1; i<=m; i++)
            {
                int u,v,l,r;
                scanf("%d%d%d%d", &u, &v, &l, &r);
                ans[i] = l;
                du[u] -= l; du[v] += l;
                addedge(u, v, r - l);
            }
            int sum = 0;
            for(int i=1; i<=n; i++) {
                if(du[i] >= 0) addedge(S, i, du[i]), sum += du[i];
                else  addedge(i, T, -du[i]);
            }

            int tmp = dinic(S, T);

            addedge(t, s, inf);
            tmp += dinic(S, T);
            if(sum == tmp) {
                printf("%d\n", edge[gtot-1].val);
            }
            else puts("please go home to sleep");
            return 0;
}