【Loj】 三种 带有上下界的网络流

其他 2018-08-05 16:06:32 阅读次数: 0

第一种 无源汇有上下界可行流

#include <bits/stdc++.h>
using namespace std;

const int N = (int) 1000 + 11;
const int M = (int) 5e5 + 11;
const int mod = (int) 1e9 + 7;
const int inf = 0x3f3f3f3f;

struct Edge{
    int from, to, cap, flow, nex;
    Edge(){}
    Edge(int _from, int _to, int _cap, int _flow, int _nex){
        from = _from, to = _to, cap = _cap, flow = _flow, nex = _nex;
    }
}edge[M];

int head[N], top;  int n, m;
void init(){
    memset(head, -1, sizeof(int) * (n + 5));
    top = 0;
}

void addedge(int a, int b, int c){
    edge[top] = Edge(a, b, c, 0, head[a]);
    head[a] = top++;
    edge[top] = Edge(b, a, 0, 0, head[b]);
    head[b] = top++;
}

bool vis[N]; int dis[N], cur[N];
bool bfs(int s, int t){
    queue<int>que;
    memset(vis, false, sizeof(bool) * (n + 5));
    memset(dis, -1, sizeof(int) * (n + 5));
    que.push(s); vis[s] = true; dis[s] = 1;
    while(!que.empty()){
        int u = que.front(); que.pop();
        for(int i = head[u]; i != -1; i = edge[i].nex){
            Edge e = edge[i];
            if(!vis[e.to] && e.cap - e.flow > 0){
                vis[e.to] = true;
                dis[e.to] = dis[u] + 1;
                if(e.to == t) return true;
                que.push(e.to);
            }
        }
    }
    return false;
}

int dfs(int now, int a, int ed){
    if(a == 0 || now == ed) return a;
    int flow = 0, f;
    for(int  &i = cur[now]; i != -1; i = edge[i].nex){
        Edge &e = edge[i];
        if(dis[e.to] == dis[now] + 1 && (f = dfs(e.to, min(e.cap - e.flow, a), ed)) > 0){
            e.flow += f;
            flow += f;
            edge[i ^ 1].flow -= f;
            a -= f;
            if(a == 0) break;
        }
    }
    return flow;
}

int max_flow(int s, int t){
   int flow = 0;
   while(bfs(s, t)){
       // puts("sdkfskdf");
        memcpy(cur, head, sizeof(int) * (n + 5));
        flow += dfs(s, inf, t);
   }

   return flow;
}


int inflow[N]; // 为了满足条件，每个点至少应该流入的流量
int low[M]; // 边的流量下界
int main(){
    while(scanf("%d%d", &n, &m) != EOF){
        init();
        memset(inflow, 0, sizeof(int) * (n + 5));
        for(int i = 0; i < m; i++){
            int s, t, upp;
            scanf("%d%d%d%d", &s, &t, &low[i], &upp);
            inflow[s] -= low[i];
            inflow[t] += low[i];
            addedge(s, t, upp - low[i]);
        }

        int S = 0, T = n + 1;
        int full_flow = 0;
        for(int i = 1; i <= n; i++){
            if(inflow[i] > 0) {
                addedge(S, i, inflow[i]);
                full_flow  += inflow[i];
            }
            else if(inflow[i] < 0) addedge(i, T, -inflow[i]);
        }

        int ans = max_flow(S, T);
        if(ans != full_flow) puts("NO");
        else { // 输出一个可行解
            puts("YES");
            for(int i = 0; i < 2 * m; i += 2){
                printf("%d\n", edge[i].flow + low[i / 2]);
            }
        }
    }
 return 0;
}

第二种 有源汇有上下界最大流

#include <bits/stdc++.h>
using namespace std;

const int N = (int) 1000 + 11;
const int M = (int) 5e5 + 11;
const int mod = (int) 1e9 + 7;
const int inf = 0x3f3f3f3f;

struct Edge{
    int from, to, cap, flow, nex;
    Edge(){}
    Edge(int _from, int _to, int _cap, int _flow, int _nex){
        from = _from, to = _to, cap = _cap, flow = _flow, nex = _nex;
    }
}edge[M];

int head[N], top;  int n, m;
void init(){
    memset(head, -1, sizeof(int) * (n + 5));
    top = 0;
}

void addedge(int a, int b, int c){
    edge[top] = Edge(a, b, c, 0, head[a]);
    head[a] = top++;
    edge[top] = Edge(b, a, 0, 0, head[b]);
    head[b] = top++;
}

bool vis[N]; int dis[N], cur[N];
bool bfs(int s, int t){
    queue<int>que;
    memset(vis, false, sizeof(bool) * (n + 5));
    memset(dis, -1, sizeof(int) * (n + 5));
    que.push(s); vis[s] = true; dis[s] = 1;
    while(!que.empty()){
        int u = que.front(); que.pop();
        for(int i = head[u]; i != -1; i = edge[i].nex){
            Edge e = edge[i];
            if(!vis[e.to] && e.cap - e.flow > 0){
                vis[e.to] = true;
                dis[e.to] = dis[u] + 1;
                if(e.to == t) return true;
                que.push(e.to);
            }
        }
    }
    return false;
}

int dfs(int now, int a, int ed){
    if(a == 0 || now == ed) return a;
    int flow = 0, f;
    for(int  &i = cur[now]; i != -1; i = edge[i].nex){
        Edge &e = edge[i];
        if(dis[e.to] == dis[now] + 1 && (f = dfs(e.to, min(e.cap - e.flow, a), ed)) > 0){
            e.flow += f;
            flow += f;
            edge[i ^ 1].flow -= f;
            a -= f;
            if(a == 0) break;
        }
    }
    return flow;
}

int max_flow(int s, int t){
   int flow = 0;
   while(bfs(s, t)){
       // puts("sdkfskdf");
        memcpy(cur, head, sizeof(int) * (n + 5));
        flow += dfs(s, inf, t);
   }

   return flow;
}


int inflow[N]; // 为了满足条件，每个点至少应该流入的流量
int main(){
    int s, t;
    while(scanf("%d%d%d%d", &n, &m, &s, &t) != EOF){
        init();
        memset(inflow, 0, sizeof(int) * (n + 5));
        for(int i = 0; i < m; i++){
            int s, t, upp, low;
            scanf("%d%d%d%d", &s, &t, &low, &upp);
            inflow[s] -= low;
            inflow[t] += low;
            addedge(s, t, upp - low);
        }
        int S = 0, T = n + 1;
        int full_flow = 0;
        for(int i = 1; i <= n; i++){
            if(inflow[i] > 0) {
                addedge(S, i, inflow[i]);
                full_flow  += inflow[i];
            }
            else if(inflow[i] < 0) addedge(i, T, -inflow[i]);
        }
        addedge(t, s, inf);
        if(max_flow(S, T) != full_flow) puts("please go home to sleep");
        else printf("%d\n", max_flow(s, t));
    }
 return 0;
}

第三种 有源汇有上下界最小流

#include <bits/stdc++.h>
using namespace std;

const int N = (int) 50003 + 11;
const int M = (int) 125003 * 10 + 11;
const int mod = (int) 1e9 + 7;
const int inf = 0x3f3f3f3f;

struct Edge{
    int from, to, cap, flow, nex;
    Edge(){}
    Edge(int _from, int _to, int _cap, int _flow, int _nex){
        from = _from, to = _to, cap = _cap, flow = _flow, nex = _nex;
    }
}edge[M];

int head[N], top;  int n, m;
void init(){
    memset(head, -1, sizeof(int) * (n + 5));
    top = 0;
}

void addedge(int a, int b, int c){
    edge[top] = Edge(a, b, c, 0, head[a]);
    head[a] = top++;
    edge[top] = Edge(b, a, 0, 0, head[b]);
    head[b] = top++;
}

bool vis[N]; int dis[N], cur[N];
bool bfs(int s, int t){
    queue<int>que;
    memset(vis, false, sizeof(bool) * (n + 5));
    memset(dis, -1, sizeof(int) * (n + 5));
    que.push(s); vis[s] = true; dis[s] = 1;
    while(!que.empty()){
        int u = que.front(); que.pop();
        for(int i = head[u]; i != -1; i = edge[i].nex){
            Edge e = edge[i];
            if(!vis[e.to] && e.cap - e.flow > 0){
                vis[e.to] = true;
                dis[e.to] = dis[u] + 1;
                if(e.to == t) return true;
                que.push(e.to);
            }
        }
    }
    return false;
}

int dfs(int now, int a, int ed){
    if(a == 0 || now == ed) return a;
    int flow = 0, f;
    for(int  &i = cur[now]; i != -1; i = edge[i].nex){
        Edge &e = edge[i];
        if(dis[e.to] == dis[now] + 1 && (f = dfs(e.to, min(e.cap - e.flow, a), ed)) > 0){
            e.flow += f;
            flow += f;
            edge[i ^ 1].flow -= f;
            a -= f;
            if(a == 0) break;
        }
    }
    return flow;
}

int max_flow(int s, int t){
   int flow = 0;
   while(bfs(s, t)){
       // puts("sdkfskdf");
        memcpy(cur, head, sizeof(int) * (n + 5));
        flow += dfs(s, inf, t);
   }

   return flow;
}


int inflow[N]; // 为了满足条件，每个点至少应该流入的流量
int main(){
    int s, t;
    while(scanf("%d%d%d%d", &n, &m, &s, &t) != EOF){
        init();
        memset(inflow, 0, sizeof(int) * (n + 5));
        for(int i = 0; i < m; i++){
            int s, t, low, upp;
            scanf("%d%d%d%d", &s, &t, &low, &upp);
            inflow[s] -= low;
            inflow[t] += low;
            addedge(s, t, upp - low);
        }

        int S = 0, T = n + 1;
        int full_flow = 0;
        for(int i = 1; i <= n; i++){
            if(inflow[i] > 0)
                addedge(S, i, inflow[i]);
            else if(inflow[i] < 0)
                addedge(i, T, -inflow[i]);
        }

        max_flow(S, T);
        addedge(t, s, inf);
        max_flow(S, T);

        bool ok = true;
        for(int i = head[S]; i != -1; i = edge[i].nex){
            if(edge[i].cap - edge[i].flow > 0){
                ok  = false; break;
            }
        }

        if(ok == false)
            puts("please go home to sleep");
        else
            printf("%d\n", edge[top - 1].cap - edge[top - 1].flow);
    }
 return 0;
}

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