hdu - 3572 - Task（最大流）

题意：有N个作业，M台机器，每个作业1天只能同1台机器运行，每台机器1天只能运行1个作业，第i个作业需要pi天完成，且只能从Si到Ei中选Pi天，问能否完成所有作业(T <= 20, N<=500, M<=200, 1 <= Pi, Si, Ei <= 500)。

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=3572

——>>建图思路原来是这样子：设一个超级源s，每个作业为1个结点，从s往每个作业分别连1条边，容量为完成该作业所需的时间，那么从s发出满流时，就是作业所需天数，最后就看最大流是否为满流即可；作业可选择的天也分别作为1个结点，每个作业分别向其可选择的天连1条边，容量为1（因为每个作业1天只能同1台机器运行，每台机器1天只能运行1个作业）；最后，所有可选择的天分别向超级汇t连1条边，容量为M（因为每天最多只有M台机器）～ok～

#include <cstdio>
#include <vector>
#include <queue>
#include <algorithm>
#include <cstring>

using namespace std;

const int maxn = 1000 + 10;
const int INF = 0x3f3f3f3f;

int N, M;
bool flag[maxn];

struct Edge{
    int u, v, cap, flow;
    Edge(int u = 0, int v = 0, int cap = 0, int flow = 0):
    u(u), v(v), cap(cap), flow(flow){}
};

struct Dinic{
    vector<Edge> edges;
    vector<int> G[maxn];
    int m, s, t;
    int d[maxn], cur[maxn];
    bool vis[maxn];

    void addEdge(int u, int v, int cap){
        edges.push_back(Edge(u, v, cap, 0));
        edges.push_back(Edge(v, u, 0, 0));
        m = edges.size();
        G[u].push_back(m-2);
        G[v].push_back(m-1);
    }

    bool bfs(){
        d[s] = 0;
        memset(vis, 0, sizeof(vis));
        queue<int> qu;
        qu.push(s);
        vis[s] = 1;
        while(!qu.empty()){
            int u = qu.front(); qu.pop();
            int sz = G[u].size();
            for(int i = 0; i < sz; i++){
                Edge& e = edges[G[u][i]];
                if(!vis[e.v] && e.cap > e.flow){
                    d[e.v] = d[u] + 1;
                    vis[e.v] = 1;
                    qu.push(e.v);
                }
            }
        }
        return vis[t];
    }

    int dfs(int u, int a){
        if(u == t || a == 0) return a;
        int f, flow = 0;
        int sz = G[u].size();
        for(int i = cur[u]; i < sz; i++){
            Edge& e = edges[G[u][i]];
            cur[u] = i;
            if(d[e.v] == d[u] + 1 && (f = dfs(e.v, min(a, e.cap-e.flow))) > 0){
                e.flow += f;
                edges[G[u][i]^1].flow -= f;
                flow += f;
                a -= f;
                if(!a) break;
            }
        }
        return flow;
    }

    int Maxflow(int s, int t){
        this->s = s;
        this->t = t;
        int flow = 0;
        while(bfs()){
            memset(cur, 0, sizeof(cur));
            flow += dfs(s, INF);
        }
        return flow;
    }

};

int main()
{
    int T, P, S, E, kase = 1;
    scanf("%d", &T);
    while(T--){
        Dinic din;
        scanf("%d%d", &N, &M);
        memset(flag, 0, sizeof(flag));
        int sum = 0;
        for(int i = 1; i <= N; i++){
            scanf("%d%d%d", &P, &S, &E);
            din.addEdge(0, i, P);
            for(int j = S; j <= E; j++){
                din.addEdge(i, N+j, 1);
                if(!flag[N+j]){
                    din.addEdge(N+j, 1001, M);
                    flag[N+j] = 1;
                }
            }
            sum += P;
        }
        if(din.Maxflow(0, 1001) == sum) printf("Case %d: Yes\n\n", kase++);
        else printf("Case %d: No\n\n", kase++);
    }
    return 0;
}

发现，以上的数据结构时空上都不如下面的数组写法：

#include <cstdio>
#include <queue>
#include <algorithm>
#include <cstring>

using namespace std;

const int maxn = 1000 + 10;
const int maxm = 502000 + 10;
const int INF = 0x3f3f3f3f;

int head[maxn], nxt[maxm], ecnt, v[maxm], flow[maxm], cap[maxm];
bool flag[maxn];
int N, M;

struct Dinic{
    int m, s, t;
    int d[maxn], cur[maxn];
    bool vis[maxn];

    Dinic(){
        memset(head, -1, sizeof(head));
        ecnt = 0;
    }

    void addEdge(int uu, int vv, int ca){
        v[ecnt] = vv; cap[ecnt] = ca; flow[ecnt] = 0; nxt[ecnt] = head[uu]; head[uu] = ecnt; ecnt++;
        v[ecnt] = uu; cap[ecnt] = 0; flow[ecnt] = 0; nxt[ecnt] = head[vv]; head[vv] = ecnt; ecnt++;
    }

    bool bfs(){
        d[s] = 0;
        memset(vis, 0, sizeof(vis));
        queue<int> qu;
        qu.push(s);
        vis[s] = 1;
        while(!qu.empty()){
            int u = qu.front(); qu.pop();
            for(int e = head[u]; e != -1; e = nxt[e]){
                if(!vis[v[e]] && cap[e] > flow[e]){
                    d[v[e]] = d[u] + 1;
                    vis[v[e]] = 1;
                    qu.push(v[e]);
                }
            }
        }
        return vis[t];
    }

    int dfs(int u, int a){
        if(u == t || a == 0) return a;
        int f, Flow = 0;
        for(int e = cur[u]; e != -1; e = nxt[e]){
            cur[u] = e;
            if(d[v[e]] == d[u] + 1 && (f = dfs(v[e], min(a, cap[e]-flow[e]))) > 0){
                flow[e] += f;
                flow[e^1] -= f;
                Flow += f;
                a -= f;
                if(!a) break;
            }
        }
        return Flow;
    }

    int Maxflow(int s, int t){
        this->s = s;
        this->t = t;
        int Flow = 0;
        while(bfs()){
            memcpy(cur, head, sizeof(head));
            Flow += dfs(s, INF);
        }
        return Flow;
    }

};

int main()
{
    int T, P, S, E, kase = 1;
    scanf("%d", &T);
    while(T--){
        Dinic din;
        scanf("%d%d", &N, &M);
        memset(flag, 0, sizeof(flag));
        int sum = 0;
        for(int i = 1; i <= N; i++){
            scanf("%d%d%d", &P, &S, &E);
            din.addEdge(0, i, P);
            for(int j = S; j <= E; j++){
                din.addEdge(i, N+j, 1);
                if(!flag[N+j]){
                    din.addEdge(N+j, 1001, M);
                    flag[N+j] = 1;
                }
            }
            sum += P;
        }
        if(din.Maxflow(0, 1001) == sum) printf("Case %d: Yes\n\n", kase++);
        else printf("Case %d: No\n\n", kase++);
    }
    return 0;
}