HDU- 6437.Videos 最“大”费用流 -化区间为点

参考和完全学习:http://www.cnblogs.com/xcantaloupe/p/9519617.html

HDU-6437

题意:

  有m场电影,电影分为两种,看一场电影可以得到对应的快乐值。有k个人,一场电影只能一个人参加,并且如果时间允许可以连续观看,但是如果连续看的电影是同一类型的,就要把快乐值减去一个w,这个w是累计的。问如何安排,可以使得k个人的快乐值最大。

思路:

  网络流问题建图真难。可以给每部电影当成一个点i,连一条从i到i+m 的边,容量为1,花费为对应的快乐值*-1,因为要求的是最大的“花费”,所以取反。再枚举点,如果时间允许,从i+m到j连一条边,若 i 和 j 类型相同,花费为w,否则为0。

这里把0点当做超级源点,m+m+1当做源点,从超级大源点到源点有k的容量,把m+m+2当做终点,就可以建图成功了。

  (参考里拿的图)

#include <algorithm>
#include  <iterator>
#include  <iostream>
#include   <cstring>
#include   <iomanip>
#include   <cstdlib>
#include    <cstdio>
#include    <string>
#include    <vector>
#include    <bitset>
#include    <cctype>
#include     <queue>
#include     <cmath>
#include      <list>
#include       <map>
#include       <set>
using namespace std;
//#pragma GCC optimize(3)
//#pragma comment(linker, "/STACK:102400000,102400000")  //c++
#define lson (l , mid , rt << 1)
#define rson (mid + 1 , r , rt << 1 | 1)
#define debug(x) cerr << #x << " = " << x << "
";
#define pb push_back
#define pq priority_queue



typedef long long ll;
typedef unsigned long long ull;

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 '
'

#define OKC ios::sync_with_stdio(false);cin.tie(0)
#define FT(A,B,C) for(int A=B;A <= C;++A)  //用来压行
#define REP(i , j , k)  for(int i = j ; i <  k ; ++i)
//priority_queue<int ,vector<int>, greater<int> >que;

const ll mos = 0x7FFFFFFFLL;  //2147483647
const ll nmos = 0x80000000LL;  //-2147483648
const int inf = 0x3f3f3f3f;
const ll inff = 0x3f3f3f3f3f3f3f3fLL; //18
const double PI=acos(-1.0);

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;
}
// #define _DEBUG;         //*//
#ifdef _DEBUG
freopen("input", "r", stdin);
// freopen("output.txt", "w", stdout);
#endif
/*-----------------------show time----------------------*/

        const int maxn = 1e5+9;
        
        struct Edge
        {   
            int to,val,cost,nxt;
        }gEdge[maxn];
        int gHead[maxn],gPre[maxn];
        int gPath[maxn],gDist[maxn];
        bool in[maxn];
        int gcount = 0;      
        int n,m,k,w;
        
        bool spfa(int s,int t){
            
            memset(gPre, -1, sizeof(gPre));
            memset(gDist,inf,sizeof(gDist));
            memset(in, false , sizeof(in));
            gDist[s] = 0; in[s] = true;
            queue<int>q;
            q.push(s);
            while(!q.empty()){
                int u = q.front();
                q.pop();    in[u] = false;
                for(int e = gHead[u]; e!=-1; e = gEdge[e].nxt){
                    int v = gEdge[e].to, w = gEdge[e].cost;
                    if(gEdge[e].val > 0 && gDist[v] > gDist[u] + w){
                        gDist[v] = gDist[u] + gEdge[e].cost;
                        gPre[v] = u;
                        gPath[v] = e;
                        if(!in[v]){
                            q.push(v);in[v] = true;
                        }
                    }
                }
            }
            if(gPre[t] == -1)return false;
            return true;
        }
        int MinCostFlow(int s,int t){
            int cost = 0,flow = 0;
            while(spfa(s,t)){
                int f = inf;
                for(int u = t; u != s; u = gPre[u]){
                    if(gEdge[gPath[u]].val < f){
                        f =gEdge[gPath[u]].val;
                    }
                }
                flow += f;
                cost += gDist[t] * f;
                for(int u=t; u!=s; u = gPre[u]){
                    gEdge[gPath[u]].val -= f;
                    gEdge[gPath[u] ^ 1].val += f;
                }
            }
            return cost;
        }
    
        void addedge(int u,int v,int val, int cost){
            gEdge[gcount].to = v;
            gEdge[gcount].val = val;
            gEdge[gcount].cost = cost;
            gEdge[gcount].nxt = gHead[u];
            gHead[u] = gcount++;

            gEdge[gcount].to = u;
            gEdge[gcount].val = 0;
            gEdge[gcount].cost = -cost;
            gEdge[gcount].nxt = gHead[v];
            gHead[v] = gcount++;

        }
        
        struct eee
        {
            int l,r,w,op;
        }e[maxn];
        /*
            0 是大源点,m+m+1是ci源点,m+m+2是终点。
        */
        void solve(){
                    memset(gHead,-1,sizeof(gHead));
                    gcount = 0;
                    scanf("%d%d%d%d", &n, &m, &k, &w);
                    addedge(0,m+m+1,k,0);
                    for(int i=1; i<=m; i++){
                        scanf("%d%d%d%d", &e[i].l, &e[i].r, &e[i].w, &e[i].op);
                    }

                    for(int i=1; i<=m; i++){
                        for(int j=1; j<=m; j++){
                            if(i==j)continue;

                            if(e[i].r <= e[j].l){
                                int tmp;
                                if(e[i].op == e[j].op)tmp = w;
                                else tmp = 0;
                                addedge(i+m,j,1,tmp);
                            }
                        }
                    }

                    for(int i=1; i<=m; i++){
                        addedge(i,i+m,1,-e[i].w);
                        addedge(i+m, m+m+2,1,0);
                        addedge(m+m+1, i,1,0);
                    }
                    printf("%d
",-1*MinCostFlow(0,m+m+2));
        }
int main(){
        int T;  scanf("%d", &T);
        while(T--){
            solve();
        }
        return 0;
}
HDU-6437
原文地址:https://www.cnblogs.com/ckxkexing/p/9525862.html