题目链接:https://www.luogu.com.cn/problem/P4553
题目大意:
思路:拆点,i->i+n的流量限制为[v, v],费用为0, .然后每个点都可以作为入点,每个点都可以作为出点。为了保证m个人,我们应再建辅助源点S。s->S流量限制为[m, m]。再由S向所有的剧情点连边。
#pragma GCC optimize(3, "Ofast", "inline")
#include<bits/stdc++.h>
#define re register
using namespace std;
const int maxn = 500 + 10;
const int maxm=1e6+10;
const int inf=1<<30;
#define getchar() (p1==p2&&(p2=(p1=buf)+fread(buf,1,1<<20,stdin),p1==p2)?EOF:*p1++)
char buf[1<<20],*p1=buf,*p2=buf;
inline int read() {
int f=0,fu=1;
char c=getchar();
while(c<'0'||c>'9') {
if(c=='-')
fu=-1;
c=getchar();
}
while(c>='0'&&c<='9') {
f=(f<<3)+(f<<1)+c-48;
c=getchar();
}
return f*fu;
}
struct po {
int to,dis,nxt,w;
} edge[maxm<<1];
struct max_folw {
int dis[maxn];
int vis[maxn];
int head[maxn];
int d[maxn];
int n,s,t,cut=-1;
int ans=0, fy=0;
void init(int N, int S, int T) {
ans=0, fy=0;
cut=-1;
n=N, s=S, t=T;
memset(head, -1, sizeof(head));
memset(d, 0, sizeof(d));
}
void add_edge(int from,int to,int w,int dis) {
edge[++cut].nxt=head[from];
edge[cut].to=to;
edge[cut].w=w;
edge[cut].dis=dis;
head[from]=cut;
}
void add(int from,int to,int w,int dis) {
add_edge(from,to,w,dis);
add_edge(to,from,0,-dis);
}
void addlr(int from,int to,int w,int l, int r){//有限制的添边
add(from,to,r-l,w);
d[to]+=l, d[from]-=l;
fy+=l*w;
}
bool spfa() {
memset(vis,0,sizeof(vis));
for(re int i=0; i<=n; i++)
dis[i]=inf;
dis[t]=0;
vis[t]=1;
deque<int> q;
q.push_back(t);
while(!q.empty()) {
int u=q.front();
vis[u]=0;
q.pop_front();
for(re int i=head[u]; i!=-1; i=edge[i].nxt) {
int v=edge[i].to;
if(edge[i^1].w>0&&dis[v]>dis[u]-edge[i].dis) {
dis[v]=dis[u]-edge[i].dis;
if(!vis[v]) {
vis[v]=1;
if(!q.empty()&&dis[v]<dis[q.front()])
q.push_front(v);
else
q.push_back(v);
}
}
}
}
return dis[s]<inf;
}
int dfs(int u,int low) {
if(u==t) {
vis[t]=1;
return low;
}
int diss=0;
vis[u]=1;
for(re int i=head[u]; i!=-1; i=edge[i].nxt) {
int v=edge[i].to;
if(!vis[v]&&edge[i].w!=0&&dis[u]-edge[i].dis==dis[v]) {
int check=dfs(v,min(edge[i].w,low));
if(check>0) {
fy+=check*edge[i].dis;
edge[i].w-=check;
edge[i^1].w+=check;
low-=check;
diss+=check;
if(low==0)
break;
}
}
}
return diss;
}
void max_flow() {
for(int i=0; i<=n; i++){//要求访问到所有点
if(d[i]>0){
add(s, i, d[i], 0);
}
if(d[i]<0){
add(i, t, -d[i], 0);
}
}
while(spfa()) {
vis[t]=1;
while(vis[t]) {
memset(vis,0,sizeof(vis));
ans+=dfs(s,inf);
}
}
}
} flow;
int main() {
int n, m; scanf("%d%d", &n, &m);
int s=0, t=2*n+1, S=2*n+2, ss=2*n+3, tt=2*n+4;
flow.init(tt+5, ss, tt);
int x;
flow.addlr(s, S, 0, m, m);
for(int i=1; i<=n; i++){
scanf("%d", &x);
flow.addlr(i, i+n, 0, x, x);
flow.add(S, i, m, 0);
flow.add(i+n, t, m, 0);
}
for(int i=1; i<n; i++){
for(int j=i+1; j<=n; j++){
scanf("%d", &x);
if(x!=-1){
flow.add(i+n, j, inf, x);
}
}
}
flow.add(t, s, inf, 0);
flow.max_flow();
printf("%d\n", flow.fy);
return 0;
}
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