321B
2024-09-30 04:37:56
MCMF必须是满足流量最大为前提下的最小费用流(这里是最大费用流)
因此还必须不断地枚举m的流量才行
#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
#include<queue>
using namespace std;
const int maxn = 1e5+11;
const int oo = 0x3f3f3f3f;
int to[maxn<<1],cost[maxn<<1],cap[maxn<<1],flow[maxn<<1],nxt[maxn<<1];
int head[maxn],tot;
void init(){
memset(head,-1,sizeof head);
tot=0;
}
void add(int u,int v,int c,int w){
to[tot]=v;
cap[tot]=c;
flow[tot]=0;
cost[tot]=w;
nxt[tot]=head[u];
head[u]=tot++;
swap(u,v);
to[tot]=v;
cap[tot]=0;
flow[tot]=0;
cost[tot]=-w;
nxt[tot]=head[u];
head[u]=tot++;
}
struct QUEUE{
int que[maxn];
int front,rear;
void init(){front=rear=0;}
void push(int x){que[rear++]=x;}
int pop(){return que[front++];}
bool empty(){return front==rear;}
}que;
int n,m,s,t;
int dis[maxn],pre[maxn];
bool vis[maxn];
bool spfa(){
que.init();
memset(dis,0x80,sizeof dis);
memset(vis,0,sizeof vis);
memset(pre,-1,sizeof pre);
que.push(s);dis[s]=0;vis[s]=1;
while(!que.empty()){
int u = que.pop();
vis[u]=0;
for(int i = head[u]; ~i; i = nxt[i]){
int v=to[i],c=cap[i],f=flow[i],w=cost[i];
if(c>f&&dis[v]<dis[u]+w){
dis[v]=dis[u]+w;
pre[v]=i;
if(!vis[v]){
vis[v]=1;
que.push(v);
}
}
}
}
if(pre[t]==-1)return 0;
return 1;
}
int mcmf(){
int mc=0,mf=0;
while(spfa()){
int mn=oo;
for(int i = pre[t]; ~i; i = pre[to[i^1]]){
mn=min(mn,cap[i]-flow[i]);
}
for(int i = pre[t]; ~i; i = pre[to[i^1]]){
flow[i]+=mn;
flow[i^1]-=mn;
mc+=cost[i]*mn;
}
mf+=mn;
}
return mc;
}
int n1,n2,n3,a[maxn],b[maxn],atr[maxn],x;
char str[199];
int main(){
while(scanf("%d%d",&n1,&n2)!=EOF){
init();
if(n1<n2){
n3=n2-n1;
n=2*n2+2;
t=n;s=t-1;
}
else{
n3=0;
n=n1+n2+2;
t=n;s=n-1;
}
for(int i = 1; i <= n1; i++){
scanf("%s%d",str,&a[i]);
if(str[0]=='A') atr[i]=1;
else atr[i]=0;
}
for(int i = 1; i <= n2; i++){
scanf("%d",&b[i]);
}
if(n3) for(int i = 1; i <= n3; i++){
atr[i+n1]=1;
a[i+n1]=0;
}
for(int i = 1; i <= n2; i++){
add(s,i,1,0);
}
for(int i = 1; i <= n1+n3; i++){
add(i+n2,t,1,0);
}
for(int i = 1; i <= n2; i++){
for(int j = 1; j <= n1+n3; j++){
if(atr[j]==1){
if(b[i]>=a[j]){
if(a[j]!=-oo) add(i,j+n2,1,b[i]-a[j]);
else add(i,j+n2,1,b[i]);
}
else add(i,j+n2,1,-9999);
}
else{
if(b[i]>a[j]){
add(i,j+n2,1,0);
}
else add(i,j+n2,1,-9999);
}
}
}
printf("%d\n",mcmf());
}
return 0;
}
#include <bits/stdc++.h>
#define inf 0x3f3f3f3f
#define INF 0x3f3f3f3f3f3f3f3fLL
#define mod 1000000007
#define pb push_back
#define sq(x) ((x)*(x))
#define sz(a) ((int)a.size())
#define x first
#define y second
#define eps 1e-8
#define bpt(x) (__builtin_popcount(x))
#define bptl(x) (__builtin_popcountll(x))
#define bit(x, y) (((x)>>(y))&1)
#define bclz(x) (__builtin_clz(x))
#define bclzl(x) (__builtin_clzll(x))
#define bctz(x) (__builtin_ctz(x))
#define bctzl(x) (__builtin_ctzll(x))
#define rands(n) (rand()%n+1)
#define rand0(n) (rands(n)-1)
#define Rands(n) ((INT)rand()*rand()%n+1)
#define Rand0(n) (Rands(n)-1)
#define PQ priority_queue<pii, vector<pii>, greater<pii> >
#define rep(i, a, b) for(int i=a; i<b; i++)
using namespace std;
typedef long long INT;
typedef vector<int> VI;
typedef pair<int, int> pii;
typedef pair<INT, INT> PII;
typedef pair<pii, int> ppi;
typedef double DO;
template<typename T, typename U> inline void smin(T &a, U b) {if (a>b) a=b;}
template<typename T, typename U> inline void smax(T &a, U b) {if (a<b) a=b;}
template<class T>inline void gn(T &x) {char c, sg=0; while (c=getchar(), (c>'9' || c<'0') && c!='-');for((c=='-'?sg=1, c=getchar():0), x=0; c>='0' && c<='9'; c=getchar()) x=(x<<1)+(x<<3)+c-'0';if (sg) x=-x;}
template<class T>inline void print(T x) {if (x<0) {putchar('-');return print(-x);}if (x<10) {putchar('0'+x);return;} print(x/10);putchar(x%10+'0');}
int power(int a, int b, int m, int ans=1) {
for (; b; b>>=1, a=1LL*a*a%m) if (b&1) ans=1LL*ans*a%m;
return ans;
}
#if ( ( _WIN32 || __WIN32__ ) && __cplusplus < 201103L)
#define lld "%I64d"
#else
#define lld "%lld"
#endif
#define NN 400
#define MC 100000
int N, M, a[NN], b[NN], V, src, tar, mx, S, T;
int adj[NN][NN], cap[NN][NN], cost[NN][NN];
int dis[NN], q[NN*NN], qf, qb, pre[NN], C, deg[NN];
char s[NN][10];
void init() {
memset(pre, -1, sizeof(pre));
memset(deg, 0, sizeof(deg));
}
void add_edge(int u, int v, int w, int c) {
adj[u][deg[u]++]=v;
adj[v][deg[v]++]=u;
cap[u][v]=w; cap[v][u]=0;
cost[u][v]=c; cost[v][u]=-c;
}
int Mincost_Maxflow() {
int ans=0, bot; C=0;
while(1) {
memset(dis, 0x3f, sizeof(dis));
qf=qb=0;
dis[src]=0; q[qb++]=src;
while(qf<qb) {
int u=q[qf++];
for(int i=0; i<deg[u]; i++) {
int v=adj[u][i];
if(cap[u][v]==0) continue;
if(dis[v]>dis[u]+cost[u][v]) {
dis[v]=dis[u]+cost[u][v];
q[qb++]=v;
pre[v]=u;
}
}
}
if(dis[tar]>=inf) return ans;
bot=inf;
for(int u=tar; u!=src; u=pre[u]) bot=min(bot, cap[pre[u]][u]);
ans+=bot;
for(int u=tar; u!=src; u=pre[u]){
cap[pre[u]][u]-=bot;
cap[u][pre[u]]+=bot;
}
C+=dis[tar]*bot;
}
return ans;
}
int main() {
gn(N); gn(M);
for(int i=1; i<=N; i++) {
scanf("%s", s[i]); gn(a[i]);
}
for(int i=1; i<=M; i++) gn(b[i]);
src=0; tar=M+N+1; S=M+N+2; T=M+N+3;
for(int k=1; k<=M; k++) {
init();
add_edge(src, S, k, 0);
for(int i=1; i<=M; i++) {
add_edge(S, i, 1, 0);
add_edge(i, T, 1, -b[i]);
for(int j=1; j<=N; j++) {
if(b[i]>=a[j] && s[j][0]=='A') add_edge(i, j+M, 1, a[j]-b[i]);
else if(b[i]>a[j] && s[j][0]=='D') add_edge(i, j+M, 1, 0);
}
}
for(int i=1; i<=N; i++) add_edge(M+i, tar, 1, 0);
add_edge(T, tar, M, MC);
Mincost_Maxflow();
if(cap[tar][T]>max(0, k-N)) continue;
mx= max(mx, -C+cap[tar][T]*MC);
}
printf("%d\n", mx);
return 0;
}
#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
#include<queue>
typedef long long ll;
using namespace std;
const int maxn = 7e4+11;
const int oo = 0x3f3f3f3f;
int to[maxn<<1],cost[maxn<<1],cap[maxn<<1],flow[maxn<<1],nxt[maxn<<1];
int _to[maxn<<1],_cost[maxn<<1],_cap[maxn<<1],_flow[maxn<<1],_nxt[maxn<<2];
int head[maxn],tot;
int _head[maxn],_tot;
void init(){
memset(head,-1,sizeof head);
tot=0;
}
void add(int u,int v,int c,int w){
to[tot]=v;
cap[tot]=c;
flow[tot]=0;
cost[tot]=w;
nxt[tot]=head[u];
head[u]=tot++;
swap(u,v);
to[tot]=v;
cap[tot]=0;
flow[tot]=0;
cost[tot]=-w;
nxt[tot]=head[u];
head[u]=tot++;
}
struct QUEUE{
int que[maxn];
int front,rear;
void init(){front=rear=0;}
void push(int x){que[rear++]=x;}
int pop(){return que[front++];}
bool empty(){return front==rear;}
}que;
int n,m,s,t;
int dis[maxn],pre[maxn];
bool vis[maxn];
bool spfa(){
que.init();
memset(dis,oo,sizeof dis);
memset(vis,0,sizeof vis);
memset(pre,-1,sizeof pre);
que.push(s);dis[s]=0;vis[s]=1;
while(!que.empty()){
int u = que.pop();
vis[u]=0;
for(int i = head[u]; ~i; i = nxt[i]){
int v=to[i],c=cap[i],f=flow[i],w=cost[i];
if(c>f&&dis[v]>dis[u]+w){
dis[v]=dis[u]+w;
pre[v]=i;
if(!vis[v]){
vis[v]=1;
que.push(v);
}
}
}
}
if(pre[t]==-1)return 0;
return 1;
}
ll mcmf(){
ll mc=0,mf=0;
while(spfa()){
int mn=oo;
for(int i = pre[t]; ~i; i = pre[to[i^1]]){
mn=min(mn,cap[i]-flow[i]);
}
for(int i = pre[t]; ~i; i = pre[to[i^1]]){
flow[i]+=mn;
flow[i^1]-=mn;
mc+=1ll*cost[i]*mn;
}
mf+=mn;
}
return mc;
}
void backup(){
memcpy(_to,to,sizeof to);
memcpy(_nxt,nxt,sizeof nxt);
memcpy(_cap,cap,sizeof cap);
memcpy(_flow,flow,sizeof flow);
memcpy(_cost,cost,sizeof cost);
memcpy(_head,head,sizeof head);
_tot=tot;
}
void recover(){
memcpy(to,_to,sizeof to);
memcpy(nxt,_nxt,sizeof nxt);
memcpy(cap,_cap,sizeof cap);
memcpy(flow,_flow,sizeof flow);
memcpy(cost,_cost,sizeof cost);
memcpy(head,_head,sizeof head);
tot=_tot;
}
int n1,n2,n3,a[maxn],b[maxn],atr[maxn],x;
char str[199];
int main(){
while(scanf("%d%d",&n1,&n2)!=EOF){
init();int ss,tt;ll maxcost=oo;
for(int i = 1; i <= n1; i++){
scanf("%s%d",str,&a[i]);
if(str[0]=='A') atr[i]=1;
else atr[i]=0;
}
for(int i = 1; i <= n2; i++){
scanf("%d",&b[i]);
}
n=n1+2*n2+4;t=n;s=t-1;tt=s-1;ss=tt-1;
int guaidian=n2,duimian=n1+n2;
ll bigInt=200000;
for(int i = 1; i <= n2; i++) add(ss,i,1,0);
for(int i = 1; i <= n1; i++) add(i+duimian,tt,1,0);
for(int i = 1; i <= n2; i++){
add(i,i+guaidian,1,bigInt);
add(i+guaidian,tt,1,-b[i]);
for(int j = 1; j <= n1; j++){
if(atr[j]==1) if(b[i]>=a[j])add(i,j+duimian,1,-(b[i]-a[j]));
if(atr[j]==0) if(b[i]>a[j])add(i,j+duimian,1,0);
}
}
backup();
for(int k = 1; k <= n2; k++){
// if(k>1)break;
recover();
add(s,ss,k,0);
add(tt,t,k,0);
if(k<=n1) maxcost=min(maxcost,mcmf());
else maxcost=min(maxcost,mcmf()+(k-n1)*bigInt);
}
maxcost=-maxcost;
printf("%lld\n",maxcost);
}
return 0;
return 0;
}
510E
#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
#include<queue>
#include<vector>
#include<set>
using namespace std;
const int maxn = 1e5+11;
const int oo = 0x3f3f3f3f;
int to[maxn<<1],nxt[maxn<<1],cap[maxn<<1],flow[maxn<<1];
int head[maxn],tot;
struct UF{
int p[256];
void init(){
for(int i = 0; i < 256; i++) p[i]=i;
}
int find(int x){
return p[x]==x?x:p[x]=find(p[x]);
}
void link(int a,int b){
a=find(a);b=find(b);
if(a!=b) p[a]=b;
}
}uf;
void init(){
memset(head,-1,sizeof head);
tot=0;
}
void add(int u,int v,int w){
to[tot]=v;
nxt[tot]=head[u];
cap[tot]=w;
flow[tot]=0;
head[u]=tot++;
swap(u,v);
to[tot]=v;
nxt[tot]=head[u];
cap[tot]=0;
flow[tot]=0;
head[u]=tot++;
}
//int n,m,s,t;
//int dis[maxn],pre[maxn],cur[maxn],gap[maxn];
//bool vis[maxn];
struct QUEUE{
int que[maxn];
int front,rear;
void init(){front=rear=0;}
void push(int u){que[rear++]=u;}
int pop(){return que[front++];}
bool empty(){return front==rear;}
}que;
int n,m,s,t;
int gap[maxn],dep[maxn];
void bfs(){
memset(dep,-1,sizeof dep);
memset(gap,0,sizeof gap);
gap[0]=1;
que.init();
que.push(t);dep[t]=0;
while(!que.empty()){
int u = que.pop();
for(int i = head[u]; ~i; i = nxt[i]){
int v=to[i];
if(~dep[v])continue;
que.push(v);
dep[v]=dep[u]+1;
gap[dep[v]]++;
}
}
}
int cur[maxn],S[maxn];
int isap(){
bfs();
memcpy(cur,head,sizeof head);
int ans=0,top=0,u=s;
while(dep[s]<n){
if(u==t){
int mn=oo;
int inser;
for(int i = 0; i < top; i++){
if(mn>cap[S[i]]-flow[S[i]]){
mn=cap[S[i]]-flow[S[i]];
inser=i;
}
}
for(int i = 0; i < top; i++){
flow[S[i]]+=mn;
flow[S[i]^1]-=mn;
}
ans+=mn;
top=inser;
u=to[S[top]^1];
continue;
}
bool flag=0;
int v;
for(int i = cur[u]; ~i; i = nxt[i]){
v=to[i];
if(cap[i]-flow[i]&&dep[v]+1==dep[u]){
flag=1;
cur[u]=i;
break;
}
}
if(flag){
S[top++]=cur[u];
u=v;
continue;
}
int mn=n;
for(int i = head[u]; ~i; i = nxt[i]){
if(cap[i]-flow[i]&&dep[to[i]]<mn){
mn=dep[to[i]];
cur[u]=i;
}
}
gap[dep[u]]--;
if(!gap[dep[u]])return ans;
dep[u]=mn+1;
gap[dep[u]]++;
if(u!=s)u=to[S[--top]^1];
}
return ans;
}
bool isnprime[maxn];
void sai(){
isnprime[0]=isnprime[1]=1;
for(int i = 2; i*i < 100000; i++){
if(!isnprime[i]){
for(int j = 2*i; j < 100000; j+=i){
isnprime[j]=1;
}
}
}
}
bool go[maxn];
vector<int> G[maxn];
int cnt;
vector<int> biao[500];
vector<int> biao2[500];
int biao3[maxn];
vector<int> biao4[maxn];
//void dfs(int u,int k){
// go[u]=1;GG[k].push_back(u);
// for(int i = 0; i < G[u].size(); i++){
// if(!go[G[u][i]]) dfs(G[u][i],k);
// }
//}
int n1,a[maxn];
bool in[maxn];
bool dfs(int now,int cur,int p,int one){
if(cur==biao[now].size()+1){return 1;}
if(cur==1){
for(int i = 0; i < biao[now].size(); i++){
in[biao[now][i]]=1; biao3[cur]=biao[now][i];
bool flag=dfs(now,cur+1,biao[now][i],biao[now][i]);
if(flag)return 1;
in[biao[now][i]]=0;
}
}
else{
int qian=p;
for(int i = 0; i < biao2[qian].size(); i++){
if(cur!=biao[now].size()) {
if(!isnprime[a[biao2[qian][i]]+a[one]])if(!isnprime[a[qian]+a[biao2[qian][i]]] && !in[biao2[qian][i]]){
in[biao2[qian][i]]=1; biao3[cur]=biao2[qian][i];
bool flag=dfs(now,cur+1,biao2[qian][i],one);
if(flag)return 1;
in[biao2[qian][i]]=0;
}
}
else{
if(!isnprime[a[qian]+a[biao2[qian][i]]] && !in[biao2[qian][i]]){
in[biao2[qian][i]]=1; biao3[cur]=biao2[qian][i];
bool flag=dfs(now,cur+1,biao2[qian][i],one);
if(flag)return 1;
in[biao2[qian][i]]=0;
}
}
}
}
}
int main(){
sai();
while(scanf("%d",&n1)!=EOF){
init();
for(int i = 1; i <= n1; i++){
scanf("%d",&a[i]);
}
n=n1+2;s=n-1;t=n;
for(int i = 1; i <= n1; i++){
if(a[i]&1) add(s,i,2);
else add(i,t,2);
}
for(int i = 1; i <= n1; i++){
if(a[i]&1) for(int j = 1; j <= n1; j++){
if(!(a[j]&1)) if(!isnprime[a[i]+a[j]]) add(i,j,1);
}
}
int ans=isap();
if(ans!=n1){
printf("Impossible\n");
continue;
}
memset(G,0,sizeof G);
for(int i = 1; i <= n1; i++){
for(int j = head[i]; ~j; j = nxt[j]){
int v=to[j],c=cap[j],f=flow[j];
if(c==0||v==s||v==t) continue;
if(f==1)G[i].push_back(v);
}
}
// for(int i = 1; i <= n1; i++){
// cout<<i<<": ";
// if(G[i].size()==0) cout<<endl;
// for(int j = 0; j < G[i].size(); j++){
// if(j==G[i].size()-1) printf("%d\n",G[i][j]);
// else printf("%d ",G[i][j]);
// }
// }
uf.init();
for(int i = 1; i <= n1; i++){
for(int j = 0; j < G[i].size(); j++){
uf.link(i,G[i][j]);
}
}
for(int i = 1; i <= n1; i++) uf.find(i);
cnt=0;
memset(biao,0,sizeof biao);
for(int i = 1; i <= n1; i++){
if(uf.p[i]==i){
cnt++;
}
biao[uf.p[i]].push_back(i);
}
printf("%d\n",cnt);
int cnt2=0;
memset(biao4,0,sizeof biao4);
for(int i = 1; i <= n1; i++){
if(biao[i].size()) printf("%d ",biao[i].size()),cnt2++;
for(int j = 0; j < biao[i].size(); j++){
biao4[cnt2].push_back(biao[i][j]);
// if(j==biao[i].size()-1) printf("%d\n",biao[i][j]);
// else printf("%d ",biao[i][j]);
}
}
memcpy(biao,biao4,sizeof biao);
// cout<<cnt2-cnt<<"ewe"<<endl;
for(int i = 1; i <= cnt; i++){
memset(biao2,0,sizeof biao2);
for(int j = 0; j < biao[i].size(); j++){
for(int k = 0; k < biao[i].size(); k++){
if(j!=k) if(!isnprime[a[biao[i][j]]+a[biao[i][k]]]) biao2[biao[i][j]].push_back(biao[i][k]),cout<<a[biao[i][j]]<<" "<<a[biao[i][k]]<<endl;
}
}
memset(biao3,0,sizeof biao3); memset(in,0,sizeof in);
dfs(i,1,0,666);
for(int j = 1; j <= biao[i].size(); j++){
if(j==biao[i].size()) printf("%d\n",biao3[j]);
else printf("%d ",biao3[j]);
}
}
}
return 0;
}
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