[LOJ2288][THUWC2017]大葱的神力：搜索+背包DP+费用流+随机化

分析

测试点1、2：搜索+剪枝。

测试点3：只有一个抽屉，直接01背包。

测试点4、5：每个物品体积相同，说明每个抽屉能放下的物品个数固定，建图跑费用流。

测试点6：每个物品体积相近，经过验证发现每个抽屉能放下的物品个数仍然固定，费用流。

测试点7：除了第一个物品，其他物品体积相同。所以可以枚举第一个物品放在哪个抽屉，然后费用流。

测试点8、9、10：随机化贪心，如果不是人品爆发基本不可能过（博主没过）。

代码

测试点3

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <cctype>
#include <algorithm>
#define rin(i,a,b) for(int i=(a);i<=(b);i++)
#define rec(i,a,b) for(int i=(a);i>=(b);i--)
#define trav(i,a) for(int i=head[(a)];i;i=e[i].nxt)
typedef long long LL;
using std::cin;
using std::cout;
using std::endl;

inline int read(){
	int x;scanf("%d",&x);return x;
}

const int MAXN=2005;
const int MAXS=10005;
int n,m,s,v[MAXN],w[MAXN];
int f[MAXN][MAXS],pre[MAXN][MAXS];
int ans[MAXN];

int main(){
	freopen("drawer3.in","r",stdin);
	freopen("drawer3.out","w",stdout);
	n=read(),m=read();
	rin(i,1,n) v[i]=read();
	s=read();
	rin(i,1,n) w[i]=read();
	rin(i,1,n) rec(j,s,v[i]){
		f[i][j]=f[i-1][j];
		pre[i][j]=j;
		if(f[i-1][j-v[i]]+w[i]>f[i][j]){
			f[i][j]=f[i-1][j-v[i]]+w[i];
			pre[i][j]=j-v[i];
		}
	}
	int now=s,pos=n;
	while(pos){
		if(pre[pos][now]<now) ans[pos]=1;
		now=pre[pos][now];
		pos--;
	}
	rin(i,1,n) printf("%d ",ans[i]);
	printf("
");
	return 0;
}

测试点4、5、6

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <cctype>
#include <algorithm>
#include <queue>
#define rin(i,a,b) for(int i=(a);i<=(b);i++)
#define rec(i,a,b) for(int i=(a);i>=(b);i--)
#define trav(i,a) for(int i=head[(a)];i;i=e[i].nxt)
typedef long long LL;
using std::cin;
using std::cout;
using std::endl;

inline int read(){
	int x;scanf("%d",&x);return x;
}

const int MAXN=1005;
const int MAXM=205;
int n,m,S,T,mincost,v,c[MAXM],w[MAXN][MAXM],ecnt=1,head[MAXN+MAXM];
int dis[MAXN+MAXM],pre[MAXN+MAXM];
bool book[MAXN+MAXM];
std::queue<int> q;
struct Edge{
	int to,nxt,cap,ost;
}e[(MAXN+MAXM+MAXN*MAXM)<<1];

inline void add_edge(int bg,int ed,int cap,int ost){
	ecnt++;
	e[ecnt].to=ed;
	e[ecnt].nxt=head[bg];
	e[ecnt].cap=cap;
	e[ecnt].ost=ost;
	head[bg]=ecnt;
}

inline bool spfa(){
	memset(dis,0x3f,sizeof dis);
	while(!q.empty()) q.pop();
	dis[S]=0;
	q.push(S);
	book[S]=1;
	while(!q.empty()){
		int x=q.front();q.pop();
		trav(i,x){
			int ver=e[i].to;
			if(dis[ver]>dis[x]+e[i].ost&&e[i].cap){
				dis[ver]=dis[x]+e[i].ost;
				pre[ver]=i;
				if(!book[ver]){
					q.push(ver);
					book[ver]=1;
				}
			}
		}
		book[x]=0;
	}
	return dis[T]<1e9;
}

inline void upd(){
	int now=T,flow=1e9;
	while(now!=S){
		flow=std::min(flow,e[pre[now]].cap);
		now=e[pre[now]^1].to;
	}
	now=T;
	while(now!=S){
		e[pre[now]].cap-=flow;
		e[pre[now]^1].cap+=flow;
		now=e[pre[now]^1].to;
	}
	mincost+=flow*dis[T];
}

inline void ek(){
	while(spfa()) upd();
}

int main(){
	freopen("drawer6.in","r",stdin);
	freopen("drawer6.out","w",stdout);
	n=read(),m=read();
	S=n+m+1,T=S+1;
	rin(i,1,n){
		v=read();
		add_edge(S,i,1,0);
		add_edge(i,S,0,0);
	}
	rin(i,1,m){
		c[i]=read()/v;
		add_edge(n+i,T,c[i],0);
		add_edge(T,n+i,0,0);
	}
	rin(i,1,n) rin(j,1,m){
		w[i][j]=read();
		add_edge(i,n+j,1,-w[i][j]);
		add_edge(n+j,i,0,w[i][j]);
	}
	ek();
	rin(i,1,n){
		bool flag=0;
		trav(j,i){
			int ver=e[j].to;
			if(ver==S) continue;
			if(!e[j].cap){
				printf("%d ",ver-n);
				flag=1;break;
			}
		}
		if(!flag) printf("0 ");
	}
	printf("
");
	return 0;
}

测试点7

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <cctype>
#include <algorithm>
#include <queue>
#define rin(i,a,b) for(int i=(a);i<=(b);i++)
#define rec(i,a,b) for(int i=(a);i>=(b);i--)
#define trav(i,a) for(int i=head[(a)];i;i=e[i].nxt)
typedef long long LL;
using std::cin;
using std::cout;
using std::endl;

inline int read(){
	int x;scanf("%d",&x);return x;
}

const int MAXN=1005;
const int MAXM=205;
int n,m,S,T,mincost,v,c[MAXM],w[MAXN][MAXM],ecnt=1,head[MAXN+MAXM];
int dis[MAXN+MAXM],pre[MAXN+MAXM];
bool book[MAXN+MAXM];
std::queue<int> q;
struct Edge{
	int to,nxt,cap,ost;
}e[(MAXN+MAXM+MAXN*MAXM)<<1];

inline void add_edge(int bg,int ed,int cap,int ost){
	ecnt++;
	e[ecnt].to=ed;
	e[ecnt].nxt=head[bg];
	e[ecnt].cap=cap;
	e[ecnt].ost=ost;
	head[bg]=ecnt;
}

inline bool spfa(){
	memset(dis,0x3f,sizeof dis);
	while(!q.empty()) q.pop();
	dis[S]=0;
	q.push(S);
	book[S]=1;
	while(!q.empty()){
		int x=q.front();q.pop();
		trav(i,x){
			int ver=e[i].to;
			if(dis[ver]>dis[x]+e[i].ost&&e[i].cap){
				dis[ver]=dis[x]+e[i].ost;
				pre[ver]=i;
				if(!book[ver]){
					q.push(ver);
					book[ver]=1;
				}
			}
		}
		book[x]=0;
	}
	return dis[T]<1e9;
}

inline void upd(){
	int now=T,flow=1e9;
	while(now!=S){
		flow=std::min(flow,e[pre[now]].cap);
		now=e[pre[now]^1].to;
	}
	now=T;
	while(now!=S){
		e[pre[now]].cap-=flow;
		e[pre[now]^1].cap+=flow;
		now=e[pre[now]^1].to;
	}
	mincost+=flow*dis[T];
}

inline void ek(){
	while(spfa()) upd();
}

int main(){
	freopen("drawer7.in","r",stdin);
	freopen("drawer7.out","w",stdout);
	n=read(),m=read();
	S=n+m+1,T=S+1;
	int v1=read();
	rin(i,2,n){
		v=read();
	}
	rin(i,1,m){
		c[i]=read();
	}
	rin(i,1,n) rin(j,1,m){
		w[i][j]=read();
	}
	int minpos=-1,umincost=0;
	rin(k,1,m){
		ecnt=1,mincost=0;
		memset(head,0,sizeof head);
		c[k]-=v1;
		mincost-=w[1][k];
		rin(i,2,n){
			add_edge(S,i,1,0);
			add_edge(i,S,0,0);
		}
		rin(i,1,m){
			add_edge(n+i,T,c[i]/v,0);
			add_edge(T,n+i,0,0);
		}
		rin(i,2,n) rin(j,1,m){
			add_edge(i,n+j,1,-w[i][j]);
			add_edge(n+j,i,0,w[i][j]);
		}
		ek();
		if(mincost<umincost){
			umincost=mincost;
			minpos=k;
		}
		c[k]+=v1;
	}
	ecnt=1,mincost=0;
	memset(head,0,sizeof head);
	rin(i,2,n){
		add_edge(S,i,1,0);
		add_edge(i,S,0,0);
	}
	rin(i,1,m){
		add_edge(n+i,T,c[i]/v,0);
		add_edge(T,n+i,0,0);
	}
	rin(i,2,n) rin(j,1,m){
		add_edge(i,n+j,1,-w[i][j]);
		add_edge(n+j,i,0,w[i][j]);
	}
	ek();
	if(mincost<umincost){
		umincost=mincost;
		minpos=0;
	}
	else{
		int k=minpos;
		ecnt=1,mincost=0;
		memset(head,0,sizeof head);
		c[k]-=v1;
		mincost-=w[1][k];
		rin(i,2,n){
			add_edge(S,i,1,0);
			add_edge(i,S,0,0);
		}
		rin(i,1,m){
			add_edge(n+i,T,c[i]/v,0);
			add_edge(T,n+i,0,0);
		}
		rin(i,2,n) rin(j,1,m){
			add_edge(i,n+j,1,-w[i][j]);
			add_edge(n+j,i,0,w[i][j]);
		}
		ek();
	}
	printf("%d ",minpos);
	rin(i,2,n){
		bool flag=0;
		trav(j,i){
			int ver=e[j].to;
			if(ver==S) continue;
			if(!e[j].cap){
				printf("%d ",ver-n);
				flag=1;break;
			}
		}
		if(!flag) printf("0 ");
	}
	printf("
");
	return 0;
}

测试点8、9、10

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <cctype>
#include <algorithm>
#include <ctime>
#include <vector>
#define rin(i,a,b) for(int i=(a);i<=(b);i++)
#define rec(i,a,b) for(int i=(a);i>=(b);i--)
#define trav(i,a) for(int i=head[(a)];i;i=e[i].nxt)
typedef long long LL;
using std::cin;
using std::cout;
using std::endl;

inline int read(){
	int x;scanf("%d",&x);return x;
}

const int MAXN=1005;
const int MAXM=305;
int n,m,v[MAXN],c[MAXM],blg[MAXN];
bool vis[MAXN];
std::vector<int> vec[MAXM],maxvec[MAXM];
struct Pair{
	int id,w;
	inline friend bool operator < (Pair A,Pair B){
		return 1.0*A.w/v[A.id]>1.0*B.w/v[B.id];
	}
}a[MAXM][MAXN];

inline int work(){
	memset(vis,0,sizeof vis);
	int ret=0;
	rin(i,1,m){
		vec[i].clear();
		int rem=c[i];
		rin(j,1,n){
			if(vis[a[i][j].id]||rem<v[a[i][j].id]) continue;
			if((rand()%(n*2))>n+vec[i].size()) continue;
			vec[i].push_back(a[i][j].id);
			vis[a[i][j].id]=1;
			rem-=v[a[i][j].id];
			ret+=a[i][j].w;
		}
	}
	return ret;
}

int main(){
	freopen("drawer10.in","r",stdin);
	freopen("drawer10.out","w",stdout);
	srand(time(0));
	n=read(),m=read();
	rin(i,1,n) v[i]=read();
	rin(i,1,m) c[i]=read();
	rin(i,1,n) rin(j,1,m) a[j][i]=(Pair){i,read()};
	rin(i,1,m) std::sort(a[i]+1,a[i]+n+1);
	int maxans=0;
	rin(k,1,10000){
		int temp=work();
		if(temp>maxans){
			memset(blg,0,sizeof blg);
			rin(i,1,m) rin(j,0,(int)vec[i].size()-1)
				blg[vec[i][j]]=i;
			maxans=temp;
		}
	}
	rin(i,1,n) printf("%d ",blg[i]);
	printf("
");
	return 0;
}