[随机化调整] Ural 1144 The Emperor's Riddle

论文：唐文斌--浅谈“调整”思想在信息学竞赛中的应用

参考了 http://blog.csdn.net/nlj1999/article/details/50849965

有N（N ≤ 10000）箱黄金，第i箱黄金的价值为A[i]（0≤A[i]≤1000）。皇帝要将这N箱黄金赏给M（M≤1000）位将军，每个人可以获得任意箱，但是一箱黄金不能分开发，只能发一位将军。请找出一种分黄金的方案，使得获得最多黄金的将军与获得最少黄金的将军两人得到的黄金数相差不超过K。题目保证有解。

#include<cstdio>
#include<cstdlib>
#include<algorithm>
#include<queue>
#include<cstring>
#include<functional>
#include<ctime>
#define cl(x) memset(x,0,sizeof(x))
using namespace std;
typedef pair<int,int> abcd;

inline char nc(){
static char buf[100000],*p1=buf,*p2=buf;
if (p1==p2) { p2=(p1=buf)+fread(buf,1,100000,stdin); if (p1==p2) return EOF; }
return *p1++;
}

inline void read(int &x){
char c=nc(),b=1;
for (;!(c>='0' && c<='9');c=nc()) if (c=='-') b=-1;
for (x=0;c>='0' && c<='9';x=x*10+c-'0',c=nc()); x*=b;
}

const int N=10005;

struct edge{
int v,next;
}G
;
int head
,inum;

inline void add(int u,int v,int p){
G[p].v=v; G[p].next=head[u]; head[u]=p;
}

int n,m,K,tot,Ans;
int a
;

priority_queue<abcd,vector<abcd>,greater<abcd> > Q;

int belong
,sum
;

inline int check(){
cl(sum);
for (int i=1;i<=n;i++) sum[belong[i]]+=a[i];
int maxv=0,minv=1<<30;
for (int i=1;i<=m;i++)
maxv=max(maxv,sum[i]),minv=min(minv,sum[i]);
return maxv-minv;
}

abcd val
;

inline int G1(){
for (int i=1;i<=n;i++) val[i]=abcd(a[i],i);
sort(val+1,val+n+1);
for (int i=1;i<=m;i++) Q.push(abcd(0,i));
for (int i=n;i;i--){
abcd t=Q.top(); Q.pop();
belong[val[i].second]=t.second;
Q.push(abcd(t.first+val[i].first,t.second));
}
}

int tag
,cur
,tmp
;
int s
,lst
;

inline bool cmp(int a,int b){
return s[a]<s[b];
}

inline bool G2(){
for (int i=1;i<=n;i++) tag[i]=rand()&1;

for (int i=1;i<=m;i++) s[i]=0;
for (int i=1;i<=n;i++) if (tag[i]==0) s[belong[i]]+=a[i];
sort(lst+1,lst+m+1,cmp);
for (int i=1;i<=m;i++) cur[lst[i]]=i;
for (int i=1;i<=n;i++) if (tag[i]==0) tmp[i]=cur[belong[i]];

for (int i=1;i<=m;i++) s[i]=0;
for (int i=1;i<=n;i++) if (tag[i]==1) s[belong[i]]+=a[i];
sort(lst+1,lst+m+1,cmp);
for (int i=1;i<=m;i++) cur[lst[m-i+1]]=i;
for (int i=1;i<=n;i++) if (tag[i]==1) tmp[i]=cur[belong[i]];

for (int i=1;i<=n;i++) belong[i]=tmp[i];
}

inline void Print(){
printf("%d\n",Ans);
for (int i=1;i<=m;i++,putchar('\n'))
for (int p=head[i];p;p=G[p].next)
printf("%d ",G[p].v);
}

int main(){
srand(10086);
freopen("t.in","r",stdin);
freopen("t.out","w",stdout);
read(n); read(m); read(K);
for (int i=1;i<=n;i++) read(a[i]),tot+=a[i];
G1();
for (int i=1;i<=m;i++) lst[i]=i;
while ((Ans=check())>K)
G2();
for (int i=1;i<=n;i++) add(belong[i],i,++inum);
Print();
return 0;
}