BZOJ2670 : Almost

#include<cstdio>
#include<algorithm>
using namespace std;
const int N=100010,M=30010,K=500,inf=2000010;
typedef long long ll;
int n,m,i,x,f[N],L,R;ll s[N],a[N],b[N];
struct E{int l,r,p;}e[M];
inline bool cmp(const E&a,const E&b){return f[a.l]==f[b.l]?a.r<b.r:f[a.l]<f[b.l];}
ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
struct P{
  ll u,d;
  P(){}
  P(ll _u,ll _d){u=_u,d=_d;}
  bool operator<(const P&b){return u*b.d<d*b.u;}
  void reset(){u=-inf,d=1;}
  void write(){
    if(!u)puts("0/1");
    else{
      ll t=gcd(u>0?u:-u,d);
      printf("%lld/%lld\n",u/t,d/t);
    }
  }
}ans[M],best,tmp,now;
struct HullA{
  int q[N],t;
  void init(){t=0;}
  void add(int x){
    while(t>1&&(a[q[t]]-a[q[t-1]])*(x-q[t])>=(a[x]-a[q[t]])*(q[t]-q[t-1]))t--;
    q[++t]=x;
  }
  void ask(int x,P&ans){
    if(!t)return;
    int l=2,r=t,o=1,mid;
    while(l<=r){
      mid=(l+r)>>1;
      if((a[q[mid]]-a[q[mid-1]])*(x-q[mid])<=(b[x]-a[q[mid]])*(q[mid]-q[mid-1]))l=(o=mid)+1;else r=mid-1;
    }
    now=P(b[x]-a[q[o]],x-q[o]);
    if(ans<now)ans=now;
  }
}hA,tA;
struct HullB{
  int q[N],t;
  void init(){t=0;}
  void add(int x){
    while(t>1&&(b[q[t]]-b[q[t-1]])*(x-q[t])<=(b[x]-b[q[t]])*(q[t]-q[t-1]))t--;
    q[++t]=x;
  }
  void ask(int x,P&ans){
    if(!t)return;
    int l=1,r=t-1,o=t,mid;
    while(l<=r){
      mid=(l+r)>>1;
      if((b[q[mid+1]]-b[q[mid]])*(q[mid]-x)<=(b[q[mid]]-a[x])*(q[mid+1]-q[mid]))r=(o=mid)-1;else l=mid+1;
    }
    now=P(b[q[o]]-a[x],q[o]-x);
    if(ans<now)ans=now;
  }
}hB;
inline void read(int&a){
  char c;bool f=0;a=0;
  while(!((((c=getchar())>=‘0‘)&&(c<=‘9‘))||(c==‘-‘)));
  if(c!=‘-‘)a=c-‘0‘;else f=1;
  while(((c=getchar())>=‘0‘)&&(c<=‘9‘))(a*=10)+=c-‘0‘;
  if(f)a=-a;
}
inline void vio(int l,int r){
  tA.init();
  tmp.reset();
  while(l<=r)tA.ask(l,tmp),tA.add(l++);
}
inline void ask(int l,int r){
  while(l<=r)hB.ask(l++,tmp);
}
int main(){
  read(n),read(m);
  for(i=1;i<=n;i++)read(x),s[i]=s[i-1]+x;
  for(i=1;i<=n;i++)a[i]=s[i-1],b[i]=s[i];
  for(i=1;i<=n;i++)f[i]=min(((i-1)/K+1)*K,n);
  for(i=1;i<=m;i++){
    read(e[i].l),read(e[i].r),e[i].p=i;
    if(e[i].l+K+5>=e[i].r){
      vio(e[i].l,e[i].r);
      ans[i]=tmp;
      e[i].l=0;
    }
  }
  sort(e+1,e+m+1,cmp);
  for(i=1;i<=m;i++)if(e[i].l){
    if(f[e[i].l]!=L){
      L=f[e[i].l];
      R=L-1;
      hA.init();
      hB.init();
      best.reset();
    }
    while(R<e[i].r)hB.add(++R),hA.ask(R,best),hA.add(R);
    vio(e[i].l,L-1);
    ask(e[i].l,L-1);
    ans[e[i].p]=best<tmp?tmp:best;
  }
  for(i=1;i<=m;i++)ans[i].write();
  return 0;
}