【HDOJ6606】Distribution of books（二分，BIT）

题意：给定一个长为n的数组，要求挑它前缀的一段，将其分成k段，使得每段和的最大值最小

1<=k<=n<=2e5，abs(a[i])<=1e9

思路：

 刚开始写了线段树TLE

改维护后缀的BIT也TLE

暴力sort改归并排序才卡过去

怀疑用map离散化不靠谱

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef pair<int,int> PII;
typedef pair<ll,ll> Pll;
typedef vector<int> VI;
typedef vector<PII> VII;
typedef pair<ll,ll>P;
#define N  400010
#define M  200010
#define fi first
#define se second
#define MP make_pair
#define pi acos(-1)
#define mem(a,b) memset(a,b,sizeof(a))
#define rep(i,a,b) for(int i=(int)a;i<=(int)b;i++)
#define per(i,a,b) for(int i=(int)a;i>=(int)b;i--)
#define lowbit(x) x&(-x)
#define Rand (rand()*(1<<16)+rand())
#define id(x) ((x)<=B?(x):m-n/(x)+1)
#define ls p<<1
#define rs p<<1|1

const ll MOD=1e9+7,inv2=(MOD+1)/2;
      double eps=1e-4;
      ll INF=1e10;
      ll inf=5e13;
      int dx[4]={-1,1,0,0};
      int dy[4]={0,0,-1,1};

map<ll,int> mp;
int t[N],n,k,id;
ll s[M],a[M],b[M],c[N];

int read()
{
   int v=0,f=1;
   char c=getchar();
   while(c<48||57<c) {if(c=='-') f=-1; c=getchar();}
   while(48<=c&&c<=57) v=(v<<3)+v+v+c-48,c=getchar();
   return v*f;
}

void update(int x,int y)
{
    while(x)
    {
        t[x]=max(t[x],y);
        x-=lowbit(x);
    }
}

int query(int x)
{
    int res=-2e6;
    while(x<=id)
    {
        res=max(res,t[x]);
        x+=lowbit(x);
    }
    return res;
}

int isok(ll mid)
{
    mp.clear();
    int m=0;
    rep(i,1,n+1) b[i]=a[i]-mid;
    int i=1,j=1;
    while(i<=n+1&&j<=n+1)
    {
        m++;
        if(a[i]<b[j])
        {
            c[m]=a[i];
            i++;
        }
         else
         {
             c[m]=b[j];
             j++;
         }
    }
    while(i<=n+1)
    {
        c[++m]=a[i];
        i++;
    }
    while(j<=n+1)
    {
        c[++m]=b[j];
        j++;
    }
    id=1;
    mp[c[1]]=1;
    rep(i,2,m)
     if(c[i]!=c[i-1]) mp[c[i]]=++id;
    rep(i,1,id) t[i]=-2e6;
    update(mp[0],0);
    int ans=0,flag=0;
    rep(i,1,n)
    {
        int tmp=query(mp[s[i]-mid]);
        ans=max(ans,tmp+1);
        if(ans>=k) return 1;
        update(mp[s[i]],tmp+1);
    }
    return 0;
}

int main()
{
    int cas=read();
    while(cas--)
    {
        n=read(),k=read();
        s[0]=0;
        rep(i,1,n)
        {
            int x=read();
            s[i]=s[i-1]+x;
        }
        rep(i,1,n+1) a[i]=s[i-1];
        sort(a+1,a+n+1+1);
        ll l=-1e10,r=1e10,last=1e10;
        while(l<=r)
        {
            ll mid=(l+r)>>1;
            if(isok(mid)){last=mid; r=mid-1;}
             else l=mid+1;
        }
        printf("%I64d
",last);
    }

    return 0;
}