hdu6701 Make Rounddog Happy

Posted 2022-08-23 encodetalker

hdu

刚看题的时候想维护一个分段函数想了好久，最后发现实在是伤身体，看完sol的第一句话我就发现我是sb

考虑分治，每次找到分值区间的某一个最大值的位置，枚举合法区间的左端点，同时确定区间的右端点的范围，处理完成后分治下去求解子区间

防止复杂度退化成\(O(n^2)\)我们可以借鉴启发式合并的思想，每次枚举左端点的时候从长度较小的子区间里枚举，这样的最坏复杂的就是\(O(nlogn)\)的（你从后往前看其实就是个启发式合并的过程）.用st表预处理区间最大值的位置

#include<iostream>
#include<string.h>
#include<string>
#include<stdio.h>
#include<algorithm>
#include<vector>
#include<math.h>
#include<queue>
#include<set>
#include<map>
using namespace std;
typedef long long ll;
typedef long double db;
typedef pair<int,int> pii;
const int N=10000;
const db pi=acos(-1.0);
#define lowbit(x) (x)&(-x)
#define sqr(x) (x)*(x)
#define rep(i,a,b) for (register int i=a;i<=b;i++)
#define per(i,a,b) for (register int i=a;i>=b;i--)
#define fir first
#define sec second
#define mp(a,b) make_pair(a,b)
#define pb(a) push_back(a)
#define maxd 998244353
#define eps 1e-8
int n,k,pos[300300],a[300300],L[300300],R[300300],maxp[300300][20],low[300300];
ll ans=0;

int read()

    int x=0,f=1;char ch=getchar();
    while ((ch<'0') || (ch>'9')) if (ch=='-') f=-1;ch=getchar();
    while ((ch>='0') && (ch<='9')) x=x*10+(ch-'0');ch=getchar();
    return x*f;


int query(int l,int r)

    int p=low[r-l+1];
    //cout << "query " << l << " " << r << " " << p << endl;
    //cout << l << " " << r-(1<<p)+1 << endl;
    int x1=maxp[l][p],x2=maxp[r-(1<<p)+1][p];
    if (a[x1]>a[x2]) return x1;else return x2;


void solve(int l,int r)

    if (r<l) return;
    int pos=query(l,r),minlen=a[pos]-k;
    //cout << l << " " << r << " " << pos << endl;
    //system("pause");
    if (pos-l<r-pos)
    
        rep(i,l,pos)
        
            int nowl=max(i+minlen-1,pos),nowr=min(r,R[i]);
            if (nowr>=nowl) ans+=(nowr-nowl+1);
        
    
    else
    
        rep(i,pos,r)
        
            int nowl=max(l,L[i]),nowr=min(i-minlen+1,pos);
            if (nowr>=nowl) ans+=(nowr-nowl+1);
        
    
    solve(l,pos-1);solve(pos+1,r);

    
int main()

    int T=read();
    while (T--)
    
        n=read();k=read();
        rep(i,1,n) a[i]=read();maxp[i][0]=i;
        for (int p=1;(1<<p)<=n;p++)
            for (int i=1;i+(1<<p)-1<=n;i++)
            
                int l=maxp[i][p-1],r=maxp[i+(1<<(p-1))][p-1];
                if (a[l]>a[r]) maxp[i][p]=l;else maxp[i][p]=r;
            
        low[1]=0;rep(i,2,n) low[i]=low[i>>1]+1;
        rep(i,1,n) pos[i]=0;
        rep(i,1,n)
        
            L[i]=pos[a[i]]+1;
            pos[a[i]]=i;
        
        rep(i,2,n) L[i]=max(L[i],L[i-1]);
        rep(i,1,n) pos[i]=n+1;
        per(i,n,1)
        
            R[i]=pos[a[i]]-1;
            pos[a[i]]=i;
        
        per(i,n-1,1) R[i]=min(R[i],R[i+1]);
        ans=0;
        //rep(i,1,n) cout << L[i] << " " << R[i] << endl;
        solve(1,n);
        printf("%lld\n",ans);
    
    return 0;