:heavy_check_mark: RMQ<O(N),O(1)>
(data_structure/RMQ.hpp)

Depends on

Verified with

Code

#pragma once
#include<assert.h>
#include<vector>
#include<stack>
#include<numeric>
#include<cmath>
#include<algorithm>
#include"small_rmq.hpp"
#include"sparse_table.hpp"
#include"../functional/MIN.hpp"
#include"../alga/maybe.hpp"
/**
 * @brief RMQ&amp;lt;O(N),O(1)&amp;gt;
 * @see https://noshi91.hatenablog.com/entry/2018/08/16/125415
 */

template<typename T>
class RMQ{
    constexpr static int b=64;
    std::vector<T>v;
    std::vector<small_rmq<T>*>backet;
    sparse_table<T,MIN<T>>* st=0;
    public:
    RMQ(std::vector<T>v):v(v){
        std::vector<T>tmp2;
        for(int i=0;i<(int)v.size();i+=b){
            std::vector<T>tmp;
            T mn=std::numeric_limits<T>::max();
            for(int j=0;i+j<(int)v.size()&&j<b;j++){
                tmp.push_back(v[i+j]);
                if(mn>v[i+j])mn=v[i+j];
            }
            tmp2.push_back(mn);
            backet.push_back(new small_rmq<T>(tmp));
        }
        st=new sparse_table<T,MIN<T>>(tmp2);
    }
    T query(int s,int t){
        if(s/b==t/b)return v[s/b*b+backet[s/b]->query(s%b,t%b)];
        T res=std::numeric_limits<T>::max();

        res=std::min(res,v[s/b*b+backet[s/b]->query(s%b,b)]);
        res=std::min(res,st->get(s/b+1,t/b).unwrap_or(std::numeric_limits<T>::max()));
        if(t%b!=0)res=std::min(res,v[t/b*b+backet[t/b]->query(0,t%b)]);

        return res;
    }
};
#line 2 "data_structure/RMQ.hpp"
#include<assert.h>
#include<vector>
#include<stack>
#include<numeric>
#include<cmath>
#include<algorithm>
#line 3 "data_structure/small_rmq.hpp"

/**
 * RMQ(small) &amp;lt;O(N),O(1)&amp;gt;(N<=64)
 */

template<typename T>
class small_rmq{
    using u64=unsigned long long;
    std::vector<u64>table;
    std::vector<T> v;
    public:
    small_rmq(std::vector<T> v):v(v){
        assert(v.size()<=64);
        std::vector<int>tmp(v.size());
        table.resize(v.size(),0);
        std::stack<T>stk;
        for(int i=0;i<(int)v.size();++i){
            tmp.resize(v.size());
            while(!stk.empty()&&v[stk.top()]>=v[i]){
                stk.pop();
            }
            tmp[i]=stk.empty()?-1:stk.top();
            stk.emplace(i);
        }
        for(int i=0;i<(int)v.size();++i){
            if(tmp[i]!=-1)table[i]=table[tmp[i]]|(1ULL<<(tmp[i]));
        }
    }
    T query(int l,int r){
        assert(l!=r);
        const u64 tmp=table[r-1]&~((1ULL<<l)-1);
        if(tmp==0)return r-1;
        else return __builtin_ctzll(tmp);
    }
};
#line 3 "data_structure/sparse_table.hpp"
#include<functional>
#line 2 "alga/maybe.hpp"
#include<cassert>

/**
 * @brief Maybe
 * @see https://ja.wikipedia.org/wiki/%E3%83%A2%E3%83%8A%E3%83%89_(%E3%83%97%E3%83%AD%E3%82%B0%E3%83%A9%E3%83%9F%E3%83%B3%E3%82%B0)#Maybe%E3%83%A2%E3%83%8A%E3%83%89
 */

template<typename T>
struct maybe{
    bool _is_none;
    T val;
    maybe():_is_none(true){}
    maybe(T val):_is_none(false),val(val){}
    T unwrap()const{
        assert(!_is_none);
        return val;
    }
    T unwrap_or(T e)const{
        return _is_none?e:val;
    }
    bool is_none()const{return _is_none;}
    bool is_some()const{return !_is_none;}
};

template<typename T,typename F>
auto expand(F op){
    return [&op](const maybe<T>& s,const maybe<T>& t){
        if(s.is_none())return t;
        if(t.is_none())return s;
        return maybe<T>(op(s.unwrap(),t.unwrap()));
    };
}
#line 7 "data_structure/sparse_table.hpp"
/**
 * @brief SparseTable
 */

template<typename T,typename F>
class sparse_table{
    F f;
    std::vector<std::vector<T>>data;
    public:
    sparse_table(std::vector<T> v,F f=F()):f(f){
        int n=v.size(),log=log2(n)+1;
        data.resize(n,std::vector<T>(log));
        for(int i=0;i<n;i++)data[i][0]=v[i];
        for(int j=1;j<log;j++)for(int i=0;i+(1<<(j-1))<n;i++){
            data[i][j]=f(data[i][j-1],data[i+(1<<(j-1))][j-1]);
        }
    }
    maybe<T> get(int l,int r){
        if(l==r)return maybe<T>();
        if(r<l)std::swap(l,r);
        int k=std::log2(r-l);
        return maybe<T>(f(data[l][k],data[r-(1<<k)][k]));
    }
};
#line 3 "functional/MIN.hpp"

/**
 * @brief 最小値
 */

template<typename T>
struct MIN{
    T operator()(const T& s,const T& t){
        return std::min(s,t);
    }
};
#line 12 "data_structure/RMQ.hpp"
/**
 * @brief RMQ&amp;lt;O(N),O(1)&amp;gt;
 * @see https://noshi91.hatenablog.com/entry/2018/08/16/125415
 */

template<typename T>
class RMQ{
    constexpr static int b=64;
    std::vector<T>v;
    std::vector<small_rmq<T>*>backet;
    sparse_table<T,MIN<T>>* st=0;
    public:
    RMQ(std::vector<T>v):v(v){
        std::vector<T>tmp2;
        for(int i=0;i<(int)v.size();i+=b){
            std::vector<T>tmp;
            T mn=std::numeric_limits<T>::max();
            for(int j=0;i+j<(int)v.size()&&j<b;j++){
                tmp.push_back(v[i+j]);
                if(mn>v[i+j])mn=v[i+j];
            }
            tmp2.push_back(mn);
            backet.push_back(new small_rmq<T>(tmp));
        }
        st=new sparse_table<T,MIN<T>>(tmp2);
    }
    T query(int s,int t){
        if(s/b==t/b)return v[s/b*b+backet[s/b]->query(s%b,t%b)];
        T res=std::numeric_limits<T>::max();

        res=std::min(res,v[s/b*b+backet[s/b]->query(s%b,b)]);
        res=std::min(res,st->get(s/b+1,t/b).unwrap_or(std::numeric_limits<T>::max()));
        if(t%b!=0)res=std::min(res,v[t/b*b+backet[t/b]->query(0,t%b)]);

        return res;
    }
};
Back to top page