セグメント木
(segment_tree/segment_tree.hpp)

#pragma once
#include<vector>
#include"../alga/maybe.hpp"

/**
 * @brief セグメント木
 * @see https://en.wikipedia.org/wiki/Segment_tree
 */

template<typename T,typename F>
class segment_tree{
	maybe<T>* node;
    F op;
	int n=1;
	public:
    segment_tree(){}
	segment_tree(int sz,F op=F()):op(op){
		while(n<=sz)n<<=1;
		node=new maybe<T>[n*2];
		for(int i=0;i<n*2;i++)node[i]=maybe<T>();
	}
    segment_tree(const std::vector<T>&v,F op=F()):op(op){
        auto f=expand<T,F>(op);
        const int sz=v.size();
		while(n<=sz)n<<=1;
		node=new maybe<T>[n*2]();
        for(int i=0;i<sz;i++)node[i+n]=maybe<T>(v[i]);
        for(int i=n-1;i>=1;i--)node[i]=f(node[i*2],node[i*2+1]);
	}
    maybe<T> get(int l,int r){
        auto f=expand<T,F>(op);
        l+=n;r+=n;
        maybe<T> s,t;
        while(l<r){
            if(l&1)s=f(s,node[l++]);
            if(r&1)t=f(node[--r],t);
            l>>=1;r>>=1;
        }
        return f(s,t);
    }
    void apply(int t,T _val){
        auto f=expand<T,F>(op);
        t+=n;
        maybe<T> val=maybe<T>(_val);
        while(t){
            node[t]=f(node[t],val);
            t=t>>1;
        }
    }
    void apply_left(int t,T _val){
        auto f=expand<T,F>(op);
        t+=n;
        maybe<T> val=maybe<T>(_val);
        while(t){
            node[t]=f(val,node[t]);
            t=t>>1;
        }
    }
    void change(int t,T val){
        auto f=expand<T,F>(op);
        t+=n;
        node[t]=maybe<T>(val);
        while(t>1){
            t=t>>1;
            node[t]=f(node[t*2],node[t*2+1]);
        }
    }
};

#line 2 "segment_tree/segment_tree.hpp"
#include<vector>
#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 4 "segment_tree/segment_tree.hpp"

/**
 * @brief セグメント木
 * @see https://en.wikipedia.org/wiki/Segment_tree
 */

template<typename T,typename F>
class segment_tree{
	maybe<T>* node;
    F op;
	int n=1;
	public:
    segment_tree(){}
	segment_tree(int sz,F op=F()):op(op){
		while(n<=sz)n<<=1;
		node=new maybe<T>[n*2];
		for(int i=0;i<n*2;i++)node[i]=maybe<T>();
	}
    segment_tree(const std::vector<T>&v,F op=F()):op(op){
        auto f=expand<T,F>(op);
        const int sz=v.size();
		while(n<=sz)n<<=1;
		node=new maybe<T>[n*2]();
        for(int i=0;i<sz;i++)node[i+n]=maybe<T>(v[i]);
        for(int i=n-1;i>=1;i--)node[i]=f(node[i*2],node[i*2+1]);
	}
    maybe<T> get(int l,int r){
        auto f=expand<T,F>(op);
        l+=n;r+=n;
        maybe<T> s,t;
        while(l<r){
            if(l&1)s=f(s,node[l++]);
            if(r&1)t=f(node[--r],t);
            l>>=1;r>>=1;
        }
        return f(s,t);
    }
    void apply(int t,T _val){
        auto f=expand<T,F>(op);
        t+=n;
        maybe<T> val=maybe<T>(_val);
        while(t){
            node[t]=f(node[t],val);
            t=t>>1;
        }
    }
    void apply_left(int t,T _val){
        auto f=expand<T,F>(op);
        t+=n;
        maybe<T> val=maybe<T>(_val);
        while(t){
            node[t]=f(val,node[t]);
            t=t>>1;
        }
    }
    void change(int t,T val){
        auto f=expand<T,F>(op);
        t+=n;
        node[t]=maybe<T>(val);
        while(t>1){
            t=t>>1;
            node[t]=f(node[t*2],node[t*2+1]);
        }
    }
};