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:heavy_check_mark: Verify/LC_static_range_lis_query.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/static_range_lis_query"

#include "Template/template.hpp"

#include "Utility/fastio.hpp"

#include "DataStructure/rangelis.hpp"


int main(){
    int n,q;
    read(n,q);
    vector<int> p(n);
    read(p);

    RangeLIS buf(p);
    while(q--){
        int L,R;
        read(L,R);
        print(buf.query(L,R));
    }
    return 0;
}
#line 1 "Verify/LC_static_range_lis_query.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/static_range_lis_query"

#line 1 "Template/template.hpp"
#include <bits/stdc++.h>

using namespace std;

#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b-1); i >= (int)(a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())

using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;

template <typename T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T, typename U> T ceil(T x, U y) {
    assert(y != 0);
    if (y < 0)
        x = -x, y = -y;
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U> T floor(T x, U y) {
    assert(y != 0);
    if (y < 0)
        x = -x, y = -y;
    return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T> int popcnt(T x) {
    return __builtin_popcountll(x);
}
template <typename T> int topbit(T x) {
    return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <typename T> int lowbit(T x) {
    return (x == 0 ? -1 : __builtin_ctzll(x));
}

#ifdef LOCAL
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define show(...) true
#endif
template <typename T> void _show(int i, T name) {
    cerr << '\n';
}
template <typename T1, typename T2, typename... T3>
void _show(int i, const T1 &a, const T2 &b, const T3 &...c) {
    for (; a[i] != ',' && a[i] != '\0'; i++)
        cerr << a[i];
    cerr << ":" << b << " ";
    _show(i + 1, a, c...);
}
template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
    os << "P(" << p.first << ", " << p.second << ")";
    return os;
}
template <typename T, template <class> class C>
ostream &operator<<(ostream &os, const C<T> &v) {
    os << "[";
    for (auto d : v)
        os << d << ", ";
    os << "]";
    return os;
}
#line 2 "Utility/fastio.hpp"
#include <unistd.h>

namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf


uint32_t pil = 0, pir = 0, por = 0;

struct Pre {
    char num[10000][4];
    constexpr Pre() : num() {
        for (int i = 0; i < 10000; i++) {
            int n = i;
            for (int j = 3; j >= 0; j--) {
                num[i][j] = n % 10 | '0';
                n /= 10;
            }
        }
    }
} constexpr pre;

inline void load() {
    memmove(ibuf, ibuf + pil, pir - pil);
    pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
    pil = 0;
    if (pir < SZ)
        ibuf[pir++] = '\n';
}

inline void flush() {
    fwrite(obuf, 1, por, stdout);
    por = 0;
}

void rd(char &c) {
    do {
        if (pil + 1 > pir)
            load();
        c = ibuf[pil++];
    } while (isspace(c));
}

void rd(string &x) {
    x.clear();
    char c;
    do {
        if (pil + 1 > pir)
            load();
        c = ibuf[pil++];
    } while (isspace(c));
    do {
        x += c;
        if (pil == pir)
            load();
        c = ibuf[pil++];
    } while (!isspace(c));
}

template <typename T> void rd_real(T &x) {
    string s;
    rd(s);
    x = stod(s);
}

template <typename T> void rd_integer(T &x) {
    if (pil + 100 > pir)
        load();
    char c;
    do
        c = ibuf[pil++];
    while (c < '-');
    bool minus = 0;
    if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
        if (c == '-') {
            minus = 1, c = ibuf[pil++];
        }
    }
    x = 0;
    while ('0' <= c) {
        x = x * 10 + (c & 15), c = ibuf[pil++];
    }
    if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
        if (minus)
            x = -x;
    }
}

void rd(int &x) {
    rd_integer(x);
}
void rd(ll &x) {
    rd_integer(x);
}
void rd(i128 &x) {
    rd_integer(x);
}
void rd(uint &x) {
    rd_integer(x);
}
void rd(ull &x) {
    rd_integer(x);
}
void rd(u128 &x) {
    rd_integer(x);
}
void rd(double &x) {
    rd_real(x);
}
void rd(long double &x) {
    rd_real(x);
}

template <class T, class U> void rd(pair<T, U> &p) {
    return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T> void rd_tuple(T &t) {
    if constexpr (N < std::tuple_size<T>::value) {
        auto &x = std::get<N>(t);
        rd(x);
        rd_tuple<N + 1>(t);
    }
}
template <class... T> void rd(tuple<T...> &tpl) {
    rd_tuple(tpl);
}

template <size_t N = 0, typename T> void rd(array<T, N> &x) {
    for (auto &d : x)
        rd(d);
}
template <class T> void rd(vector<T> &x) {
    for (auto &d : x)
        rd(d);
}

void read() {}
template <class H, class... T> void read(H &h, T &...t) {
    rd(h), read(t...);
}

void wt(const char c) {
    if (por == SZ)
        flush();
    obuf[por++] = c;
}
void wt(const string s) {
    for (char c : s)
        wt(c);
}
void wt(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++)
        wt(s[i]);
}

template <typename T> void wt_integer(T x) {
    if (por > SZ - 100)
        flush();
    if (x < 0) {
        obuf[por++] = '-', x = -x;
    }
    int outi;
    for (outi = 96; x >= 10000; outi -= 4) {
        memcpy(out + outi, pre.num[x % 10000], 4);
        x /= 10000;
    }
    if (x >= 1000) {
        memcpy(obuf + por, pre.num[x], 4);
        por += 4;
    } else if (x >= 100) {
        memcpy(obuf + por, pre.num[x] + 1, 3);
        por += 3;
    } else if (x >= 10) {
        int q = (x * 103) >> 10;
        obuf[por] = q | '0';
        obuf[por + 1] = (x - q * 10) | '0';
        por += 2;
    } else
        obuf[por++] = x | '0';
    memcpy(obuf + por, out + outi + 4, 96 - outi);
    por += 96 - outi;
}

template <typename T> void wt_real(T x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << double(x);
    string s = oss.str();
    wt(s);
}

void wt(int x) {
    wt_integer(x);
}
void wt(ll x) {
    wt_integer(x);
}
void wt(i128 x) {
    wt_integer(x);
}
void wt(uint x) {
    wt_integer(x);
}
void wt(ull x) {
    wt_integer(x);
}
void wt(u128 x) {
    wt_integer(x);
}
void wt(double x) {
    wt_real(x);
}
void wt(long double x) {
    wt_real(x);
}

template <class T, class U> void wt(const pair<T, U> val) {
    wt(val.first);
    wt(' ');
    wt(val.second);
}
template <size_t N = 0, typename T> void wt_tuple(const T t) {
    if constexpr (N < std::tuple_size<T>::value) {
        if constexpr (N > 0) {
            wt(' ');
        }
        const auto x = std::get<N>(t);
        wt(x);
        wt_tuple<N + 1>(t);
    }
}
template <class... T> void wt(tuple<T...> tpl) {
    wt_tuple(tpl);
}
template <class T, size_t S> void wt(const array<T, S> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
        if (i)
            wt(' ');
        wt(val[i]);
    }
}
template <class T> void wt(const vector<T> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
        if (i)
            wt(' ');
        wt(val[i]);
    }
}

void print() {
    wt('\n');
}
template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) {
    wt(head);
    if (sizeof...(Tail))
        wt(' ');
    print(forward<Tail>(tail)...);
}
void __attribute__((destructor)) _d() {
    flush();
}
} // namespace fastio


using fastio::flush;
using fastio::print;
using fastio::read;

inline void first(bool i = true) {
    print(i ? "first" : "second");
}
inline void Alice(bool i = true) {
    print(i ? "Alice" : "Bob");
}
inline void yes(bool i = true) {
    print(i ? "yes" : "no");
}
inline void Yes(bool i = true) {
    print(i ? "Yes" : "No");
}
inline void No() {
    print("No");
}
inline void YES(bool i = true) {
    print(i ? "YES" : "NO");
}
inline void NO() {
    print("NO");
}
inline void Yay(bool i = true) {
    print(i ? "Yay!" : ":(");
}
inline void Possible(bool i = true) {
    print(i ? "Possible" : "Impossible");
}
inline void POSSIBLE(bool i = true) {
    print(i ? "POSSIBLE" : "IMPOSSIBLE");
}

/**
 * @brief Fast IO
 */
#line 2 "DataStructure/wavelet.hpp"

template<typename T>struct WaveletMatrix{
    struct BitVector{
        vector<unsigned long long> buf;
        vector<int> rui;
        BitVector(const vector<char>& a={}){
            int n=a.size();
            buf.assign((n+63)>>6,0);
            rui.assign(buf.size()+1,0);
            rep(i,0,n)if(a[i]){
                buf[i>>6]|=1ull<<(i&63);
                rui[(i>>6)+1]++;
            }
            rep(i,0,buf.size())rui[i+1]+=rui[i];
        }
        int rank(int k,bool f=1){
            int ret=rui[k>>6]+__builtin_popcountll(buf[k>>6]&((1ull<<(k&63))-1));
            if(!f)return k-ret;
            else return ret;
        }
    };
    int N,lg;
    vector<int> mid;
    vector<BitVector> buf;
    WaveletMatrix(){}
    WaveletMatrix(vector<T> a):N(a.size()),lg(0){
        T mx=0;
        for(auto& x:a)chmax(mx,x);
        while((T(1)<<lg)<=mx)lg++;
        mid.resize(lg);
        buf.resize(lg);
        for(int d=lg-1;d>=0;d--){
            vector<char> add;
            vector nxt(2,vector<T>());
            for(auto& x:a){
                add.push_back(x>>d&1);
                nxt[x>>d&1].push_back(x);
            }
            mid[d]=(int)nxt[0].size();
            buf[d]=BitVector(add);
            swap(a,nxt[0]);
            a.insert(a.end(),ALL(nxt[1]));
        }
    }
    int rank(int L,int R,T x){
        if((T(1)<<lg)<=x)return 0;
        for(int d=lg-1;d>=0;d--){
            bool f=(x>>d&1);
            L=buf[d].rank(L,f)+(f?mid[d]:0);
            R=buf[d].rank(R,f)+(f?mid[d]:0);
        }
        return R-L;
    }
    T quantile(int L,int R,int k){
        T ret=0;
        for(int d=lg-1;d>=0;d--){
            int l0=buf[d].rank(L,0),r0=buf[d].rank(R,0);
            if(k<r0-l0)L=l0,R=r0;
            else{
                k-=r0-l0;
                ret|=T(1)<<d;
                L+=mid[d]-l0,R+=mid[d]-r0;
            }
        }
        return ret;
    }
    int freq(int L,int R,T x){
        if((T(1)<<lg)<=x)return R-L;
        int ret=0;
        for(int d=lg-1;d>=0;d--){
            bool f=(x>>d&1);
            if(f)ret+=buf[d].rank(R,0)-buf[d].rank(L,0);
            L=buf[d].rank(L,f)+(f?mid[d]:0);
            R=buf[d].rank(R,f)+(f?mid[d]:0);
        }
        return ret;
    }
    int freq(int L,int R,T a,T b){
        return freq(L,R,b)-freq(L,R,a);
    }
    T prev(int L,int R,T x){
        int cnt=freq(L,R,x);
        return cnt==R-L?T(-1):quantile(L,R,cnt);
    }
    T next(int L,int R,T x){
        int cnt=freq(L,R,x);
        return cnt==0?T(-1):quantile(L,R,cnt-1);
    }
};

/**
 * @brief Wavelet Matrix
 * @docs docs/wavelet.md
 */
#line 3 "DataStructure/rangelis.hpp"

struct RangeLIS{
    WaveletMatrix<int> wm;
    int N;
    RangeLIS(vector<int> p){
        N=1;
        while(N<int(p.size()))N<<=1;
        rep(i,p.size(),N)p.push_back(i);
        auto init=seaweed(p);
        wm=WaveletMatrix<int>(init);
    }
    int query(int L,int R){
        if(L>=R)return 0;
        return R-L-wm.freq(0,R,L,N);
    }
private:
    vector<int> seaweed(const vector<int>& p){
        int n=p.size();
        if(n==1)return {inf};
        vector<int> lo,hi,lpos,hpos;
        rep(i,0,n){
            if(p[i]<n/2){
                lo.push_back(p[i]);
                lpos.push_back(i);
            }
            else{
                hi.push_back(p[i]-n/2);
                hpos.push_back(i);
            }
        }
        auto x=seaweed(lo),y=seaweed(hi);
        vector<int> s(n),t(n);
        iota(ALL(s),0);
        iota(ALL(t),0);
        int xi=0,yi=0;
        rep(i,0,n){
            if(p[i]<n/2){
                if(x[xi]==inf)s[i]=inf;
                else s[i]=lpos[x[xi]];
                xi++;
            }
            else{
                if(y[yi]==inf)t[i]=inf;
                else t[i]=hpos[y[yi]];
                yi++;
            }
        }
        vector<int> a(n,inf),b(n);
        vector<int> revs(n,inf);
        rep(i,0,n)if(s[i]!=inf)revs[s[i]]=i;
        int pos=n-1;
        vector<int> tos(n,inf),tot(n,inf);
        for(int i=n-1;i>=0;i--)if(revs[i]!=inf){
            a[revs[i]]=pos;
            tos[pos--]=i;
        }
        rep(i,0,n)if(a[i]==inf)a[i]=pos--;
        pos=0;
        vector<int> used(n);
        rep(i,0,n)if(t[i]!=inf){
            b[pos]=t[i];
            tot[pos++]=i;
            used[t[i]]=1;
        }
        rep(i,0,n)if(!used[i]){
            b[pos++]=i;
        }
        auto c=squaredot(a,b);
        vector<int> res(n,inf);
        rep(i,0,n)if(tot[i]!=inf and tos[c[i]]!=inf){
            res[tot[i]]=tos[c[i]];
        }
        return res;
    }
    vector<int> squaredot(const vector<int>& a,const vector<int>& b){
        int n=a.size();
        if(n==1)return {0};
        vector<int> alo,ahi,blo,bhi;
        vector<int> inva(n);
        rep(i,0,n)inva[a[i]]=i;
        int aloi=0,ahii=0;
        vector<int> azip(n),alov,ahiv;
        rep(i,0,n){
            if(inva[i]<n/2){
                azip[inva[i]]=aloi++;
                alov.push_back(i);
            }
            else{
                azip[inva[i]]=ahii++;
                ahiv.push_back(i);
            }
            if(b[i]<n/2)blo.push_back(b[i]);
            else bhi.push_back(b[i]-n/2);
        }
        rep(i,0,n){
            if(i<n/2)alo.push_back(azip[i]);
            else ahi.push_back(azip[i]);
        }
        auto sublo=squaredot(alo,blo);
        auto subhi=squaredot(ahi,bhi);
        vector<int> clo(n,inf),chi(n,inf),res(n,inf);
        int subloi=0,subhii=0;
        rep(i,0,n){
            if(b[i]<n/2)clo[i]=alov[sublo[subloi++]];
            else chi[i]=ahiv[subhi[subhii++]];
        }
        vector<int> invclo(n,inf),invchi(n,inf);
        rep(i,0,n){
            if(clo[i]!=inf)invclo[clo[i]]=i;
            if(chi[i]!=inf)invchi[chi[i]]=i;
        }
        int cloi=n,cloj=-1,chii=n,chij=-1;
        int ldelta=0,hdelta=0;
        for(;;){
            if(cloi<0 and chij>=n)break;
            if(ldelta>0){
                cloj++;
                if(cloj<n and chi[cloj]!=inf and chi[cloj]<cloi)ldelta--;
                if(cloj<n and clo[cloj]!=inf and clo[cloj]>=cloi)ldelta--;
            }
            else{
                cloi--;
                if(cloi>=0 and invchi[cloi]!=inf and invchi[cloi]<=cloj)ldelta++;
                if(cloi>=0 and invclo[cloi]!=inf and invclo[cloi]>cloj)ldelta++;
            }
            if(0<=cloj and cloj<n and clo[cloj]!=inf and clo[cloj]<=cloi)res[cloj]=clo[cloj];
            if(hdelta>=0){
                chij++;
                if(chij<n and chi[chij]!=inf and chi[chij]<chii)hdelta--;
                if(chij<n and clo[chij]!=inf and clo[chij]>=chii)hdelta--;
            }
            else{
                chii--;
                if(chii>=0 and invchi[chii]!=inf and invchi[chii]<=chij)hdelta++;
                if(chii>=0 and invclo[chii]!=inf and invclo[chii]>chij)hdelta++;
            }
            if(0<=chij and chij<n and chi[chij]!=inf and chi[chij]>=chii)res[chij]=chi[chij];
            if(cloi==chii and cloj==chij)res[cloj]=cloi;
        }
        return res;
    }
};

/**
 * @brief Range LIS Query
 */
#line 6 "Verify/LC_static_range_lis_query.test.cpp"

int main(){
    int n,q;
    read(n,q);
    vector<int> p(n);
    read(p);

    RangeLIS buf(p);
    while(q--){
        int L,R;
        read(L,R);
        print(buf.query(L,R));
    }
    return 0;
}
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