結果

問題 No.3423 Minimum Xor Query
コンテスト
ユーザー noya2
提出日時 2026-01-11 16:19:18
言語 C++23
(gcc 15.2.0 + boost 1.89.0)
結果
MLE  
実行時間 -
コード長 11,673 bytes
記録
記録タグの例:
初AC ショートコード 純ショートコード 純主流ショートコード 最速実行時間
コンパイル時間 4,153 ms
コンパイル使用メモリ 361,196 KB
実行使用メモリ 578,588 KB
最終ジャッジ日時 2026-01-11 16:19:46
合計ジャッジ時間 16,818 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
other TLE * 1 MLE * 2 -- * 15
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ソースコード

diff #
raw source code 

#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
    is >> p.first >> p.second;
    return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << std::min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(std::vector<T> &v){
    std::sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "c.cpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/segment_tree.hpp"

namespace noya2{

template <class S, S (*op)(S, S), S (*e)()> struct segtree {
  public:
    segtree() : segtree(0) {}
    segtree(int n) : segtree(std::vector<S>(n, e())) {}
    segtree(const std::vector<S>& v) : _n(int(v.size())) {
        log = 0;
        size = 1;
        while (size < _n) size <<= 1, log++;

        d = std::vector<S>(2 * size, e());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    S get(int p) {
        assert(0 <= p && p < _n);
        return d[p + size];
    }

    S prod(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        S sml = e(), smr = e();
        l += size;
        r += size;

        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return op(sml, smr);
    }

    S all_prod() { return d[1]; }

    template <bool (*f)(S)> int max_right(int l) {
        return max_right(l, [](S x) { return f(x); });
    }
    template <class F> int max_right(int l, F f) {
        assert(0 <= l && l <= _n);
        assert(f(e()));
        if (l == _n) return _n;
        l += size;
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(op(sm, d[l]))) {
                while (l < size) {
                    l = (2 * l);
                    if (f(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*f)(S)> int min_left(int r) {
        return min_left(r, [](S x) { return f(x); });
    }
    template <class F> int min_left(int r, F f) {
        assert(0 <= r && r <= _n);
        assert(f(e()));
        if (r == 0) return 0;
        r += size;
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(op(d[r], sm))) {
                while (r < size) {
                    r = (2 * r + 1);
                    if (f(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

  private:
    int _n, size, log;
    std::vector<S> d;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};

} // namespace noya2
#line 4 "c.cpp"

struct S {
    int lv, rv, ans;
};

S op(S a, S b){
    if (a.lv == -1) return b;
    if (b.lv == -1) return a;
    S c;
    c.lv = a.lv;
    c.rv = b.rv;
    c.ans = min(a.ans,b.ans);
    chmin(c.ans,a.rv^b.lv);
    return c;
}
S e(){
    return {-1,-1,iinf};
}

const ull lmsk = (1ULL << 20) - 1;
const ull rmsk = lmsk << 20;
const ull amsk = ((1ULL << 21) - 1) << 40;

ull op0(ull a, ull b){
    if (a >> 62 & 1) return b;
    if (b >> 62 & 1) return a;
    ull c = (a & lmsk) | (b & rmsk);
    ull ans = min(a & amsk, b & amsk);
    chmin(ans, (((a & rmsk) >> 20) ^ (b & lmsk)) << 40);
    return c | ans;
}
ull e0(){
    return (1ULL << 62);
}
ull val0(ull x){
    return (1ULL << 60) | (x << 20) | x;
}

struct dat0 {
    static constexpr int mx = 1<<20;
    segtree<ull,op0,e0> seg;
    vector<uint16_t>cnt;
    int dup;
    dat0 () : seg(mx), cnt(mx), dup(0) {}
    void insert(int x){
        if (cnt[x]++ == 0){
            // seg.set(x,S{x,x,iinf});
            seg.set(x,val0(x));
        }
        if (cnt[x] == 2){
            dup++;
        }
    }
    void erase(int x){
        if (--cnt[x] == 0){
            seg.set(x,e0());
        }
        if (cnt[x] == 1){
            dup--;
        }
    }
    int get(){
        if (dup >= 1) return 0;
        // return seg.all_prod().ans;
        return (seg.all_prod() & amsk) >> 40;
    }
    int query(int x){
        insert(x);
        int ret = get();
        erase(x);
        return ret;
    }
};

struct dat {
    multiset<int> st;
    multiset<int> diffs;
    int query(int x){
        int ret = iinf;
        auto ite = st.lower_bound(x);
        if (ite != st.end()){
            chmin(ret,x^(*ite));
        }
        if (ite != st.begin()){
            chmin(ret,x^(*prev(ite)));
        }
        return ret;
    }
    void insert(int x){
        auto ite = st.insert(x);
        if (next(ite) != st.end()){
            diffs.insert((*next(ite))^x);
        }
        if (ite != st.begin()){
            diffs.insert(x^(*prev(ite)));
        }
        if (next(ite) != st.end() && ite != st.begin()){
            diffs.erase(diffs.find((*next(ite))^(*prev(ite))));
        }
    }
    void erase(int x){
        auto ite = st.erase(st.find(x));
        if (ite != st.end()){
            diffs.erase(diffs.find((*ite)^x));
        }
        if (ite != st.begin()){
            diffs.erase(diffs.find(x^(*prev(ite))));
        }
        if (ite != st.end() && ite != st.begin()){
            diffs.insert((*ite)^(*prev(ite)));
        }
    }
    int get(){
        if (diffs.empty()) return iinf;
        return *diffs.begin();
    }
    void show(){
        out(vector<int>(all(st)));
        out(vector<int>(all(diffs)));
    }
};

struct dat2 {
    set<int> st;
    int query(int x){
        int ret = iinf;
        auto ite = st.lower_bound(x);
        if (ite != st.end()){
            chmin(ret,x^(*ite));
        }
        if (ite != st.begin()){
            chmin(ret,x^(*prev(ite)));
        }
        return ret;
    }
    void insert(int x){
        st.insert(x);
    }
};

void solve(){
    int n, q; in(n,q);
    vector<int> a(n); in(a);
    // const int w = 512;
    // const int w = 1024;
    const int w = 700;
    // const int w = 3;
    {
        n = (n + w - 1) / w * w;
        a.resize(n);
    }
    vector<dat0> sts(n/w);
    {
        dat0 st;
        rep(b,n/w){
            int l = b * w, r = l + w;
            repp(i,l,r){
                st.insert(a[i]);
            }
            sts[b] = st;
        }
    }
    auto query = [&](int r){
        int br = r / w;
        int ret = iinf;
        if (br > 0){
            chmin(ret,sts[br-1].get());
        }
        if (br > 0){
            repp(i,br*w,r){
                chmin(ret,sts[br-1].query(a[i]));
            }
        }
        dat2 st;
        repp(i,br*w,r){
            chmin(ret,st.query(a[i]));
            st.insert(a[i]);
        }
        return ret;
    };
    auto upd = [&](int i, int v){
        rep(b,n/w){
            int r = b * w + w;
            if (i >= r) continue;
            sts[b].erase(a[i]);
            sts[b].insert(v);
        }
        a[i] = v;
    };
    while (q--){
        int t; in(t);
        if (t == 1){
            int i, v; in(i,v); i--;
            upd(i,v);
        }
        else if (t == 2){
            int r; in(r);
            int ans = query(r);
            out(ans);
        }
    }
}

int main(){
    int t = 1; //in(t);
    while (t--) { solve(); }
}
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