sparse_table.cpp

#include <bits/stdc++.h>

using namespace std;

#define cin_2d(vec, n, m) for(int i = 0; i < n; i++) for(int j = 0; j < m && cin >> vec[i][j]; j++);
#define cout_2d(vec, n, m) for(int i = 0; i < n; i++, cout << "\n") for(int j = 0; j < m && cout << vec[i][j] << " "; j++);
#define fixed(n) fixed << setprecision(n)
#define ceil(n, m) (((n) / (m)) + ((n) % (m) ? 1 : 0))
#define fill(vec, value) memset(vec, value, sizeof(vec));
#define mul_mod(a, b, m) (((a % m) * (b % m)) % m)
#define add_mod(a, b, m) (((a % m) + (b % m)) % m)
#define all(vec) vec.begin(), vec.end()
#define rall(vec) vec.rbegin(), vec.rend()
#define sz(x) int(x.size())
#define debug(x) cout << #x << ": " << (x) << "\n";
#define fi first
#define se second
#define ll long long
#define ull unsigned long long
#define Mod  1'000'000'007
#define OO 2'000'000'000
#define EPS 1e-9
#define PI acos(-1)
template < typename T = int > using Pair = pair < T, T >;
vector < string > RET = {"NO", "YES"};

template < typename T = int > istream& operator >> (istream &in, vector < T > &v) {
    for (auto &x : v) in >> x;
    return in;
}

template < typename T = int > ostream& operator << (ostream &out, const vector < T > &v) { 
    for (const T &x : v) out << x << ' '; 
    return out;
}

template < typename T >
struct MinOp {
    constexpr T operator()(const T& a, const T& b) const { return a < b ? a : b; }
};

/*
 * Sparse_Table — Static RMQ / Range Query in O(1) or O(log n)
 *
 * Template params:
 *   T        = answer/value type              (default int)
 *   Op       = binary combine functor         (default MinOp<T> = min)
 *   Base     = 0 → 0-indexed, 1 → 1-indexed  (default 0)
 *   numsType = input array type               (default T)
 *
 * Constructor:
 *   Sparse_Table<T, Op, Base, numsType> st(
 *       int N,
 *       vector<numsType>& vec,
 *       Op op = Op{},
 *       T def = numeric_limits<T>::max()   // identity for Op — change when not using min
 *   );
 *
 * Methods:
 *   query(int L, int R, bool is_overlap = false) → T
 *     is_overlap = false → O(1), only correct for idempotent ops (min, max, gcd)
 *     is_overlap = true  → O(log n), correct for all ops (sum, etc.)
 *
 * Example (range min, 0-indexed — default):
 *   Sparse_Table<int> st(n, arr);
 *   cout << st.query(1, n);
 *
 * Example (range min, 1-indexed):
 *   Sparse_Table<int, MinOp<int>, 1> st(n, arr);
 *   cout << st.query(1, n);
 *
 * Example (range sum via lambda, 0-indexed):
 *   auto sumOp = [](ll a, ll b){ return a + b; };
 *   Sparse_Table<ll, decltype(sumOp)> st(n, arr, sumOp, 0LL);
 *   cout << st.query(0, n - 1, true);
 *
 * Example (range sum via plain function):
 *   ll mySum(ll a, ll b) { return a + b; }
 *   Sparse_Table<ll, decltype(&mySum)> st(n, arr, &mySum, 0LL);
 *   cout << st.query(0, n - 1, true);
 */
template < typename T = int, typename Op = MinOp < T >, int Base = 0, typename numsType = T >
class Sparse_Table {
private:

    int n, LOG;
    vector < vector < T > > table;
    vector < int > Bin_Log;
    Op operation;
    T DEFAULT;

    void Build_Table() {
        for (int log = 1; log < LOG; log++)
            for (int i = 1; i + (1 << log) - 1 <= n; i++)
                table[i][log] = operation(table[i][log - 1], table[i + (1 << (log - 1))][log - 1]);
    }

    T query_1(int L, int R) {
        int log = Bin_Log[R - L + 1];
        return operation(table[L][log], table[R - (1 << log) + 1][log]);
    }

    T query_log_n(int L, int R) {
        T answer = DEFAULT;
        for (int log = LOG; log >= 0; log--) {
            if (L + (1 << log) - 1 <= R) {
                answer = operation(answer, table[L][log]);
                L += 1 << log;
            }
        }
        return answer;
    }

public:

    Sparse_Table(
        int N = 0,
        const vector < numsType >& vec = vector < numsType >(),
        Op op = Op{},
        T def = numeric_limits < T > ::max()
    ) : n(N), LOG(__lg(n) + 1), operation(op), DEFAULT(def) {
        table = vector < vector < T > > (n + 10, vector < T > (LOG, DEFAULT));
        Bin_Log = vector < int > (n + 10);
        for (int i = 2; i <= n; i++)
            Bin_Log[i] = Bin_Log[i >> 1] + 1;
        for (int i = 1; i <= N; i++)
            table[i][0] = T(vec[i - !Base]);
        Build_Table();
    }

    T query(int L, int R, bool is_overlap = false) {
        return !is_overlap ? query_1(L, R) : query_log_n(L, R);
    }

};

void Solve(){
    
}

int main(){
    ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
    int t = 1;
    //cin >> t;
    while(t--)
        Solve();
    return 0;
}