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Disjoint Sparse Table
(DataStructure/disjointsparsetable.hpp)

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• Last update: 2026-01-30 05:37:33+09:00
• Include: #include "DataStructure/disjointsparsetable.hpp"
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Verified with

• Verify/LC_staticrmq-2.test.cpp

Code

#pragma once

template <typename T, T (*f)(T, T)> struct DisjointSparseTable {
    vector<vector<T>> buf;
    vector<int> height;
    DisjointSparseTable() {}
    DisjointSparseTable(const vector<T> &a) {
        int n = a.size(), LG = 0;
        while ((1 << LG) <= n)
            LG++;
        buf.assign(LG, vector<T>(n));
        height.assign(1 << LG, 0);
        rep(i, 2, 1 << LG) height[i] = height[i >> 1] + 1;
        rep(i, 0, n) buf[0][i] = a[i];
        rep(lg, 1, LG) {
            int add = 1 << lg;
            for (int j = 0; j < n; j += (add << 1)) {
                int pos = min(j + add, n);
                buf[lg][pos - 1] = a[pos - 1];
                for (int k = pos - 2; k >= j; k--)
                    buf[lg][k] = f(a[k], buf[lg][k + 1]);
                if (n <= pos)
                    break;
                buf[lg][pos] = a[pos];
                for (int k = pos + 1; k < min(pos + add, n); k++)
                    buf[lg][k] = f(buf[lg][k - 1], a[k]);
            }
        }
    }
    T query(int L, int R) {
        if (L >= --R)
            return buf[0][L];
        return f(buf[height[L ^ R]][L], buf[height[L ^ R]][R]);
    }
};

/**
 * @brief Disjoint Sparse Table
 */

#line 2 "DataStructure/disjointsparsetable.hpp"

template <typename T, T (*f)(T, T)> struct DisjointSparseTable {
    vector<vector<T>> buf;
    vector<int> height;
    DisjointSparseTable() {}
    DisjointSparseTable(const vector<T> &a) {
        int n = a.size(), LG = 0;
        while ((1 << LG) <= n)
            LG++;
        buf.assign(LG, vector<T>(n));
        height.assign(1 << LG, 0);
        rep(i, 2, 1 << LG) height[i] = height[i >> 1] + 1;
        rep(i, 0, n) buf[0][i] = a[i];
        rep(lg, 1, LG) {
            int add = 1 << lg;
            for (int j = 0; j < n; j += (add << 1)) {
                int pos = min(j + add, n);
                buf[lg][pos - 1] = a[pos - 1];
                for (int k = pos - 2; k >= j; k--)
                    buf[lg][k] = f(a[k], buf[lg][k + 1]);
                if (n <= pos)
                    break;
                buf[lg][pos] = a[pos];
                for (int k = pos + 1; k < min(pos + add, n); k++)
                    buf[lg][k] = f(buf[lg][k - 1], a[k]);
            }
        }
    }
    T query(int L, int R) {
        if (L >= --R)
            return buf[0][L];
        return f(buf[height[L ^ R]][L], buf[height[L ^ R]][R]);
    }
};

/**
 * @brief Disjoint Sparse Table
 */

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