algo/ds/sparse_table.h

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• Last update: 2026-07-26 23:08:04-04:00

Depends on

• algo/common.h
• algo/utils/bits.h

Required by

• algo/graph/lca.h

Verified with

• verify/ds/sparse_table.test.cpp
• verify/graph/tree_lca.test.cpp

Code

#pragma once
#include "algo/common.h"
#include "algo/utils/bits.h"

namespace algo::ds {

// An op has to be a type here, and std::min and std::max name overload sets
// rather than single functions, so wrap them.
template <typename T>
struct min_op {
    T operator()(T a, T b) const {
        return std::min(a, b);
    }
};

template <typename T>
struct max_op {
    T operator()(T a, T b) const {
        return std::max(a, b);
    }
};

template <typename T, typename Op = min_op<T>>
struct sparse_table {
    // Must be constructed with idempotent function. Call init() after if using
    // this constructor.
    sparse_table(index_t _n, Op op = Op())
        : n(_n), k(utils::lg2(n)), op(op),
          st(std::max<index_t>(k + 1, 1), std::vector<T>(n)) {
    }
    // Must be constructed with idempotent function
    sparse_table(const std::vector<T> &a, Op op = Op())
        : sparse_table((index_t)a.size(), op) {
        init(a);
    }
    void init(const std::vector<T> &a) {
        assert((index_t)a.size() <= n);
        std::copy(a.begin(), a.end(), st[0].begin());
        for (index_t i = 1; i <= k; i++) {
            for (index_t j = 0; j + (index_t(1) << i) <= n; j++) {
                st[i][j] =
                    op(st[i - 1][j], st[i - 1][j + (index_t(1) << (i - 1))]);
            }
        }
    }
    // Queries on [l, r]
    T query(index_t l, index_t r) {
        index_t i = utils::lg2(r - l + 1);
        return op(st[i][l], st[i][r - (index_t(1) << i) + 1]);
    }
    friend std::ostream &operator<<(std::ostream &os, const sparse_table &t) {
        return os << t.st[0];
    }

private:
    // k is the max level index and is -1 when n is 0, so the row count is
    // floored at 1 to keep level 0 present for init() to copy into.
    index_t n, k;
    Op op;
    std::vector<std::vector<T>> st;
};

} // namespace algo::ds

#line 2 "algo/common.h"
#ifndef PREPROCESS
#include <bits/stdc++.h>
#include <cassert>
#endif

namespace algo {

// Indices and sizes into library containers. Signed, so the usual "walk down to
// -1" loops still terminate; widening the whole library is a change here alone.
using index_t = int;

} // namespace algo
#line 3 "algo/utils/bits.h"

namespace algo::utils {

// Returns number of set bits in x
constexpr int popcnt(int64_t x) {
    return __builtin_popcountll(x);
}
// Returns floor(log_2(x))
constexpr int lg2(uint64_t x) {
    return std::bit_width(x) - 1;
}

} // namespace algo::utils
#line 4 "algo/ds/sparse_table.h"

namespace algo::ds {

// An op has to be a type here, and std::min and std::max name overload sets
// rather than single functions, so wrap them.
template <typename T>
struct min_op {
    T operator()(T a, T b) const {
        return std::min(a, b);
    }
};

template <typename T>
struct max_op {
    T operator()(T a, T b) const {
        return std::max(a, b);
    }
};

template <typename T, typename Op = min_op<T>>
struct sparse_table {
    // Must be constructed with idempotent function. Call init() after if using
    // this constructor.
    sparse_table(index_t _n, Op op = Op())
        : n(_n), k(utils::lg2(n)), op(op),
          st(std::max<index_t>(k + 1, 1), std::vector<T>(n)) {
    }
    // Must be constructed with idempotent function
    sparse_table(const std::vector<T> &a, Op op = Op())
        : sparse_table((index_t)a.size(), op) {
        init(a);
    }
    void init(const std::vector<T> &a) {
        assert((index_t)a.size() <= n);
        std::copy(a.begin(), a.end(), st[0].begin());
        for (index_t i = 1; i <= k; i++) {
            for (index_t j = 0; j + (index_t(1) << i) <= n; j++) {
                st[i][j] =
                    op(st[i - 1][j], st[i - 1][j + (index_t(1) << (i - 1))]);
            }
        }
    }
    // Queries on [l, r]
    T query(index_t l, index_t r) {
        index_t i = utils::lg2(r - l + 1);
        return op(st[i][l], st[i][r - (index_t(1) << i) + 1]);
    }
    friend std::ostream &operator<<(std::ostream &os, const sparse_table &t) {
        return os << t.st[0];
    }

private:
    // k is the max level index and is -1 when n is 0, so the row count is
    // floored at 1 to keep level 0 present for init() to copy into.
    index_t n, k;
    Op op;
    std::vector<std::vector<T>> st;
};

} // namespace algo::ds

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