examples/segment_tree.range_minimum_query.test.cpp

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Last update: 2023-12-09 20:36:27+09:00
Problem: https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/all/DSL_2_A

Depends on

Code

#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/all/DSL_2_A"
#include <iostream>
#include "examples/segment_tree.hpp"
#include "examples/monoids.hpp"
#include "examples/macros.hpp"
using namespace std;

int main() {
    int n, q; cin >> n >> q;
    segment_tree<min_monoid> segtree(n);
    REP (i, n) {
        segtree.point_set(i, (1u << 31) - 1);
    }
    REP (i, q) {
        int com, x, y; cin >> com >> x >> y;
        if (com == 0) {
            segtree.point_set(x, y);
        } else if (com == 1) {
            cout << segtree.range_concat(x, y + 1) << endl;
        }
    }
    return 0;
}

#line 1 "examples/segment_tree.range_minimum_query.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/all/DSL_2_A"
#include <iostream>
#line 2 "examples/segment_tree.hpp"
#include <cassert>
#include <vector>

/**
 * @brief a Segment Tree (generalized with monoids) 
 * @tparam Monoid is a monoid; commutativity is not required
 * @see https://en.wikipedia.org/wiki/Segment_tree
 */
template <class Monoid>
struct segment_tree {
    typedef typename Monoid::value_type value_type;
    const Monoid mon;
    int n;
    std::vector<value_type> a;

    segment_tree() = default;
    segment_tree(int n_, const Monoid & mon_ = Monoid()) : mon(mon_) {
        n = 1; while (n < n_) n *= 2;
        a.resize(2 * n - 1, mon.unit());
    }

    /**
     * @brief set $a_i$ as b in $O(\log n)$
     * @arg i is 0-based
     */
    void point_set(int i, value_type b) {
        assert (0 <= i and i < n);
        a[i + n - 1] = b;
        for (i = (i + n) / 2; i > 0; i /= 2) {  // 1-based
            a[i - 1] = mon.mult(a[2 * i - 1], a[2 * i]);
        }
    }

    /**
     * @brief compute $a_l \cdot a _ {l + 1} \cdot ... \cdot a _ {r - 1}$ in $O(\log n)$
     * @arg l, r are 0-based
     */
    value_type range_concat(int l, int r) {
        assert (0 <= l and l <= r and r <= n);
        value_type lacc = mon.unit(), racc = mon.unit();
        for (l += n, r += n; l < r; l /= 2, r /= 2) {  // 1-based loop, 2x faster than recursion
            if (l % 2 == 1) lacc = mon.mult(lacc, a[(l ++) - 1]);
            if (r % 2 == 1) racc = mon.mult(a[(-- r) - 1], racc);
        }
        return mon.mult(lacc, racc);
    }
};
#line 2 "examples/monoids.hpp"
#include <algorithm>
#include <cstdint>

struct plus_monoid {
    typedef int64_t value_type;
    value_type unit() const { return 0; }
    value_type mult(value_type a, value_type b) const { return a + b; }
};

struct max_monoid {
    typedef int64_t value_type;
    value_type unit() const { return INT64_MIN; }
    value_type mult(value_type a, value_type b) const { return std::max(a, b); }
};

struct min_monoid {
    typedef int64_t value_type;
    value_type unit() const { return INT64_MAX; }
    value_type mult(value_type a, value_type b) const { return std::min(a, b); }
};
#line 2 "examples/macros.hpp"
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) begin(x), end(x)
#line 6 "examples/segment_tree.range_minimum_query.test.cpp"
using namespace std;

int main() {
    int n, q; cin >> n >> q;
    segment_tree<min_monoid> segtree(n);
    REP (i, n) {
        segtree.point_set(i, (1u << 31) - 1);
    }
    REP (i, q) {
        int com, x, y; cin >> com >> x >> y;
        if (com == 0) {
            segtree.point_set(x, y);
        } else if (com == 1) {
            cout << segtree.range_concat(x, y + 1) << endl;
        }
    }
    return 0;
}