structure/others/sparse-table.hpp

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• Last update: 2024-10-04 14:05:18+02:00
• Include: #include "structure/others/sparse-table.hpp"

Required by

• graph/tree/rmq-lowest-common-ancestor.hpp
• structure/others/linear-sparse-table.hpp

Verified with

• test/aoj-grl-5-c-3.test.cpp

Code

#include <bits/stdc++.h>
using namespace std;

/*
半群：若集合 S 和二元运算 op : S X S -> S 满足对任意 x, y, z \in S 都有 op(op(x, y), z) = op(x, (y, z)), 称 (S, op) 为半群
幂等半群的区间查询,
1. fold 查询 [l, r) 的值

需要补充一些二分函数，O(log) 找到值
*/
// using F = function<int(int, int)>
template <typename T, typename F>
struct SparseTable {
    F f;
    vector<vector<T> > st;
    vector<int> lookup;

    SparseTable() = default;

    explicit SparseTable(const vector<T> &v, const F &f) : f(f) {
        const int n = (int)v.size();
        const int b = 32 - __builtin_clz(n);
        st.assign(b, vector<T>(n));
        for (int i = 0; i < v.size(); i++) {
            st[0][i] = v[i];
        }
        for (int i = 1; i < b; i++) {
            for (int j = 0; j + (1 << i) <= n; j++) {
                st[i][j] = f(st[i - 1][j], st[i - 1][j + (1 << (i - 1))]);
            }
        }
        lookup.resize(v.size() + 1);
        for (int i = 2; i < lookup.size(); i++) {
            lookup[i] = lookup[i >> 1] + 1;
        }
    }

    inline T fold(int l, int r) const {
        int b = lookup[r - l];
        return f(st[b][l], st[b][r - (1 << b)]);
    }
};

template <typename T, typename F>
SparseTable<T, F> get_sparse_table(const vector<T> &v, const F &f) {
    return SparseTable<T, F>(v, f);
}

#line 1 "structure/others/sparse-table.hpp"
#include <bits/stdc++.h>
using namespace std;

/*
半群：若集合 S 和二元运算 op : S X S -> S 满足对任意 x, y, z \in S 都有 op(op(x, y), z) = op(x, (y, z)), 称 (S, op) 为半群
幂等半群的区间查询,
1. fold 查询 [l, r) 的值

需要补充一些二分函数，O(log) 找到值
*/
// using F = function<int(int, int)>
template <typename T, typename F>
struct SparseTable {
    F f;
    vector<vector<T> > st;
    vector<int> lookup;

    SparseTable() = default;

    explicit SparseTable(const vector<T> &v, const F &f) : f(f) {
        const int n = (int)v.size();
        const int b = 32 - __builtin_clz(n);
        st.assign(b, vector<T>(n));
        for (int i = 0; i < v.size(); i++) {
            st[0][i] = v[i];
        }
        for (int i = 1; i < b; i++) {
            for (int j = 0; j + (1 << i) <= n; j++) {
                st[i][j] = f(st[i - 1][j], st[i - 1][j + (1 << (i - 1))]);
            }
        }
        lookup.resize(v.size() + 1);
        for (int i = 2; i < lookup.size(); i++) {
            lookup[i] = lookup[i >> 1] + 1;
        }
    }

    inline T fold(int l, int r) const {
        int b = lookup[r - l];
        return f(st[b][l], st[b][r - (1 << b)]);
    }
};

template <typename T, typename F>
SparseTable<T, F> get_sparse_table(const vector<T> &v, const F &f) {
    return SparseTable<T, F>(v, f);
}

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