Sparse Table
(structure/SparseTable.cpp)

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• Last update: 2021-09-12 23:44:25+09:00

概要

前計算を $O(N\ log N)$,クエリを $O(1)$ で処理するデータ構造。$f(a,f(b,c))=f(f(a,b),f(b,c))=f(f(a,b),c)$ が成り立つようなものしか載せられない。

例えばRMQはOKだが、RSQはNG。

• query(l,r) : $[l,r)$ の演算の結果

計算量

• 構築 : $O(N\ log N)$
• query(l,r) : $O(1)$

Depends on

• template/template.cpp

Verified with

• test/SparseTable.test.cpp

Code

#pragma once
#include "../template/template.cpp"

template <class T, T (*f)(T, T)>
struct SparseTable {
    vector<T> table[20];
    vector<int> log;
    SparseTable(vector<T> v)
        : log(v.size() + 1) {
        int mx = 0;
        while (1 << (mx + 1) <= len(v)) ++mx;
        rep(i, mx + 1) {
            table[i].resize(len(v));
            rep(j, v.size() - (1 << i) + 1) {
                if (i)
                    table[i][j] = f(table[i - 1][j], table[i - 1][j + (1 << (i - 1))]);
                else
                    table[i][j] = v[j];
            }
        }
        for (int i = 2; i <= len(v); i++) log[i] = log[i >> 1] + 1;
    }
    T query(int l, int r) {
        return f(table[log[r - l]][l], table[log[r - l]][r - (1 << log[r - l])]);
    }
};
/*
@brief Sparse Table
@docs docs/SparseTable.md
*/

#line 2 "template/template.cpp"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define rep(i, n) for (int i = 0; i < n; i++)
#define REP(i, n) for (int i = 1; i < n; i++)
#define rev(i, n) for (int i = n - 1; i >= 0; i--)
#define REV(i, n) for (int i = n - 1; i > 0; i--)
#define all(v) v.begin(), v.end()
#define PL pair<ll, ll>
#define PI pair<int, int>
#define pi acos(-1)
#define len(s) (int)s.size()
#define compress(v) \
    sort(all(v));   \
    v.erase(unique(all(v)), v.end());
#define comid(v, x) lower_bound(all(v), x) - v.begin()

template<class T>
using prique=priority_queue<T,vector<T>,greater<>>;

template <class T, class U>
inline bool chmin(T &a, U b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T, class U>
inline bool chmax(T &a, U b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
constexpr ll inf = 3e18;
#line 3 "structure/SparseTable.cpp"

template <class T, T (*f)(T, T)>
struct SparseTable {
    vector<T> table[20];
    vector<int> log;
    SparseTable(vector<T> v)
        : log(v.size() + 1) {
        int mx = 0;
        while (1 << (mx + 1) <= len(v)) ++mx;
        rep(i, mx + 1) {
            table[i].resize(len(v));
            rep(j, v.size() - (1 << i) + 1) {
                if (i)
                    table[i][j] = f(table[i - 1][j], table[i - 1][j + (1 << (i - 1))]);
                else
                    table[i][j] = v[j];
            }
        }
        for (int i = 2; i <= len(v); i++) log[i] = log[i >> 1] + 1;
    }
    T query(int l, int r) {
        return f(table[log[r - l]][l], table[log[r - l]][r - (1 << log[r - l])]);
    }
};
/*
@brief Sparse Table
@docs docs/SparseTable.md
*/

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