C++ Library for Competitive Programming
#include "emthrm/misc/inversion_number.hpp"
数列 $A$ に対して $A_i > A_j$ を満たす組 $(i, j)$ ($i < j$) の個数である。
バブルソートに必要な交換回数に等しい。
$O(N\log{N})$
名前 | 戻り値 |
---|---|
template <typename T> long long inversion_number(const std::vector<T>& a);
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$A$ の転倒数 |
https://onlinejudge.u-aizu.ac.jp/solutions/problem/ALDS1_5_D/review/4087800/emthrm/C++14
#ifndef EMTHRM_MISC_INVERSION_NUMBER_HPP_
#define EMTHRM_MISC_INVERSION_NUMBER_HPP_
#include <algorithm>
#include <iterator>
#include <vector>
#include "emthrm/data_structure/fenwick_tree/fenwick_tree.hpp"
namespace emthrm {
template <typename T>
long long inversion_number(const std::vector<T>& a) {
const int n = a.size();
std::vector<T> b = a;
std::sort(b.begin(), b.end());
b.erase(std::unique(b.begin(), b.end()), b.end());
FenwickTree<int> bit(b.size());
long long res = 0;
for (int i = 0; i < n; ++i) {
const int idx = std::distance(
b.begin(), std::lower_bound(b.begin(), b.end(), a[i]));
res += i - bit.sum(idx + 1);
bit.add(idx, 1);
}
return res;
}
} // namespace emthrm
#endif // EMTHRM_MISC_INVERSION_NUMBER_HPP_
#line 1 "include/emthrm/misc/inversion_number.hpp"
#include <algorithm>
#include <iterator>
#include <vector>
#line 1 "include/emthrm/data_structure/fenwick_tree/fenwick_tree.hpp"
#include <bit>
#line 6 "include/emthrm/data_structure/fenwick_tree/fenwick_tree.hpp"
namespace emthrm {
template <typename Abelian>
struct FenwickTree {
explicit FenwickTree(const int n, const Abelian ID = 0)
: n(n), ID(ID), data(n, ID) {}
void add(int idx, const Abelian val) {
for (; idx < n; idx |= idx + 1) {
data[idx] += val;
}
}
Abelian sum(int idx) const {
Abelian res = ID;
for (--idx; idx >= 0; idx = (idx & (idx + 1)) - 1) {
res += data[idx];
}
return res;
}
Abelian sum(const int left, const int right) const {
return left < right ? sum(right) - sum(left) : ID;
}
Abelian operator[](const int idx) const { return sum(idx, idx + 1); }
int lower_bound(Abelian val) const {
if (val <= ID) [[unlikely]] return 0;
int res = 0;
for (int mask = std::bit_ceil(static_cast<unsigned int>(n + 1)) >> 1;
mask > 0; mask >>= 1) {
const int idx = res + mask - 1;
if (idx < n && data[idx] < val) {
val -= data[idx];
res += mask;
}
}
return res;
}
private:
const int n;
const Abelian ID;
std::vector<Abelian> data;
};
} // namespace emthrm
#line 9 "include/emthrm/misc/inversion_number.hpp"
namespace emthrm {
template <typename T>
long long inversion_number(const std::vector<T>& a) {
const int n = a.size();
std::vector<T> b = a;
std::sort(b.begin(), b.end());
b.erase(std::unique(b.begin(), b.end()), b.end());
FenwickTree<int> bit(b.size());
long long res = 0;
for (int i = 0; i < n; ++i) {
const int idx = std::distance(
b.begin(), std::lower_bound(b.begin(), b.end(), a[i]));
res += i - bit.sum(idx + 1);
bit.add(idx, 1);
}
return res;
}
} // namespace emthrm