結果
| 問題 |
No.738 平らな農地
|
| ユーザー |
 Slephy
|
| 提出日時 | 2022-08-24 00:11:44 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,032 ms / 2,000 ms |
| コード長 | 31,368 bytes |
| コンパイル時間 | 5,636 ms |
| コンパイル使用メモリ | 305,520 KB |
| 最終ジャッジ日時 | 2025-01-31 03:23:33 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 5 |
| other | AC * 87 |
ソースコード
//#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
// using mint = modint1000000007;
// using mint = modint998244353;
// using mint = modint;
// const int MOD = mint::mod();
#endif
#ifdef LOCAL_DEBUG
#define cout cout<<' '
#endif
using ll = long long;
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
// constexpr int MOD = (int)1e9 + 7;
// constexpr int MOD = (int)998244353;
constexpr int INF = (int)1e9 + 1001010;
constexpr ll llINF = (ll)4e18 + 11000010;
constexpr double PI = 3.14159265358979;
constexpr double EPS = 1e-10;
#define Isize(x) (int)((x).size())
#define ALL(x) (x).begin(),(x).end()
#define RALL(x) (x).rbegin(),(x).rend()
#define endn "\n"
#define SUM(v) accumulate(ALL(v), 0LL)
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define popcount __builtin_popcount
#define popcountll __builtin_popcountll
template <class T> inline vector<vector<T>> vector2(const size_t &i, const size_t &j, const T &init = T()) {
return vector<vector<T>>(i, vector<T>(j, init));
}
template <class T> inline vector<vector<vector<T>>> vector3(const size_t &i, const size_t &j, const int &k, const T &init = T()) {
return vector<vector<vector<T>>>(i, vector<vector<T>>(j, vector<T>(k, init)));
}
template <class T> inline vector<vector<vector<vector<T>>>> vector4(const size_t &i, const size_t &j, const size_t &k, const size_t &l, const T &init = T()) {
return vector<vector<vector<vector<T>>>>(i, vector<vector<vector<T>>>(j, vector<vector<T>>(k, vector<T>(l, init))));
}
const string VEC_ELEM_SEPARATION = " ";
const string VEC_VEC_SEPARATION = endn;
template<class T> istream & operator >> (istream &i, vector<T> &A) {for(auto &I : A) {i >> I;} return i;}
template<class T> ostream & operator << (ostream &o, const vector<vector<T>> &A) {int i=A.size(); for(auto &I : A){o << I << (--i ? VEC_VEC_SEPARATION : "");} return o;}
template<class T> ostream & operator << (ostream &o, const vector<T> &A) {int i=A.size(); for(auto &I : A){o << I << (--i ? VEC_ELEM_SEPARATION : "");} return o;}
template<class T> ostream & operator << (ostream &o, const deque<T> &A) {int i=A.size(); for(auto &I : A){o << I << (--i ? VEC_ELEM_SEPARATION : "");} return o;}
template<class T, class U> istream & operator >> (istream &i, pair<T,U> &A) {i >> A.first >> A.second; return i;}
template<class T, class U> ostream & operator << (ostream &o, const pair<T,U> &A) {o << A.first << " " << A.second; return o;}
template<class T, class U, class V> istream & operator >> (istream &i, tuple<T,U,V>&A) {i >> get<0>(A) >> get<1>(A) >> get<2>(A); return i;}
template<class T, class U, class V> ostream & operator << (ostream &o, const tuple<T,U,V> &A) {o << get<0>(A) << " " << get<1>(A) << " " << get<2>(A); return o;}
template<class T> vector<T>& operator ++(vector<T> &A) {for(auto &I : A) {I++;} return A;}
template<class T> vector<T>& operator ++(vector<T> &A, int n) {for(auto &I : A) {I++;} return A;}
template<class T> vector<T>& operator --(vector<T> &A) {for(auto &I : A) {I--;} return A;}
template<class T> vector<T>& operator --(vector<T> &A, int n) {for(auto &I : A) {I--;} return A;}
template<class T, class U> bool chmax(T &a, const U &b){return ((a < b) ? (a = b, true) : false);}
template<class T, class U> bool chmin(T &a, const U &b){return ((a > b) ? (a = b, true) : false);}
ll floor(ll a, ll b){assert(b != 0); return((a%b != 0 && ((a>0) != (b>0))) ? a/b-1 : a/b);}
ll ceil (ll a, ll b){assert(b != 0); return((a%b != 0 && ((a>0) == (b>0))) ? a/b+1 : a/b);}
ll gcd(ll a, ll b){return ((b==0) ? a : gcd(b, a%b));}
ll lcm(ll a, ll b){return a / gcd(a,b) * b;}
bool is_in(ll n, ll inf, ll sup){return(inf <= n && n <= sup);}
// ================================== ここまでテンプレ ==================================
// MIT License
// from : https://github.com/MitI-7/WaveletMatrix
// blog : https://miti-7.hatenablog.com/entry/2018/04/28/152259
enum {
NOTFOUND = 0xFFFFFFFFFFFFFFFFLLU
};
class SuccinctBitVector {
private:
const uint64_t size; // ビットベクトルのサイズ
static const uint64_t blockBitNum = 16;
static const uint64_t LEVEL_L = 512;
static const uint64_t LEVEL_S = 16;
std::vector<uint64_t> L; // 大ブロック
std::vector<uint16_t> S; // 小ブロック
std::vector<uint16_t> B; // ビットベクトル
uint64_t numOne = 0; // 1bitの数
public:
explicit SuccinctBitVector(const uint64_t n) : size(n) {
const uint64_t s = (n + blockBitNum - 1) / blockBitNum + 1; // ceil(n, blockSize)
this->B.assign(s, 0);
this->L.assign(n / LEVEL_L + 1, 0);
this->S.assign(n / LEVEL_S + 1, 0);
}
// B[pos] = bit
void setBit(const uint64_t bit, const uint64_t pos){
assert(bit == 0 or bit == 1);
assert(pos < this->size);
const uint64_t blockPos = pos / blockBitNum;
const uint64_t offset = pos % blockBitNum;
if (bit == 1) { B.at(blockPos) |= (1LLU << offset); }
else { B.at(blockPos) &= (~(1LLU << offset)); }
}
// B[pos]
uint64_t access(const uint64_t pos) {
assert(pos < this->size);
const uint64_t blockPos = pos / blockBitNum;
const uint64_t offset = pos % blockBitNum;
return ((B.at(blockPos) >> offset) & 1);
}
void build() {
uint64_t num = 0;
for (uint64_t i = 0; i <= size; i++){
if (i % LEVEL_L == 0) {
L.at(i / LEVEL_L) = num;
}
if (i % LEVEL_S == 0) {
S.at(i / LEVEL_S) = num - L.at(i / LEVEL_L);
}
if (i != size and i % blockBitNum == 0) {
num += this->popCount(this->B.at(i / blockBitNum));
}
}
this-> numOne = num;
}
// B[0, pos)のbitの数
uint64_t rank(const uint64_t bit, const uint64_t pos) {
assert(bit == 0 or bit == 1);
assert(pos <= this->size);
if (bit) {
return L[pos / LEVEL_L] + S[pos / LEVEL_S] + popCount(B[pos / blockBitNum] & ((1 << (pos % blockBitNum)) - 1));
}
else {
return pos - rank(1, pos);
}
}
// rank番目のbitの位置 + 1(rankは1-origin)
uint64_t select(const uint64_t bit, const uint64_t rank) {
assert(bit == 0 or bit == 1);
assert(rank > 0);
if (bit == 0 and rank > this->size - this-> numOne) { return NOTFOUND; }
if (bit == 1 and rank > this-> numOne) { return NOTFOUND; }
// 大ブロックL内を検索
uint64_t large_idx = 0;
{
uint64_t left = 0;
uint64_t right = L.size();
while (right - left > 1) {
uint64_t mid = (left + right) / 2;
uint64_t r = L.at(mid);
r = (bit) ? r : mid * LEVEL_L - L.at(mid);
if (r < rank) {
left = mid;
large_idx = mid;
} else {
right = mid;
}
}
}
// 小ブロックS内を検索
uint64_t small_idx = (large_idx * LEVEL_L) / LEVEL_S;
{
uint64_t left = (large_idx * LEVEL_L) / LEVEL_S;
uint64_t right = std::min(((large_idx + 1) * LEVEL_L) / LEVEL_S, (uint64_t)S.size());
while (right - left > 1) {
uint64_t mid = (left + right) / 2;
uint64_t r = L.at(large_idx) + S.at(mid);
r = (bit) ? r :mid * LEVEL_S - r;
if (r < rank) {
left = mid;
small_idx = mid;
} else {
right = mid;
}
}
}
// Bをブロック単位で順番に探索
uint64_t rank_pos = 0;
{
const uint64_t begin_block_idx = (small_idx * LEVEL_S) / blockBitNum;
uint64_t total_bit = L.at(large_idx) + S.at(small_idx);
if (bit == 0) {
total_bit = small_idx * LEVEL_S - total_bit;
}
for (uint64_t i = 0;; ++i) {
uint64_t b = popCount(B.at(begin_block_idx + i));
if (bit == 0) {
b = blockBitNum - b;
}
if (total_bit + b >= rank) {
uint64_t block = (bit) ? B.at(begin_block_idx + i) : ~B.at(begin_block_idx + i);
rank_pos = (begin_block_idx + i) * blockBitNum + selectInBlock(block, rank - total_bit);
break;
}
total_bit += b;
}
}
return rank_pos + 1;
}
uint64_t getNumOne() const {
return numOne;
}
void debug() {
std::cout << "LEVEL_L(" << L.size() << ")" << std::endl;
for (uint64_t i = 0 ; i < L.size(); ++i) {
std::cout << L.at(i) << ", ";
}
std::cout << std::endl;
std::cout << "LEVEL_S(" << S.size() << ")" << std::endl;
for (uint64_t i = 0 ; i < S.size(); ++i) {
std::cout << S.at(i) << ", ";
}
std::cout << std::endl;
}
private:
uint64_t popCount(uint64_t x) {
x = (x & 0x5555555555555555ULL) + ((x >> 1) & 0x5555555555555555ULL);
x = (x & 0x3333333333333333ULL) + ((x >> 2) & 0x3333333333333333ULL);
x = (x + (x >> 4)) & 0x0f0f0f0f0f0f0f0fULL;
x = x + (x >> 8);
x = x + (x >> 16);
x = x + (x >> 32);
return x & 0x7FLLU;
}
uint64_t selectInBlock(uint64_t x, uint64_t rank) {
uint64_t x1 = x - ((x & 0xAAAAAAAAAAAAAAAALLU) >> 1);
uint64_t x2 = (x1 & 0x3333333333333333LLU) + ((x1 >> 2) & 0x3333333333333333LLU);
uint64_t x3 = (x2 + (x2 >> 4)) & 0x0F0F0F0F0F0F0F0FLLU;
uint64_t pos = 0;
for (;; pos += 8){
uint64_t rank_next = (x3 >> pos) & 0xFFLLU;
if (rank <= rank_next) break;
rank -= rank_next;
}
uint64_t v2 = (x2 >> pos) & 0xFLLU;
if (rank > v2) {
rank -= v2;
pos += 4;
}
uint64_t v1 = (x1 >> pos) & 0x3LLU;
if (rank > v1){
rank -= v1;
pos += 2;
}
uint64_t v0 = (x >> pos) & 0x1LLU;
if (v0 < rank){
rank -= v0;
pos += 1;
}
return pos;
}
};
class WaveletMatrix {
private:
std::vector<SuccinctBitVector> bit_arrays;
std::vector<uint64_t> begin_one; // 各bitに着目したときの1の開始位置
std::map<uint64_t, uint64_t> begin_alphabet; // 最後のソートされた配列で各文字の開始位置
std::vector<std::vector<uint64_t>> cumulative_sum; // 各bitに着目したときの累積和
uint64_t size; // 与えられた配列のサイズ
uint64_t maximum_element; // 文字数
uint64_t bit_size; // 文字を表すのに必要なbit数
public:
WaveletMatrix (const std::vector<uint64_t> &array) {
assert(array.size() > 0);
size = array.size();
maximum_element = *max_element(array.begin(), array.end()) + 1;
bit_size = get_num_of_bit(maximum_element);
if (bit_size == 0) {
bit_size = 1;
}
for (uint64_t i = 0; i < bit_size; ++i) {
SuccinctBitVector sv(size);
bit_arrays.push_back(sv);
}
this->begin_one.resize(bit_size);
this->cumulative_sum.resize(bit_size + 1, std::vector<uint64_t>(size + 1, 0));
for (uint64_t j = 0; j < array.size(); ++j) {
this->cumulative_sum.at(0).at(j + 1) = this->cumulative_sum.at(0).at(j) + array[j];
}
std::vector<uint64_t> v(array);
for (uint64_t i = 0; i < bit_size; ++i) {
std::vector<uint64_t> temp;
// 0をtempにいれてく
for (uint64_t j = 0; j < v.size(); ++j) {
uint64_t c = v.at(j);
uint64_t bit = (c >> (bit_size - i - 1)) & 1; // 上からi番目のbit
if (bit == 0) {
temp.push_back(c);
bit_arrays.at(i).setBit(0, j);
}
}
this->begin_one.at(i) = temp.size();
// 1をtempにいれてく
for (uint64_t j = 0; j < v.size(); ++j) {
uint64_t c = v.at(j);
uint64_t bit = (c >> (bit_size - i - 1)) & 1; // 上からi番目のbit
if (bit == 1) {
temp.push_back(c);
bit_arrays.at(i).setBit(1, j);
}
}
for (uint64_t j = 0; j < temp.size(); ++j) {
this->cumulative_sum.at(i + 1).at(j + 1) = this->cumulative_sum.at(i + 1).at(j) + temp.at(j);
}
bit_arrays.at(i).build();
v = temp;
}
// ソートされた配列内での各文字の位置を取得
for (int i = v.size() - 1; i >= 0; --i) {
this->begin_alphabet[v.at(i)] = i;
}
}
// v[pos]
uint64_t access(uint64_t pos) {
if (pos >= this->size) { return NOTFOUND; }
uint64_t c = 0;
for (uint64_t i = 0; i < bit_arrays.size(); ++i) {
uint64_t bit = bit_arrays.at(i).access(pos); // もとの数値のi番目のbit
c = (c <<= 1) | bit;
pos = bit_arrays.at(i).rank(bit, pos);
if (bit) {
pos += this->begin_one.at(i);
}
}
return c;
}
// i番目のcの位置 + 1を返す。rankは1-origin
uint64_t select(uint64_t c, uint64_t rank) {
assert(rank > 0);
if (c >= maximum_element) {
return NOTFOUND;
}
if (this->begin_alphabet.find(c) == this->begin_alphabet.end()) {
return NOTFOUND;
}
uint64_t index = this->begin_alphabet.at(c) + rank;
for (uint64_t i = 0; i < bit_arrays.size(); ++i){
uint64_t bit = ((c >> i) & 1); // 下からi番目のbit
if (bit == 1) {
index -= this->begin_one.at(bit_size - i - 1);
}
index = this->bit_arrays.at(bit_size - i - 1).select(bit, index);
}
return index;
}
// v[begin_pos, end_pos)で最大値のindexを返す
uint64_t maxRange(uint64_t begin_pos, uint64_t end_pos) {
return quantileRange(begin_pos, end_pos, end_pos - begin_pos - 1);
}
// v[begin_pos, end_pos)で最小値のindexを返す
uint64_t minRange(uint64_t begin_pos, uint64_t end_pos) {
return quantileRange(begin_pos, end_pos, 0);
}
// v[begin_pos, end_pos)でk番目に小さい数値のindexを返す(kは0-origin)
// つまり小さい順に並べてk番目の値
uint64_t quantileRange(uint64_t begin_pos, uint64_t end_pos, uint64_t k) {
if ((end_pos > size || begin_pos >= end_pos) || (k >= end_pos - begin_pos)) {
return NOTFOUND;
}
uint64_t val = 0;
for (uint64_t i = 0; i < bit_size; ++i) {
const uint64_t num_of_zero_begin = bit_arrays.at(i).rank(0, begin_pos);
const uint64_t num_of_zero_end = bit_arrays.at(i).rank(0, end_pos);
const uint64_t num_of_zero = num_of_zero_end - num_of_zero_begin; // beginからendまでにある0の数
const uint64_t bit = (k < num_of_zero) ? 0 : 1; // k番目の値の上からi番目のbitが0か1か
if (bit) {
k -= num_of_zero;
begin_pos = this->begin_one.at(i) + begin_pos - num_of_zero_begin;
end_pos = this->begin_one.at(i) + end_pos - num_of_zero_end;
}
else {
begin_pos = num_of_zero_begin;
end_pos = num_of_zero_begin + num_of_zero;
}
val = ((val << 1) | bit);
}
uint64_t left = 0;
for (uint64_t i = 0; i < bit_size; ++i) {
const uint64_t bit = (val >> (bit_size - i - 1)) & 1; // 上からi番目のbit
left = bit_arrays.at(i).rank(bit, left); // cのi番目のbitと同じ数値の数
if (bit) {
left += this->begin_one.at(i);
}
}
const uint64_t rank = begin_pos + k - left + 1;
return select(val, rank) - 1;
}
// v[0, pos)のcの数
uint64_t rank(uint64_t c, uint64_t pos) {
assert(pos < size);
if (c >= maximum_element) {
return 0;
}
if (this->begin_alphabet.find(c) == this->begin_alphabet.end()) {
return 0;
}
for (uint64_t i = 0; i < bit_size; ++i) {
uint64_t bit = (c >> (bit_size - i - 1)) & 1; // 上からi番目のbit
pos = bit_arrays.at(i).rank(bit, pos); // cのi番目のbitと同じ数値の数
if (bit) {
pos += this->begin_one.at(i);
}
}
uint64_t begin_pos = this->begin_alphabet.at(c);
return pos - begin_pos;
}
// v[begin_pos, end_pos)で[min, max)に入る値の個数
uint64_t rangeFreq(uint64_t begin_pos, uint64_t end_pos, uint64_t min_c, uint64_t max_c) {
if ((end_pos > size || begin_pos >= end_pos) || (min_c >= max_c) || min_c >= maximum_element) {
return 0;
}
const auto maxi_t = rankAll(max_c, begin_pos, end_pos);
const auto mini_t = rankAll(min_c, begin_pos, end_pos);
return std::get<1>(maxi_t) - std::get<1>(mini_t);
}
// v[0, pos)でcより小さい文字の数
uint64_t rankLessThan(uint64_t c, uint64_t begin, uint64_t end) {
auto t = rankAll(c, begin, end);
return std::get<1>(t);
}
// v[0, pos)でcより大きい文字の数
uint64_t rankMoreThan(uint64_t c, uint64_t begin, uint64_t end) {
auto t = rankAll(c, begin, end);
return std::get<2>(t);
}
// v[begin, end)で(cと同じ値の数、cより小さい値の数、cより大きい値の数)を求める
std::tuple<uint64_t, uint64_t, uint64_t> rankAll(const uint64_t c, uint64_t begin, uint64_t end) {
assert(end <= size);
const uint64_t num = end - begin;
if (begin >= end) {
return std::make_tuple(0, 0, 0);
}
if (c >= maximum_element || end == 0) {
return std::make_tuple(0, num, 0);
}
uint64_t rank_less_than = 0, rank_more_than = 0;
for (size_t i = 0; i < bit_size && begin < end; ++i) {
const uint64_t bit = (c >> (bit_size - i - 1)) & 1;
const uint64_t rank0_begin = this->bit_arrays.at(i).rank(0, begin);
const uint64_t rank0_end = this->bit_arrays.at(i).rank(0, end);
const uint64_t rank1_begin = begin - rank0_begin;
const uint64_t rank1_end = end - rank0_end;
if (bit) {
rank_less_than += (rank0_end - rank0_begin); // i番目のbitが0のものは除外される
begin = this->begin_one.at(i) + rank1_begin;
end = this->begin_one.at(i) + rank1_end;
} else {
rank_more_than += (rank1_end - rank1_begin); // i番目のbitが1のものは除外される
begin = rank0_begin;
end = rank0_end;
}
}
const uint64_t rank = num - rank_less_than - rank_more_than;
return std::make_tuple(rank, rank_less_than, rank_more_than);
}
// T[s, e)で出現回数が多い順にk個の(値，頻度)を返す
// 頻度が同じ場合は値が小さいものが優先される
std::vector<std::pair<uint64_t, uint64_t>> topk(uint64_t s, uint64_t e, uint64_t k) {
assert(s < e);
std::vector<std::pair<uint64_t, uint64_t>> result;
// (頻度，深さ，値)の順でソート
auto c = [](const std::tuple<uint64_t, uint64_t, uint64_t, uint64_t, uint64_t> &l, const std::tuple<uint64_t, uint64_t, uint64_t, uint64_t, uint64_t> &r) {
// width
if (std::get<0>(l) != std::get<0>(r)) {
return std::get<0>(l) < std::get<0>(r);
}
// depth
if (std::get<3>(l) != std::get<3>(r)) {
return std::get<3>(l) > std::get<3>(r);
}
// value
if (std::get<4>(l) != std::get<4>(r)) {
return std::get<4>(l) > std::get<4>(r);
}
return true;
};
std::priority_queue<std::tuple<uint64_t, uint64_t, uint64_t, uint64_t, uint64_t>, std::vector<std::tuple<uint64_t, uint64_t, uint64_t, uint64_t, uint64_t>>, decltype(c)> que(c); // width, left, right, depth, value
que.push(std::make_tuple(e - s, s, e, 0, 0));
while (not que.empty()) {
auto element = que.top(); que.pop();
uint64_t width, left, right, depth, value;
std::tie(width, left, right, depth, value) = element;
if (depth >= this->bit_size) {
result.emplace_back(std::make_pair(value, right - left));
if (result.size() >= k) {
break;
}
continue;
}
// 0
const uint64_t left0 = this->bit_arrays.at(depth).rank(0, left);
const uint64_t right0 = this->bit_arrays.at(depth).rank(0, right);
if (left0 < right0) {
que.push(std::make_tuple(right0 - left0, left0, right0, depth + 1, value));
}
// 1
const uint64_t left1 = this->begin_one.at(depth) + this->bit_arrays.at(depth).rank(1, left);
const uint64_t right1 = this->begin_one.at(depth) + this->bit_arrays.at(depth).rank(1, right);
if (left1 < right1) {
que.push(std::make_tuple(right1 - left1, left1, right1, depth + 1, value | (1 << (bit_size - depth - 1))));
}
}
return result;
};
// T[begin_pos, end_pos)でx <= c < yを満たすcの和を返す
uint64_t rangeSum(const uint64_t begin, const uint64_t end, const uint64_t x, const uint64_t y) {
return rangeSum(begin, end, 0, 0, x, y);
}
// T[begin_pos, end_pos)でx <= c < yを満たす最大のcを返す
uint64_t prevValue(const uint64_t begin_pos, const uint64_t end_pos, const uint64_t x, uint64_t y) {
assert(end_pos <= size);
const uint64_t num = end_pos - begin_pos;
if (x >= y or y == 0) {
return NOTFOUND;
}
if (y > maximum_element) {
y = maximum_element;
}
if (begin_pos >= end_pos) {
return NOTFOUND;
}
if (x >= maximum_element || end_pos == 0) {
return NOTFOUND;
}
y--; // x <= c <= yにする
std::stack<std::tuple<uint64_t, uint64_t, uint64_t, uint64_t, bool>> s; // (begin, end, depth, c, tight)
s.emplace(std::make_tuple(begin_pos, end_pos, 0, 0, true));
while (not s.empty()) {
uint64_t b, e, depth, c;
bool tight;
std::tie(b, e, depth, c, tight) = s.top(); s.pop();
if (depth == bit_size) {
if (c >= x) {
return c;
}
continue;
}
const uint64_t bit = (y >> (bit_size - depth - 1)) & 1;
const uint64_t rank0_begin = this->bit_arrays.at(depth).rank(0, b);
const uint64_t rank0_end = this->bit_arrays.at(depth).rank(0, e);
const uint64_t rank1_begin = b - rank0_begin;
const uint64_t rank1_end = e - rank0_end;
// d番目のbitが0のものを使う
const uint64_t b0 = rank0_begin;
const uint64_t e0 = rank0_end;
if (b0 != e0) { // 範囲がつぶれてない
const uint64_t c0 = ((c << 1) | 0);
s.emplace(std::make_tuple(b0, e0, depth + 1, c0, tight and bit == 0));
}
// d番目のbitが1のものを使う
const uint64_t b1 = this->begin_one.at(depth) + rank1_begin;
const uint64_t e1 = this->begin_one.at(depth) + rank1_end;
if (b1 != e1) {
if (not tight or bit == 1) {
const auto c1 = ((c << 1) | 1);
s.emplace(std::make_tuple(b1, e1, depth + 1, c1, tight));
}
}
}
return NOTFOUND;
}
// T[begin_pos, end_pos)でx <= c < yを満たす最小のcを返す
uint64_t nextValue(const uint64_t begin_pos, const uint64_t end_pos, const uint64_t x, const uint64_t y) {
assert(end_pos <= size);
const uint64_t num = end_pos - begin_pos;
if (x >= y or y == 0) {
return NOTFOUND;
}
if (begin_pos >= end_pos) {
return NOTFOUND;
}
if (x >= maximum_element || end_pos == 0) {
return NOTFOUND;
}
std::stack<std::tuple<uint64_t, uint64_t, uint64_t, uint64_t, bool>> s; // (begin, end, depth, c, tight)
s.emplace(std::make_tuple(begin_pos, end_pos, 0, 0, true));
while (not s.empty()) {
uint64_t b, e, depth, c;
bool tight;
std::tie(b, e, depth, c, tight) = s.top(); s.pop();
if (depth == bit_size) {
if (c < y) {
return c;
}
continue;
}
const uint64_t bit = (x >> (bit_size - depth - 1)) & 1;
const uint64_t rank0_begin = this->bit_arrays.at(depth).rank(0, b);
const uint64_t rank0_end = this->bit_arrays.at(depth).rank(0, e);
const uint64_t rank1_begin = b - rank0_begin;
const uint64_t rank1_end = e - rank0_end;
// d番目のbitが1のものを使う
const uint64_t b1 = this->begin_one.at(depth) + rank1_begin;
const uint64_t e1 = this->begin_one.at(depth) + rank1_end;
if (b1 != e1) {
const auto c1 = ((c << 1) | 1);
s.emplace(std::make_tuple(b1, e1, depth + 1, c1, tight and bit == 1));
}
// d番目のbitが0のものを使う
const uint64_t b0 = rank0_begin;
const uint64_t e0 = rank0_end;
if (b0 != e0) {
if (not tight or bit == 0) {
const uint64_t c0 = ((c << 1) | 0);
s.emplace(std::make_tuple(b0, e0, depth + 1, c0, tight));
}
}
}
return NOTFOUND;
}
// T[s1, e1)とT[s2, e2)に共通して出現する要素を求める
std::vector<std::tuple<uint64_t, uint64_t, uint64_t>> intersect(uint64_t _s1, uint64_t _e1, uint64_t _s2, uint64_t _e2) {
assert(_s1 < _e1);
assert(_s2 < _e2);
std::vector<std::tuple<uint64_t, uint64_t, uint64_t>> intersection;
std::queue<std::tuple<uint64_t, uint64_t, uint64_t, uint64_t, uint64_t, uint64_t>> que; // s1, e1, s2, e2, depth, value
que.push(std::make_tuple(_s1, _e1, _s2, _e2, 0, 0));
while (not que.empty()) {
auto e = que.front(); que.pop();
uint64_t s1, e1, s2, e2, depth, value;
std::tie(s1, e1, s2, e2, depth, value) = e;
if (depth >= this->bit_size) {
intersection.emplace_back(std::make_tuple(value, e1 - s1, e2 - s2));
continue;
}
// 0
uint64_t s1_0 = this->bit_arrays.at(depth).rank(0, s1);
uint64_t e1_0 = this->bit_arrays.at(depth).rank(0, e1);
uint64_t s2_0 = this->bit_arrays.at(depth).rank(0, s2);
uint64_t e2_0 = this->bit_arrays.at(depth).rank(0, e2);
if (s1_0 != e1_0 and s2_0 != e2_0) {
que.push(std::make_tuple(s1_0, e1_0, s2_0, e2_0, depth + 1, value));
}
// 1
uint64_t s1_1 = this->begin_one.at(depth) + this->bit_arrays.at(depth).rank(1, s1);
uint64_t e1_1 = this->begin_one.at(depth) + this->bit_arrays.at(depth).rank(1, e1);
uint64_t s2_1 = this->begin_one.at(depth) + this->bit_arrays.at(depth).rank(1, s2);
uint64_t e2_1 = this->begin_one.at(depth) + this->bit_arrays.at(depth).rank(1, e2);
if (s1_1 != e1_1 and s2_1 != e2_1) {
que.push(std::make_tuple(s1_1, e1_1, s2_1, e2_1, depth + 1, value | (1 << bit_size - depth - 1)));
}
}
return intersection;
};
private:
uint64_t get_num_of_bit(uint64_t x) {
if (x == 0) return 0;
x--;
uint64_t bit_num = 0;
while (x >> bit_num) {
++bit_num;
}
return bit_num;
}
uint64_t rangeSum(const uint64_t begin, const uint64_t end, const uint64_t depth, const uint64_t c, const uint64_t x, const uint64_t y) {
if (begin == end) {
return 0;
}
if (depth == bit_size) {
if (x <= c and c < y) {
return c * (end - begin); // 値 * 頻度
}
return 0;
}
const uint64_t next_c = ((uint64_t)1 << (bit_size - depth - 1)) | c; // 上からdepth番目のbitを立てる
const uint64_t all_one_c = (((uint64_t)1 << (bit_size - depth - 1)) - 1) | next_c; // depth以降のbitをたてる(これ以降全部1を選んだときの値)
if(all_one_c < x or y <= c) {
return 0;
}
// [begin, pos)のすべての要素は[x, y)
if (x <= c and all_one_c < y) {
return this->cumulative_sum.at(depth).at(end) - this->cumulative_sum.at(depth).at(begin);
}
const uint64_t rank0_begin = this->bit_arrays.at(depth).rank(0, begin);
const uint64_t rank0_end = this->bit_arrays.at(depth).rank(0, end);
const uint64_t rank1_begin = begin - rank0_begin;
const uint64_t rank1_end = end - rank0_end;
return rangeSum(rank0_begin, rank0_end, depth + 1, c, x, y) +
rangeSum(this->begin_one.at(depth) + rank1_begin, this->begin_one[depth] + rank1_end, depth + 1, next_c, x, y);
}
}; // WaveletMatrix
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
int n, k; cin >> n >> k;
vector<uint64_t> a(n); cin >> a;
WaveletMatrix wm(a);
uint64_t ans = (uint64_t)llINF;
for(int i = 0; i < n-k+1; i++){
uint64_t begin = i;
uint64_t end = i + k;
uint64_t idx = wm.quantileRange(begin, end, k/2);
uint64_t m = wm.access(idx);
uint64_t less_sum = wm.rangeSum(begin, end, 0, m);
uint64_t more_sum = wm.rangeSum(begin, end, m, INF);
uint64_t less_freq = wm.rangeFreq(begin, end, 0, m);
uint64_t more_freq = wm.rangeFreq(begin, end, m, INF);
uint64_t less = m * less_freq - less_sum;
uint64_t more = more_sum - m * more_freq;
ans = min(ans, less + more);
}
cout << ans << endl;
return 0;
}