結果
| 問題 |
No.738 平らな農地
|
| ユーザー |
 T101010101
|
| 提出日時 | 2024-03-19 12:13:35 |
| 言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,567 ms / 2,000 ms |
| コード長 | 43,974 bytes |
| コンパイル時間 | 26,415 ms |
| コンパイル使用メモリ | 481,580 KB |
| 最終ジャッジ日時 | 2025-02-20 07:29:49 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（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
#pragma region Macros
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,fma,abm,mmx,avx,avx2")
#include <bits/extc++.h>
#include <immintrin.h>
// #include <atcoder/all>
// using namespace atcoder;
using namespace std;
using namespace __gnu_pbds;
// #include <boost/multiprecision/cpp_dec_float.hpp>
// #include <boost/multiprecision/cpp_int.hpp>
// namespace mp = boost::multiprecision;
// using Bint = mp::cpp_int;
// using Bdouble = mp::number<mp::cpp_dec_float<256>>;
#define pb emplace_back
#define int ll
#define endl '\n'
#define sqrt __builtin_sqrt
#define cbrt __builtin_cbrt
#define hypot __builtin_hypot
using ll = long long;
using ld = long double;
const ld PI = acosl(-1);
const int INF = 1 << 30;
const ll INFL = 1LL << 61;
const int MOD = 998244353;
// const int MOD = 1000000007;
const ld EPS = 1e-10;
const bool equals(ld a, ld b) { return fabs((a) - (b)) < EPS; }
const vector<int> dx = {0, 1, 0, -1, 1, 1, -1, -1}; // → ↓ ← ↑ ↘ ↙ ↖ ↗
const vector<int> dy = {1, 0, -1, 0, 1, -1, -1, 1};
struct Edge {
int from, to;
ll cost;
Edge(int to, ll cost) : to(to), cost(cost) {}
Edge(int from, int to, ll cost) : from(from), to(to), cost(cost) {}
};
chrono::system_clock::time_point start, now;
__attribute__((constructor))
void constructor() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout << fixed << setprecision(10);
start = chrono::system_clock::now();
}
__int128_t POW(__int128_t x, int n) {
__int128_t ret = 1;
assert(n >= 0);
if (x == 1 or n == 0) ret = 1;
else if (x == -1 && n % 2 == 0) ret = 1;
else if (x == -1) ret = -1;
else if (n % 2 == 0) {
assert(x < INFL);
ret = POW(x * x, n / 2);
} else {
assert(x < INFL);
ret = x * POW(x, n - 1);
}
return ret;
}
int per(int x, int y) { // x = qy + r (0 <= r < y) を満たすq
assert(y != 0);
if (x >= 0 && y > 0) return x / y;
if (x >= 0 && y < 0) return x / y - (x % y < 0);
if (x < 0 && y < 0) return x / y + (x % y < 0);
return x / y - (x % y < 0); // (x < 0 && y > 0)
}
// int perl(ld x, ld y) { // perld(4.5, 2.1) = 2 // TODO
// if (-EPS < x && x < 0 or 0 < x && x < EPS) x = 0;
// if (-EPS < y && y < 0 or 0 < x && x < EPS) y = 0;
// assert(!equals(y, 0));
// if (x >= 0 && y > 0) return floor(x / y)+EPS;
// if (x >= 0 && y < 0) return floor(x / y) - (x - floor(x/y)*y < -EPS);
// if (x < 0 && y < 0) return floor(x / y) + (x - floor(x/y)*y < -EPS);
// return floor(x / y) - (x - floor(x/y)*y < -EPS); // (x < 0 && y > 0)
// }
int mod(int x, int y) { // x = qy + r (0 <= r < y) を満たすr
assert(y != 0);
if (x >= 0) return x % y;
__int128_t ret = x % y; // (x < 0)
ret += (__int128_t)abs(y) * INFL;
ret %= abs(y);
return ret;
}
// ld modl(ld x, ld y) { // TODO
// assert(!equals(y, 0));
// if (x >= -EPS) return (x - floor(x/y)*y);
// ld ret = x - floor(x/y)*y; // (x < 0)
// ret += abs(y) * INFL; // TODO : オーバーフローする?
// ret = x - floor(x/abs(y))*abs(y);
// return ret;
// }
// int floor(int x, int y) { // TODO
// assert(y != 0);
// if (b < 0) a = -a, b = -b;
// return a >= 0 ? a / b : (a + 1) / b - 1;
// }
// int ceil(int x, int y) { // TODO
// assert(y != 0);
// if (b < 0) a = -a, b = -b;
// return a > 0 ? (a - 1) / b + 1 : a / b;
// }
// int floorl(ld x, ld y) { return 0; } // TODO
// int ceill(ld x, ld y) { return 0; } // TODO
// int gauss(int x, int y) {
// assert(y != 0);
// return x / y;
// } // 整数部分(未verify)
// int gauss(ld x, ld y) { return 0; } // TODO
pair<int, int> max(const pair<int, int> &a, const pair<int, int> &b) {
if (a.first > b.first or a.first == b.first && a.second > b.second) {
return a;
}
return b;
}
pair<int, int> min(const pair<int, int> &a, const pair<int, int> &b) {
if (a.first < b.first or a.first == b.first && a.second < b.second) {
return a;
}
return b;
}
template <class T> bool chmax(T &a, const T& b) {
if (a < b) { a = b; return true; }
return false;
}
template <class T> bool chmin(T &a, const T& b) {
if (a > b) { a = b; return true; }
return false;
}
template <class T> T mid(T a, T b, T c) {
return a + b + c - max({a, b, c}) - min({a, b, c});
}
template <class T> void sort(T &a, T &b, T &c, bool rev = false) {
if (rev == false) {
if (a > b) swap(a, b);
if (a > c) swap(a, c);
if (b > c) swap(b, c);
} else {
if (c > b) swap(c, b);
if (c > a) swap(c, a);
if (b > a) swap(b, a);
}
}
template <class T> void sort(T &a, T &b, T &c, T &d, bool rev = false) {
if (rev == false) {
if (a > b) swap(a, b); if (a > c) swap(a, c); if (a > d) swap(a, d);
if (b > c) swap(b, c); if (b > d) swap(b, d);
if (c > d) swap(c, d);
} else {
if (d > c) swap(d, c); if (d > b) swap(d, b); if (d > a) swap(d, a);
if (c > b) swap(c, b); if (c > a) swap(c, a);
if (b > a) swap(b, a);
}
}
int countl_zero(int x) { return __builtin_clzll(x); }
int countl_one(int x) {
int ret = 0; while (x % 2) { x /= 2; ret++; }
return ret;
}
int countr_zero(int x) { return __builtin_ctzll(x); }
int countr_one(int x) {
int ret = 0, k = 63 - __builtin_clzll(x);
while (k != -1 && (x & (1LL << k))) { k--; ret++; }
return ret;
}
int popcount(int x) { return __builtin_popcountll(x); }
int unpopcount(int x) { return 64 - __builtin_clzll(x) - __builtin_popcountll(x); }
int top_bit(int x) { return 63 - __builtin_clzll(x);} // 2^kの位
int bot_bit(int x) { return __builtin_ctz(x);} // 2^kの位
int MSB(int x) { return 1 << (63 - __builtin_clzll(x)); } // mask
int LSB(int x) { return (x & -x); } // mask
int bit_width(int x) { return 64 - __builtin_clzll(x); } // 桁数
int ceil_log2(int x) { return 63 - __builtin_clzll(x); }
int bit_floor(int x) { return 1 << (63 - __builtin_clzll(x)); }
int floor_log2(int x) { return 64 - __builtin_clzll(x-1); }
int bit_ceil(int x) { return 1 << (64 - __builtin_clzll(x-1)) - (x==1); }
int hamming(int a, int b) { return popcount(a ^ b); }
int compcnt(int x) { return (popcount(x^(x >> 1)) + (x&1)) / 2; }
class UnionFind {
public:
UnionFind() = default;
UnionFind(int N) : par(N), sz(N, 1) {
iota(par.begin(), par.end(), 0);
}
int root(int x) {
if (par[x] == x) return x;
return (par[x] = root(par[x]));
}
bool unite(int x, int y) {
int rx = root(x);
int ry = root(y);
if (rx == ry) return false;
if (sz[rx] < sz[ry]) swap(rx, ry);
sz[rx] += sz[ry];
par[ry] = rx;
return true;
}
bool issame(int x, int y) { return (root(x) == root(y)); }
int size(int x) { return sz[root(x)]; }
vector<vector<int>> groups(int N) {
vector<vector<int>> G(N);
for (int x = 0; x < N; x++) {
G[root(x)].push_back(x);
}
G.erase(
remove_if(G.begin(), G.end(),
[&](const vector<int>& V) { return V.empty(); }),
G.end());
return G;
}
private:
vector<int> par;
vector<int> sz;
};
template<int mod> class Modint{
public:
int val = 0;
Modint(int x = 0) { while (x < 0) x += mod; val = x % mod; }
Modint(const Modint &r) { val = r.val; }
Modint operator -() { return Modint(-val); } // 単項
Modint operator +(const Modint &r) { return Modint(*this) += r; }
Modint operator +(const int &q) { Modint r(q); return Modint(*this) += r; }
Modint operator -(const Modint &r) { return Modint(*this) -= r; }
Modint operator -(const int &q) { Modint r(q); return Modint(*this) -= r; }
Modint operator *(const Modint &r) { return Modint(*this) *= r; }
Modint operator *(const int &q) { Modint r(q); return Modint(*this) *= r; }
Modint operator /(const Modint &r) { return Modint(*this) /= r; }
Modint operator /(const int &q) { Modint r(q); return Modint(*this) /= r; }
Modint& operator ++() { val++; if (val >= mod) val -= mod; return *this; } // 前置
Modint operator ++(signed) { ++*this; return *this; } // 後置
Modint& operator --() { val--; if (val < 0) val += mod; return *this; }
Modint operator --(signed) { --*this; return *this; }
Modint &operator +=(const Modint &r) { val += r.val; if (val >= mod) val -= mod; return *this; }
Modint &operator +=(const int &q) { Modint r(q); val += r.val; if (val >= mod) val -= mod; return *this; }
Modint &operator -=(const Modint &r) { if (val < r.val) val += mod; val -= r.val; return *this; }
Modint &operator -=(const int &q) { Modint r(q); if (val < r.val) val += mod; val -= r.val; return *this; }
Modint &operator *=(const Modint &r) { val = val * r.val % mod; return *this; }
Modint &operator *=(const int &q) { Modint r(q); val = val * r.val % mod; return *this; }
Modint &operator /=(const Modint &r) {
int a = r.val, b = mod, u = 1, v = 0;
while (b) {int t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v);}
val = val * u % mod; if (val < 0) val += mod;
return *this;
}
Modint &operator /=(const int &q) {
Modint r(q); int a = r.val, b = mod, u = 1, v = 0;
while (b) {int t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v);}
val = val * u % mod; if (val < 0) val += mod;
return *this;
}
bool operator ==(const Modint& r) { return this -> val == r.val; }
bool operator <(const Modint& r) { return this -> val < r.val; }
bool operator >(const Modint& r) { return this -> val > r.val; }
bool operator !=(const Modint& r) { return this -> val != r.val; }
};
using mint = Modint<MOD>;
// using Mint = modint998244353;
istream &operator >>(istream &is, mint& x) {
int t; is >> t;
x = t;
return (is);
}
ostream &operator <<(ostream &os, const mint& x) {
return os << x.val;
}
mint modpow(const mint &x, int n) {
assert(n >= 0); // TODO: n <= -1
if (n == 0) return 1;
mint t = modpow(x, n / 2);
t = t * t;
if (n & 1) t = t * x;
return t;
}
int modpow(__int128_t x, int n, int mod) {
assert(n >= 0 && mod > 0); // TODO: n <= -1
__int128_t ret = 1;
while (n > 0) {
if (n % 2 == 1) ret = ret * x % mod;
x = x * x % mod;
n /= 2;
}
return ret;
}
int modinv(__int128_t x, int mod) {
assert(mod > 0 && x > 0);
if (x == 1) return 1;
return mod - modinv(mod % x, mod) * (mod / x) % mod;
}
istream &operator >>(istream &is, __int128_t& x) {
string S; is >> S;
__int128_t ret = 0;
int f = 1;
if (S[0] == '-') f = -1;
for (int i = 0; i < S.length(); i++)
if ('0' <= S[i] && S[i] <= '9')
ret = ret * 10 + S[i] - '0';
x = ret * f;
return (is);
}
ostream &operator <<(ostream &os, __int128_t x) {
ostream::sentry s(os);
if (s) {
__uint128_t tmp = x < 0 ? -x : x;
char buffer[128];
char *d = end(buffer);
do {
--d;
*d = "0123456789"[tmp % 10];
tmp /= 10;
} while (tmp != 0);
if (x < 0) {
--d;
*d = '-';
}
int len = end(buffer) - d;
if (os.rdbuf()->sputn(d, len) != len) {
os.setstate(ios_base::badbit);
}
}
return os;
}
__int128_t stoll(string &S) {
__int128_t ret = 0;
int f = 1;
if (S[0] == '-') f = -1;
for (int i = 0; i < S.length(); i++)
if ('0' <= S[i] && S[i] <= '9')
ret = ret * 10 + S[i] - '0';
return ret * f;
}
__int128_t gcd(__int128_t a, __int128_t b) {
return b ? gcd(b, a % b) : a;
}
__int128_t lcm(__int128_t a, __int128_t b) {
return a / gcd(a, b) * b;
// lcmが__int128_tに収まる必要あり
}
string to_string(ld x, int k) { // xの小数第k位までをstring化する
assert(k >= 0);
stringstream ss;
ss << setprecision(k + 2) << x;
string s = ss.str();
if (s.find('.') == string::npos) s += '.';
int pos = s.find('.');
for (int i = 0; k >= (int)s.size() - 1 - pos; i++) s += '0';
s.pop_back();
if (s.back() == '.') s.pop_back();
return s;
// stringstream ss; // 第k+1位を四捨五入して第k位まで返す
// ss << setprecision(k + 1) << x;
// string s = ss.str();
// if (s.find('.') == string::npos) s += '.';
// int pos = s.find('.');
// for (int i = 0; k > (int)s.size() - 1 - pos; i++) s += '0';
// if (s.back() == '.') s.pop_back();
// return s;
}
string to_string(__int128_t x) {
string ret = "";
if (x < 0) {
ret += "-";
x *= -1;
}
while (x) {
ret += (char)('0' + x % 10);
x /= 10;
}
reverse(ret.begin(), ret.end());
return ret;
}
string to_string(char c) {
string s = "";
s += c;
return s;
}
struct SXor128 {
uint64_t x = 88172645463325252LL;
unsigned Int() {
x = x ^ (x << 7);
return x = x ^ (x >> 9);
}
unsigned Int(unsigned mod) {
x = x ^ (x << 7);
x = x ^ (x >> 9);
return x % mod;
}
unsigned Int(unsigned l, unsigned r) {
x = x ^ (x << 7);
x = x ^ (x >> 9);
return x % (r - l + 1) + l;
}
double Double() {
return double(Int()) / UINT_MAX;
}
} rnd;
struct custom_hash {
static uint64_t splitmix64(uint64_t x) {
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
template<class T> size_t HashCombine(const size_t seed,const T &v){
return seed^(hash<T>()(v)+0x9e3779b9+(seed<<6)+(seed>>2));
}
template<class T,class S> struct hash<pair<T,S>>{
size_t operator()(const pair<T,S> &keyval) const noexcept {
return HashCombine(hash<T>()(keyval.first), keyval.second);
}
};
template<class T> struct hash<vector<T>>{
size_t operator()(const vector<T> &keyval) const noexcept {
size_t s=0;
for (auto&& v: keyval) s=HashCombine(s,v);
return s;
}
};
template<int N> struct HashTupleCore{
template<class Tuple> size_t operator()(const Tuple &keyval) const noexcept{
size_t s=HashTupleCore<N-1>()(keyval);
return HashCombine(s,get<N-1>(keyval));
}
};
template <> struct HashTupleCore<0>{
template<class Tuple> size_t operator()(const Tuple &keyval) const noexcept{ return 0; }
};
template<class... Args> struct hash<tuple<Args...>>{
size_t operator()(const tuple<Args...> &keyval) const noexcept {
return HashTupleCore<tuple_size<tuple<Args...>>::value>()(keyval);
}
};
vector<mint> _fac, _finv, _inv;
void COMinit(int N) {
_fac.resize(N + 1);
_finv.resize(N + 1);
_inv.resize(N + 1);
_fac[0] = _fac[1] = 1;
_finv[0] = _finv[1] = 1;
_inv[1] = 1;
for (int i = 2; i <= N; i++) {
_fac[i] = _fac[i-1] * mint(i);
_inv[i] = -_inv[MOD % i] * mint(MOD / i);
_finv[i] = _finv[i - 1] * _inv[i];
}
}
mint FAC(int N) {
if (N < 0) return 0;
return _fac[N];
}
mint COM(int N, int K) {
if (N < K) return 0;
if (N < 0 or K < 0) return 0;
return _fac[N] * _finv[K] * _finv[N - K];
}
mint PERM(int N, int K) {
if (N < K) return 0;
if (N < 0 or K < 0) return 0;
return _fac[N] * _finv[N - K];
}
mint NHK(int N, int K) {
if (N == 0 && K == 0) return 1;
return COM(N + K - 1, K);
}
#pragma endregion
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;
vector<uint64_t> L; // 大ブロック
vector<uint16_t> S; // 小ブロック
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 = 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() {
cout << "LEVEL_L(" << L.size() << ")" << endl;
for (uint64_t i = 0 ; i < L.size(); ++i) {
cout << L.at(i) << ", ";
}
cout << endl;
cout << "LEVEL_S(" << S.size() << ")" << endl;
for (uint64_t i = 0 ; i < S.size(); ++i) {
cout << S.at(i) << ", ";
}
cout << 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:
vector<SuccinctBitVector> bit_arrays;
vector<uint64_t> begin_one; // 各bitに着目したときの1の開始位置
unordered_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
vector<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 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, 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];
}
vector<uint64_t> v(array);
for (uint64_t i = 0; i < bit_size; ++i) {
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 get<1>(maxi_t) - 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 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 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
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 make_tuple(0, 0, 0);
}
if (c >= maximum_element || end == 0) {
return 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 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
vector<pair<uint64_t, uint64_t>> topk(uint64_t s, uint64_t e, uint64_t k) {
assert(s < e);
vector<pair<uint64_t, uint64_t>> result;
// (頻度，深さ，値)の順でソート
auto c = [](const tuple<uint64_t, uint64_t, uint64_t, uint64_t, uint64_t> &l, const tuple<uint64_t, uint64_t, uint64_t, uint64_t, uint64_t> &r) {
// width
if (get<0>(l) != get<0>(r)) {
return get<0>(l) < get<0>(r);
}
// depth
if (get<3>(l) != get<3>(r)) {
return get<3>(l) > get<3>(r);
}
// value
if (get<4>(l) != get<4>(r)) {
return get<4>(l) > get<4>(r);
}
return true;
};
std::priority_queue<tuple<uint64_t, uint64_t, uint64_t, uint64_t, uint64_t>, vector<tuple<uint64_t, uint64_t, uint64_t, uint64_t, uint64_t>>, decltype(c)> que(c); // width, left, right, depth, value
que.push(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;
tie(width, left, right, depth, value) = element;
if (depth >= this->bit_size) {
result.emplace_back(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(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(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 prev_value(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
stack<tuple<uint64_t, uint64_t, uint64_t, uint64_t, bool>> s; // (begin, end, depth, c, tight)
s.emplace(make_tuple(begin_pos, end_pos, 0, 0, true));
while (not s.empty()) {
uint64_t b, e, depth, c;
bool tight;
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(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(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 next_value(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;
}
stack<tuple<uint64_t, uint64_t, uint64_t, uint64_t, bool>> s; // (begin, end, depth, c, tight)
s.emplace(make_tuple(begin_pos, end_pos, 0, 0, true));
while (not s.empty()) {
uint64_t b, e, depth, c;
bool tight;
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(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(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
vector<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);
vector<tuple<uint64_t, uint64_t, uint64_t>> intersection;
queue<tuple<uint64_t, uint64_t, uint64_t, uint64_t, uint64_t, uint64_t>> que; // s1, e1, s2, e2, depth, value
que.push(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;
tie(s1, e1, s2, e2, depth, value) = e;
if (depth >= this->bit_size) {
intersection.emplace_back(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(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(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);
}
};
uint64_t uabs(uint64_t a, uint64_t b) {
return max(a, b) - min(a, b);
}
signed main() {
int N, K;
cin >> N >> K;
vector<uint64_t> A(N);
// uint64_t e10 = 3e9+EPS;
for (int i = 0; i < N; i++) {
cin >> A[i];
// A[i] = e10 + A[i];
}
WaveletMatrix WM(A); // 長さNの数列による初期化を行う
// uint64_t inf = e10 + 1e9+1;
// uint64_t zero = e10 - 1e9 - 1;
uint64_t e9 = 1e9+EPS;
uint64_t ans = INFL;
for (int i = 0; i + K <= N; i++) {
uint64_t l = i, r = i + K - 1;
uint64_t m1 = WM.quantileRange(l, r + 1, (r - l) / 2); // index
uint64_t vm1 = WM.access(m1); // value
uint64_t large1 = WM.rangeFreq(l, r + 1, vm1, e9); // value
uint64_t small1 = WM.rangeFreq(l, r + 1, 0, vm1); // value
uint64_t sumr = WM.rangeSum(l, r + 1, vm1, e9); // value
uint64_t suml = WM.rangeSum(l, r + 1, 0, vm1); // value
// cout << m1 << " " << vm1 << endl;
// cout << ma1 << " " << vma1 << " " << large1 << endl;
// cout << mi1 << " " << vmi1 << " " << small1 << endl;
// cout << suml << " " << sumr << endl;
uint64_t s1 = uabs(sumr , vm1 * large1) +
uabs(suml , vm1 * small1);
ans = min(ans, s1);
uint64_t m2 = WM.quantileRange(l, r + 1, (r - l + 1) / 2); // index
if (m2 != NOTFOUND) {
uint64_t vm2 = WM.access(m2); // value
uint64_t large2 = WM.rangeFreq(l, r + 1, vm2, e9); // value
uint64_t small2 = WM.rangeFreq(l, r + 1, 0, vm2 + 1); // value
uint64_t sumr2 = WM.rangeSum(l, r + 1, vm2, e9); // value
uint64_t suml2 = WM.rangeSum(l, r + 1, 0, vm2 + 1); // value
// cout << m2 << " " << vm2 << endl;
// cout << ma2 << " " << vma2 << " " << large2 << endl;
// cout << mi2 << " " << vmi2 << " " << small2 << endl;
// cout << suml2 << " " << sumr2 << endl;
uint64_t s2 = uabs(sumr2 , vm2 * large2) +
uabs(suml2 , vm2 * small2);
ans = min(ans, s2);
}
}
cout << ans << endl;
}