結果

問題 No.1300 Sum of Inversions
ユーザー masayoshi361
提出日時 2020-11-27 21:58:04
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,729 ms / 2,000 ms
コード長 20,372 bytes
コンパイル時間 2,924 ms
コンパイル使用メモリ 208,676 KB
実行使用メモリ 31,120 KB
最終ジャッジ日時 2024-07-26 12:34:47
合計ジャッジ時間 42,859 ms
ジャッジサーバーID
(参考情報)
judge2 / judge4
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 34
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

/* #region header */
#ifdef LOCAL
#include "cxx-prettyprint-master/prettyprint.hpp"
#define debug(x) cout << x << endl
#else
#define debug(...) 42
#endif
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
// types
using ll = long long;
using ull = unsigned long long;
using ld = long double;
typedef pair<ll, ll> Pl;
typedef pair<int, int> Pi;
typedef vector<ll> vl;
typedef vector<int> vi;
typedef vector<char> vc;
template <typename T>
using mat = vector<vector<T>>;
typedef vector<vector<int>> vvi;
typedef vector<vector<long long>> vvl;
typedef vector<vector<char>> vvc;
template <int mod>
struct modint {
int x;
modint() : x(0) {}
modint(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
modint& operator+=(const modint& p) {
if ((x += p.x) >= mod) x -= mod;
return *this;
}
modint& operator-=(const modint& p) {
if ((x += mod - p.x) >= mod) x -= mod;
return *this;
}
modint& operator*=(const modint& p) {
x = (int)(1LL * x * p.x % mod);
return *this;
}
modint& operator/=(const modint& p) {
*this *= p.inverse();
return *this;
}
modint operator-() const { return modint(-x); }
modint operator+(const modint& p) const { return modint(*this) += p; }
modint operator-(const modint& p) const { return modint(*this) -= p; }
modint operator*(const modint& p) const { return modint(*this) *= p; }
modint operator/(const modint& p) const { return modint(*this) /= p; }
bool operator==(const modint& p) const { return x == p.x; }
bool operator!=(const modint& p) const { return x != p.x; }
modint inverse() const {
int a = x, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b);
swap(u -= t * v, v);
}
return modint(u);
}
modint pow(int64_t n) const {
modint ret(1), mul(x);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
friend ostream& operator<<(ostream& os, const modint& p) {
return os << p.x;
}
friend istream& operator>>(istream& is, modint& a) {
int64_t t;
is >> t;
a = modint<mod>(t);
return (is);
}
static int get_mod() { return mod; }
};
// abreviations
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define rep_(i, a_, b_, a, b, ...) for (ll i = (a), max_i = (b); i < max_i; i++)
#define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define rrep_(i, a_, b_, a, b, ...) \
for (ll i = (b - 1), min_i = (a); i >= min_i; i--)
#define rrep(i, ...) rrep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define srep(i, a, b, c) for (ll i = (a), max_i = (b); i < max_i; i += c)
#define SZ(x) ((int)(x).size())
#define pb(x) push_back(x)
#define eb(x) emplace_back(x)
#define mp make_pair
//
#define print(x) cout << x << endl
template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
for (auto& e : v) cout << e << " ";
cout << endl;
return os;
}
void scan(int& a) { cin >> a; }
void scan(long long& a) { cin >> a; }
void scan(char& a) { cin >> a; }
void scan(double& a) { cin >> a; }
void scan(string& a) { cin >> a; }
template <class T>
void scan(vector<T>& a) {
for (auto& i : a) scan(i);
}
#define vsum(x) accumulate(all(x), 0LL)
#define vmax(a) *max_element(all(a))
#define vmin(a) *min_element(all(a))
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
// functions
// gcd(0, x) fails.
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
template <class T>
bool chmax(T& a, const T& b) {
if (a < b) {
a = b;
return 1;
}
return 0;
}
template <class T>
bool chmin(T& a, const T& b) {
if (b < a) {
a = b;
return 1;
}
return 0;
}
template <typename T>
T mypow(T x, ll n) {
T ret = 1;
while (n > 0) {
if (n & 1) (ret *= x);
(x *= x);
n >>= 1;
}
return ret;
}
ll modpow(ll x, ll n, const ll mod) {
ll ret = 1;
while (n > 0) {
if (n & 1) (ret *= x);
(x *= x);
n >>= 1;
x %= mod;
ret %= mod;
}
return ret;
}
uint64_t my_rand(void) {
static uint64_t x = 88172645463325252ULL;
x = x ^ (x << 13);
x = x ^ (x >> 7);
return x = x ^ (x << 17);
}
int popcnt(ull x) { return __builtin_popcountll(x); }
// graph template
template <typename T>
struct edge {
int src, to;
T cost;
edge(int to, T cost) : src(-1), to(to), cost(cost) {}
edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}
edge& operator=(const int& x) {
to = x;
return *this;
}
bool operator<(const edge<T>& r) const { return cost < r.cost; }
operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
using UnWeightedGraph = vector<vector<int>>;
struct Timer {
clock_t start_time;
void start() { start_time = clock(); }
int lap() {
// return x ms.
return (clock() - start_time) * 1000 / CLOCKS_PER_SEC;
}
};
/* #endregion*/
// constant
#define inf 1000000000ll
#define INF 4000000004000000000LL
#define mod 998244353ll
using mint = modint<mod>;
typedef vector<mint> vmint;
typedef vector<vector<mint>> vvmint;
#define endl '\n'
const long double eps = 0.000000000000001;
const long double PI = 3.141592653589793;
// O(√m)
// a^x = b (mod m)x-1
// x = p√m+r, p, r < √m
// a^r = bA^p
ll modlog(ll a, ll b, ll m) {
//√m
ll sqrt_m = sqrt(m) + 2;
// a^-√m
ll A = modpow(a, (mod - 2), mod);
A = modpow(A, sqrt_m, mod);
// a^0,...,a^√m
unordered_map<ll, ll> a_pows;
ll a_pow = 1;
rep(i, sqrt_m + 1) {
a_pows[a_pow] = i;
a_pow *= a;
a_pow %= m;
}
// A^0,...,A^√m
ll A_pow = 1;
rep(i, sqrt_m + 1) {
if (a_pows.count(A_pow * b)) {
return i * sqrt_m + a_pows[A_pow * b];
}
A_pow *= A;
A_pow %= m;
}
return -1;
}
int64_t euler_phi(int64_t n) {
int64_t ret = n;
for (int64_t i = 2; i * i <= n; i++) {
if (n % i == 0) {
ret -= ret / i;
while (n % i == 0) n /= i;
}
}
if (n > 1) ret -= ret / n;
return ret;
}
template <typename T>
struct BIT {
vector<T> data;
BIT(int sz) { data.assign(++sz, 0); }
//[0, k)
T sum(int k) {
T ret = 0;
for (; k > 0; k -= k & -k) ret += data[k];
return (ret);
}
T sum(int l, int r) { return sum(r) - sum(l); }
void add(int k, T x) {
for (++k; k < data.size(); k += k & -k) data[k] += x;
}
// 0-indexedk
int search(long long k) {
++k;
int res = 0;
int N = 1;
while (N < (int)data.size()) N *= 2;
for (int i = N / 2; i > 0; i /= 2) {
if (res + i < (int)data.size() && data[res + i] < k) {
k = k - data[res + i];
res = res + i;
}
}
return res;
}
// for debug
void show() {
rep(i, SZ(data) - 1) cout << sum(i + 1) - sum(i) << ' ';
cout << endl;
}
};
ll inversion_number(vi& x, int n) {
BIT<int> bit(n);
ll res = 0;
for (int& y : x) {
res += bit.sum(n - 1 - y);
bit.add(n - 1 - y, 1);
}
return res;
}
template <typename T>
struct Compress {
vector<T> xs;
Compress() = default;
Compress(const vector<T>& vs) { add(vs); }
Compress(const initializer_list<vector<T>>& vs) {
for (auto& p : vs) add(p);
}
void add(const vector<T>& vs) {
copy(begin(vs), end(vs), back_inserter(xs));
}
void add(const T& x) { xs.emplace_back(x); }
void build() {
sort(begin(xs), end(xs));
xs.erase(unique(begin(xs), end(xs)), end(xs));
}
vector<int> get(const vector<T>& vs) const {
vector<int> ret;
transform(begin(vs), end(vs), back_inserter(ret), [&](const T& x) {
return lower_bound(begin(xs), end(xs), x) - begin(xs);
});
return ret;
}
int get(const T& x) const {
return lower_bound(begin(xs), end(xs), x) - begin(xs);
}
const T& operator[](int k) const { return xs[k]; }
};
struct SuccinctIndexableDictionary {
size_t length;
size_t blocks;
vector<unsigned> bit, sum;
SuccinctIndexableDictionary() = default;
SuccinctIndexableDictionary(size_t length)
: length(length), blocks((length + 31) >> 5) {
bit.assign(blocks, 0U);
sum.assign(blocks, 0U);
}
void set(int k) { bit[k >> 5] |= 1U << (k & 31); }
void build() {
sum[0] = 0U;
for (int i = 1; i < blocks; i++) {
sum[i] = sum[i - 1] + __builtin_popcount(bit[i - 1]);
}
}
bool operator[](int k) { return (bool((bit[k >> 5] >> (k & 31)) & 1)); }
int rank(int k) {
return (sum[k >> 5] +
__builtin_popcount(bit[k >> 5] & ((1U << (k & 31)) - 1)));
}
int rank(bool val, int k) { return (val ? rank(k) : k - rank(k)); }
};
template <typename T, int MAXLOG>
struct WaveletMatrix {
size_t length;
SuccinctIndexableDictionary matrix[MAXLOG];
int mid[MAXLOG];
WaveletMatrix() = default;
WaveletMatrix(vector<T> v) : length(v.size()) {
vector<T> l(length), r(length);
for (int level = MAXLOG - 1; level >= 0; level--) {
matrix[level] = SuccinctIndexableDictionary(length + 1);
int left = 0, right = 0;
for (int i = 0; i < length; i++) {
if (((v[i] >> level) & 1)) {
matrix[level].set(i);
r[right++] = v[i];
} else {
l[left++] = v[i];
}
}
mid[level] = left;
matrix[level].build();
v.swap(l);
for (int i = 0; i < right; i++) {
v[left + i] = r[i];
}
}
}
pair<int, int> succ(bool f, int l, int r, int level) {
return {matrix[level].rank(f, l) + mid[level] * f,
matrix[level].rank(f, r) + mid[level] * f};
}
// v[k]
T access(int k) {
T ret = 0;
for (int level = MAXLOG - 1; level >= 0; level--) {
bool f = matrix[level][k];
if (f) ret |= T(1) << level;
k = matrix[level].rank(f, k) + mid[level] * f;
}
return ret;
}
T operator[](const int& k) { return access(k); }
// count i s.t. (0 <= i < r) && v[i] == x
int rank(const T& x, int r) {
int l = 0;
for (int level = MAXLOG - 1; level >= 0; level--) {
tie(l, r) = succ((x >> level) & 1, l, r, level);
}
return r - l;
}
// k-th(0-indexed) smallest number in v[l,r)
T kth_smallest(int l, int r, int k) {
assert(0 <= k && k < r - l);
T ret = 0;
for (int level = MAXLOG - 1; level >= 0; level--) {
int cnt =
matrix[level].rank(false, r) - matrix[level].rank(false, l);
bool f = cnt <= k;
if (f) {
ret |= T(1) << level;
k -= cnt;
}
tie(l, r) = succ(f, l, r, level);
}
return ret;
}
// k-th(0-indexed) largest number in v[l,r)
T kth_largest(int l, int r, int k) {
return kth_smallest(l, r, r - l - k - 1);
}
// count i s.t. (l <= i < r) && (v[i] < upper)
int range_freq(int l, int r, T upper) {
int ret = 0;
for (int level = MAXLOG - 1; level >= 0; level--) {
bool f = ((upper >> level) & 1);
if (f)
ret +=
matrix[level].rank(false, r) - matrix[level].rank(false, l);
tie(l, r) = succ(f, l, r, level);
}
return ret;
}
// count i s.t. (l <= i < r) && (lower <= v[i] < upper)
int range_freq(int l, int r, T lower, T upper) {
return range_freq(l, r, upper) - range_freq(l, r, lower);
}
// max v[i] s.t. (l <= i < r) && (v[i] < upper)
T prev_value(int l, int r, T upper) {
int cnt = range_freq(l, r, upper);
return cnt == 0 ? T(-1) : kth_smallest(l, r, cnt - 1);
}
// min v[i] s.t. (l <= i < r) && (lower <= v[i])
T next_value(int l, int r, T lower) {
int cnt = range_freq(l, r, lower);
return cnt == r - l ? T(-1) : kth_smallest(l, r, cnt);
}
};
/**
* @brief Lazy-Segment-Tree()
* @docs docs/lazy-segment-tree.md
*/
template <typename Monoid, typename OperatorMonoid>
struct LazySegmentTree {
int n, sz, height;
vector<Monoid> data;
vector<OperatorMonoid> lazy;
using F = function<Monoid(Monoid, Monoid)>;
using G = function<Monoid(Monoid, OperatorMonoid)>;
using H = function<OperatorMonoid(OperatorMonoid, OperatorMonoid)>;
const F f;
const G g;
const H h;
const Monoid M1;
const OperatorMonoid OM0;
LazySegmentTree(int n, const F f, const G g, const H h, const Monoid& M1,
const OperatorMonoid OM0)
: n(n), f(f), g(g), h(h), M1(M1), OM0(OM0) {
sz = 1;
height = 0;
while (sz < n) sz <<= 1, height++;
data.assign(2 * sz, M1);
lazy.assign(2 * sz, OM0);
}
void set(int k, const Monoid& x) { data[k + sz] = x; }
void build() {
for (int k = sz - 1; k > 0; k--) {
data[k] = f(data[2 * k + 0], data[2 * k + 1]);
}
}
inline void propagate(int k) {
if (lazy[k] != OM0) {
lazy[2 * k + 0] = h(lazy[2 * k + 0], lazy[k]);
lazy[2 * k + 1] = h(lazy[2 * k + 1], lazy[k]);
data[k] = apply(k);
lazy[k] = OM0;
}
}
inline Monoid apply(int k) {
return lazy[k] == OM0 ? data[k] : g(data[k], lazy[k]);
}
inline void recalc(int k) {
while (k >>= 1) data[k] = f(apply(2 * k + 0), apply(2 * k + 1));
}
inline void thrust(int k) {
for (int i = height; i > 0; i--) propagate(k >> i);
}
void update(int a, int b, const OperatorMonoid& x) {
if (a >= b) return;
thrust(a += sz);
thrust(b += sz - 1);
for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
if (l & 1) lazy[l] = h(lazy[l], x), ++l;
if (r & 1) --r, lazy[r] = h(lazy[r], x);
}
recalc(a);
recalc(b);
}
Monoid query(int a, int b) {
if (a >= b) return M1;
thrust(a += sz);
thrust(b += sz - 1);
Monoid L = M1, R = M1;
for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
if (l & 1) L = f(L, apply(l++));
if (r & 1) R = f(apply(--r), R);
}
return f(L, R);
}
Monoid operator[](const int& k) { return query(k, k + 1); }
template <typename C>
int find_subtree(int a, const C& check, Monoid& M, bool type) {
while (a < sz) {
propagate(a);
Monoid nxt =
type ? f(apply(2 * a + type), M) : f(M, apply(2 * a + type));
if (check(nxt))
a = 2 * a + type;
else
M = nxt, a = 2 * a + 1 - type;
}
return a - sz;
}
template <typename C>
int find_first(int a, const C& check) {
Monoid L = M1;
if (a <= 0) {
if (check(f(L, apply(1)))) return find_subtree(1, check, L, false);
return -1;
}
thrust(a + sz);
int b = sz;
for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
if (a & 1) {
Monoid nxt = f(L, apply(a));
if (check(nxt)) return find_subtree(a, check, L, false);
L = nxt;
++a;
}
}
return -1;
}
template <typename C>
int find_last(int b, const C& check) {
Monoid R = M1;
if (b >= sz) {
if (check(f(apply(1), R))) return find_subtree(1, check, R, true);
return -1;
}
thrust(b + sz - 1);
int a = sz;
for (b += sz; a < b; a >>= 1, b >>= 1) {
if (b & 1) {
Monoid nxt = f(apply(--b), R);
if (check(nxt)) return find_subtree(b, check, R, true);
R = nxt;
}
}
return -1;
}
void show() {
rep(i, n) cout << query(i, i + 1) << ' ';
cout << endl;
}
};
template <class T, class F = T>
T myreplace(T x, F y) {
if (y != numeric_limits<F>::max()) x = y;
return x;
}
template <class T>
T mymax(T x, T y) {
return max(x, y);
}
template <class T>
T mymin(T x, T y) {
return min(x, y);
}
template <class T, class F = T>
T myadd(T x, F y) {
return x + y;
}
template <class T>
struct segobj {
T val;
int size;
segobj(T x, int y) : val(x), size(y) {}
segobj() : val(0), size(0) {}
segobj& operator+=(const segobj& p) {
val += p.val;
size += p.size;
return *this;
}
segobj& operator+=(const T& p) {
val += p * size;
return *this;
}
segobj& operator=(const T& p) {
val = p * size;
return *this;
}
friend ostream& operator<<(ostream& os, const segobj& p) {
return os << p.val;
}
segobj operator+(const segobj& p) const { return segobj(*this) += p; }
segobj operator+(const T& p) const { return segobj(*this) += p; }
};
template <class T>
struct RMRRQ : LazySegmentTree<T, T> {
using Seg = LazySegmentTree<T, T>;
RMRRQ(int n)
: Seg(n, mymax<T>, myreplace<T>, myreplace<T>, numeric_limits<T>::min(),
numeric_limits<T>::max()) {}
};
template <class T>
struct RmRRQ : LazySegmentTree<T, T> {
using Seg = LazySegmentTree<T, T>;
RmRRQ(int n)
: Seg(n, mymin<T>, myreplace<T>, myreplace<T>, numeric_limits<T>::max(),
numeric_limits<T>::max()) {}
};
template <class T>
struct RMRAQ : LazySegmentTree<T, T> {
using Seg = LazySegmentTree<T, T>;
RMRAQ(int n)
: Seg(n, mymax<T>, plus<T>(), plus<T>(), numeric_limits<T>::min() / 2,
T()) {}
};
template <class T>
struct RmRAQ : LazySegmentTree<T, T> {
using Seg = LazySegmentTree<T, T>;
RmRAQ(int n)
: Seg(n, mymin<T>, plus<T>(), plus<T>(), numeric_limits<T>::max() / 2,
T()) {}
};
template <class T>
struct RSRAQ : LazySegmentTree<segobj<T>, T> {
using Seg = LazySegmentTree<segobj<T>, T>;
RSRAQ(int n)
: Seg(n, plus<segobj<T>>(), myadd<segobj<T>, T>, plus<T>(), segobj<T>(),
T()) {
rep(i, n) this->set(i, segobj<T>(0, 1));
this->build();
}
T sum(int l, int r) { return this->query(l, r).val; }
};
template <class T>
struct RSRRQ : LazySegmentTree<segobj<T>, T> {
using Seg = LazySegmentTree<segobj<T>, T>;
using obj = segobj<T>;
RSRRQ(int n)
: Seg(n, plus<obj>(), myreplace<obj, T>, myreplace<T>, segobj<T>(),
numeric_limits<T>::max()) {
rep(i, n) this->set(i, segobj<T>(0, 1));
this->build();
}
T sum(int l, int r) { return this->query(l, r).val; }
};
int main() {
cin.tie(0);
ios::sync_with_stdio(0);
cout << setprecision(30) << fixed;
int n;
cin >> n;
vl a(n);
scan(a);
mint ans = 0;
Compress<ll> cp(a);
cp.build();
RSRAQ<mint> segl(n), segr(n), cntl(n), cntr(n);
rep(i, n) {
int j = cp.get(a[i]);
segr.update(j + 1, n, a[i]);
cntr.update(j + 1, n, 1);
}
rep(i, n) {
int j = cp.get(a[i]);
cntr.update(j + 1, n, -1);
segr.update(j + 1, n, -a[i]);
ans += cntl.sum(j, j + 1) * cntr.sum(j, j + 1) * a[i];
ans += segl.sum(j, j + 1) * cntr.sum(j, j + 1) +
segr.sum(j, j + 1) * cntl.sum(j, j + 1);
cntl.update(0, j, 1);
segl.update(0, j, a[i]);
// cntr.show();
}
print(ans);
}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0