結果

問題 No.1300 Sum of Inversions
ユーザー saxofone111
提出日時 2021-03-12 20:50:18
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 722 ms / 2,000 ms
コード長 9,706 bytes
コンパイル時間 2,348 ms
コンパイル使用メモリ 207,060 KB
最終ジャッジ日時 2025-01-19 13:56:18
ジャッジサーバーID
(参考情報)
judge5 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 34
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ソースコード

diff #
プレゼンテーションモードにする

#include "bits/stdc++.h"
#define MOD 998244353
#define rep(i, n) for(ll i=0; i < (n); i++)
#define rrep(i, n) for(ll i=(n)-1; i >=0; i--)
#define ALL(v) v.begin(),v.end()
#define rALL(v) v.rbegin(),v.rend()
#define FOR(i, j, k) for(ll i=j;i<k;i++)
#define debug_print(var) cerr << #var << "=" << var <<endl;
#define DUMP(i, v)for(ll i=0;i<v.size();i++)cerr<<v[i]<<" "
#define fi first
#define se second
using namespace std;
typedef long long int ll;
typedef vector<ll> llvec;
typedef vector<double> dvec;
typedef pair<ll, ll> P;
typedef long double ld;
struct edge{ll x, c;};
ll mod(ll a, ll mod){
ll res = a%mod;
if(res<0)res=res + mod;
return res;
}
ll modpow(ll a, ll n, ll mod){
ll res=1;
while(n>0){
if(n&1) res=res*a%mod;
a=a*a%mod;
n>>=1;
}
return res;
}
ll modinv(ll a, ll mod){
ll b=mod, u=1, v=0;
while(b){
ll t=a/b;
a-=t*b; swap(a, b);
u-=t*v; swap(u, v);
}
u%=mod;
if(u<0)u+=mod;
return u;
}
ll gcd(ll a, ll b){
ll r = a%b;
if(r==0) return b;
else return gcd(b, a%b);
}
// @param b 1
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = mod(a, b);
if (a == 0) return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// (rem, mod)
std::pair<long long, long long> crt(const std::vector<long long>& r,
const std::vector<long long>& m) {
assert(r.size() == m.size());
int n = int(r.size());
// Contracts: 0 <= r0 < m0
long long r0 = 0, m0 = 1;
for (int i = 0; i < n; i++) {
assert(1 <= m[i]);
long long r1 = mod(r[i], m[i]), m1 = m[i];
if (m0 < m1) {
std::swap(r0, r1);
std::swap(m0, m1);
}
if (m0 % m1 == 0) {
if (r0 % m1 != r1) return {0, 0};
continue;
}
// assume: m0 > m1, lcm(m0, m1) >= 2 * max(m0, m1)
// (r0, m0), (r1, m1) -> (r2, m2 = lcm(m0, m1));
// r2 % m0 = r0
// r2 % m1 = r1
// -> (r0 + x*m0) % m1 = r1
// -> x*u0*g % (u1*g) = (r1 - r0) (u0*g = m0, u1*g = m1)
// -> x = (r1 - r0) / g * inv(u0) (mod u1)
// im = inv(u0) (mod u1) (0 <= im < u1)
long long g, im;
std::tie(g, im) = inv_gcd(m0, m1);
long long u1 = (m1 / g);
// |r1 - r0| < (m0 + m1) <= lcm(m0, m1)
if ((r1 - r0) % g) return {0, 0};
// u1 * u1 <= m1 * m1 / g / g <= m0 * m1 / g = lcm(m0, m1)
long long x = (r1 - r0) / g % u1 * im % u1;
// |r0| + |m0 * x|
// < m0 + m0 * (u1 - 1)
// = m0 + m0 * m1 / g - m0
// = lcm(m0, m1)
r0 += x * m0;
m0 *= u1; // -> lcm(m0, m1)
if (r0 < 0) r0 += m0;
}
return {r0, m0};
}
bool is_prime(ll n){
ll i = 2;
if(n==1)return false;
if(n==2)return true;
bool res = true;
while(i*i <n){
if(n%i==0){
res = false;
}
i = i+1;
}
//if(i==1)res = false;
if(n%i==0)res=false;
return res;
}
template <class S,
S (*op)(S, S),
S (*e)(),
class F,
S (*mapping)(F, S),
F (*composition)(F, F),
F (*id)()>
struct lazy_segtree {
public:
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
lazy_segtree() : lazy_segtree(0) {}
lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}
lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) {
log = ceil_pow2(_n);
size = 1 << log;
d = std::vector<S>(2 * size, e());
lz = std::vector<F>(size, id());
for (int i = 0; i < _n; i++) d[size + i] = v[i];
for (int i = size - 1; i >= 1; i--) {
update(i);
}
}
void set(int p, S x) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
d[p] = x;
for (int i = 1; i <= log; i++) update(p >> i);
}
S get(int p) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
return d[p];
}
S prod(int l, int r) {
assert(0 <= l && l <= r && r <= _n);
if (l == r) return e();
l += size;
r += size;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push(r >> i);
}
S sml = e(), smr = e();
while (l < r) {
if (l & 1) sml = op(sml, d[l++]);
if (r & 1) smr = op(d[--r], smr);
l >>= 1;
r >>= 1;
}
return op(sml, smr);
}
S all_prod() { return d[1]; }
void apply(int p, F f) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
d[p] = mapping(f, d[p]);
for (int i = 1; i <= log; i++) update(p >> i);
}
void apply(int l, int r, F f) {
assert(0 <= l && l <= r && r <= _n);
if (l == r) return;
l += size;
r += size;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
{
int l2 = l, r2 = r;
while (l < r) {
if (l & 1) all_apply(l++, f);
if (r & 1) all_apply(--r, f);
l >>= 1;
r >>= 1;
}
l = l2;
r = r2;
}
for (int i = 1; i <= log; i++) {
if (((l >> i) << i) != l) update(l >> i);
if (((r >> i) << i) != r) update((r - 1) >> i);
}
}
template <bool (*g)(S)> int max_right(int l) {
return max_right(l, [](S x) { return g(x); });
}
template <class G> int max_right(int l, G g) {
assert(0 <= l && l <= _n);
assert(g(e()));
if (l == _n) return _n;
l += size;
for (int i = log; i >= 1; i--) push(l >> i);
S sm = e();
do {
while (l % 2 == 0) l >>= 1;
if (!g(op(sm, d[l]))) {
while (l < size) {
push(l);
l = (2 * l);
if (g(op(sm, d[l]))) {
sm = op(sm, d[l]);
l++;
}
}
return l - size;
}
sm = op(sm, d[l]);
l++;
} while ((l & -l) != l);
return _n;
}
template <bool (*g)(S)> int min_left(int r) {
return min_left(r, [](S x) { return g(x); });
}
template <class G> int min_left(int r, G g) {
assert(0 <= r && r <= _n);
assert(g(e()));
if (r == 0) return 0;
r += size;
for (int i = log; i >= 1; i--) push((r - 1) >> i);
S sm = e();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!g(op(d[r], sm))) {
while (r < size) {
push(r);
r = (2 * r + 1);
if (g(op(d[r], sm))) {
sm = op(d[r], sm);
r--;
}
}
return r + 1 - size;
}
sm = op(d[r], sm);
} while ((r & -r) != r);
return 0;
}
private:
int _n, size, log;
std::vector<S> d;
std::vector<F> lz;
void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
void all_apply(int k, F f) {
d[k] = mapping(f, d[k]);
if (k < size) lz[k] = composition(f, lz[k]);
}
void push(int k) {
all_apply(2 * k, lz[k]);
all_apply(2 * k + 1, lz[k]);
lz[k] = id();
}
};
struct S{
ll x, d;
};
using F = ll;
S op(S a, S b){
return {mod(a.x+b.x, MOD), a.d + b.d};
}
S mapping(F a, S b){
return {mod(b.x + b.d*a, MOD), b.d};
}
F composition(F b, F a){
return mod(a+b, MOD);
}
S e(){
return S{0, 0};
}
F id(){
return 0;
}
//usage lazy_segtree<S, op, e, F, mapping, composition, id>
struct segment_tree{
ll N;
llvec v;
ll init=0;//initial value
ll f(ll a, ll b){ //function
return mod(a+b, MOD);
}
segment_tree(ll n){
N=1;
while(N<n){
N*=2;
}
v = llvec(2*N-1, init);
}
void set(ll i, ll val){
i += N-1;
v[i] = val;
while(i>0){
i = (i-1)/2;
v[i] = f(v[i*2+1], v[i*2+2]);
}
}
void add(ll i, ll val){
i += N-1;
v[i] += val;
while(i>0){
i = (i-1)/2;
v[i] = f(v[i*2+1], v[i*2+2]);
}
}
ll get(ll L, ll R){// L <= i < R
L += N-1;
R += N-1;
ll vl = init;
ll vr = init;
while(L<R){
if(L%2==0){
vl = f(vl, v[L]);
L++;
}
if(R%2==0){
vr = f(vr, v[R-1]);
R--;
}
R=(R-1)/2;
L=(L-1)/2;
}
return f(vl, vr);
}
ll operator[](ll i){
return v[i+N-1];
}
};
/**************************************
** A main function starts from here **
***************************************/
int main(){
ll N;
cin >> N;
llvec A(N);
llvec v;
rep(i, N){
cin >> A[i];
v.push_back(A[i]);
}
sort(ALL(v));
v.erase(unique(ALL(v)), v.end());
ll M = v.size();
segment_tree sg(M);
segment_tree sg2(M);
segment_tree sg3(M);
segment_tree sg4(M);
rep(i, N){
ll ind = lower_bound(ALL(v), A[i]) - v.begin();
sg2.add(ind, 1);
sg4.add(ind, A[i]);
}
ll ans = 0;
rep(i, N){
ll ind = lower_bound(ALL(v), A[i]) - v.begin();
ll L = sg2.get(0, ind);
ll R = sg.get(ind+1, M);
ans = mod(ans + mod(L * sg3.get(ind+1, M), MOD), MOD);
ans = mod(ans + mod(R * sg4.get(0, ind), MOD), MOD);
ans = mod(ans + mod(mod(R * L, MOD)*A[i], MOD), MOD);
sg.add(ind, 1);
sg3.add(ind, A[i]);
sg2.add(ind, -1);
sg4.add(ind, -A[i]);
}
cout << ans << endl;
return 0;
}
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