結果
問題 | No.1300 Sum of Inversions |
ユーザー |
![]() |
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 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 34 |
ソースコード
#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 secondusing 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/gstd::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| <= blong 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| <= bauto tmp = s;s = t;t = tmp;tmp = m0;m0 = m1;m1 = tmp;}// by [3]: |m0| <= b/g// by g != b: |m0| < b/gif (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 < m0long 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 valuell f(ll a, ll b){ //functionreturn 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 < RL += 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;}