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  1. #include <iostream>
  2. #include <bits/stdc++.h>
  3. typedef long long ll;
  4.  
  5. using namespace std;
  6.  
  7. struct Line {
  8.     mutable ll k, m, p;
  9.     bool operator<(const Line& o) const { return k < o.k; }
  10.     bool operator<(ll x) const { return p < x; }
  11. };
  12.  
  13. struct HullDynamic : multiset<Line, less<>> {
  14.     // (for doubles, use inf = 1/.0, div(a,b) = a/b)
  15.     const ll inf = 2e18;
  16.     ll div(ll a, ll b) { // floored division
  17.         return a / b - ((a ^ b) < 0 && a % b); }
  18.     bool isect(iterator x, iterator y) {
  19.         if (y == end()) { x->p = inf; return false; }
  20.         if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
  21.         else x->p = div(y->m - x->m, x->k - y->k);
  22.         return x->p >= y->p;
  23.     }
  24.     void add(ll k, ll m) {
  25.         auto z = insert({k, m, 0}), y = z++, x = y;
  26.         while (isect(y, z)) z = erase(z);
  27.         if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
  28.         while ((y = x) != begin() && (--x)->p >= y->p)
  29.             isect(x, erase(y));
  30.     }
  31.     ll query(ll x) {
  32.         assert(!empty());
  33.         auto l = *lower_bound(x);
  34.         return l.k * x + l.m;
  35.     }
  36. };
  37. const int N = 2e5 + 5;
  38. ll dp[N];
  39. ll n; 
  40. int main() {
  41. 	ios_base::sync_with_stdio(false);
  42. 	cin.tie(NULL); cout.tie(NULL);
  43. 	cin>>n;
  44. 	vector<ll>a(n + 1);
  45. 	for(int i = 1;i<=n;i++) cin>>a[i];
  46. 	vector<ll>pref(n + 1,0ll);
  47. 	for(int i = 1;i<=n;i++) pref[i] = pref[i - 1] + a[i];
  48. 	vector<ll>c(n + 1, 0ll); 
  49. 	for(ll i = 1ll; i<=n;i++) c[i] = c[i - 1] + (a[i]*i);
  50.  
  51. 	HullDynamic cht; 
  52.     dp[0] = 0ll; 
  53.     dp[1] = a[1]; 
  54.     cht.add(0ll, 0ll); 
  55.  
  56. 	for(ll i = 2;i<=n;i++){
  57. 		dp[i] = cht.query(pref[i]);
  58.         dp[i] += c[i]; 
  59.         cht.add(1ll - i, (i- 1ll)*pref[i- 1] - c[i-1]); 
  60.  
  61.     }
  62.     ll ans = 0ll; 
  63.     for(int i = 0; i<=n;i++) ans = max(ans, dp[i]); 
  64.     cout<<ans<<'\n'; 
  65.  
  66.  
  67. }
Success #stdin #stdout 0s 5320KB
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https://ideone.com/pqikb0
language:
C++ (gcc 8.3)
created:
5 days ago
visibility:
public

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