Submission #563561

#	Time	Username	Problem	Language	Result	Execution time	Memory
563561		farhan132	Split the sequence (APIO14_sequence)	C++17	100 / 100	819 ms	107112 KiB

sequence

/***Farhan132***/
//#pragma GCC optimize("Ofast")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,fma")
//#pragma GCC optimization ("unroll-loops")
//#pragma GCC optimize("fast-math")
 
#include <bits/stdc++.h>
 
 
 
using namespace std;
 
typedef long long ll;
typedef unsigned long long ull;
typedef double dd;
typedef vector<ll> vll;
typedef pair<ll , ll> ii;
typedef vector< ii > vii;
typedef pair < pair < ll , ll > , pair < ll , ll > > cm; 
typedef tuple < ll,  ll, ll > tp;
 
#define ff first
#define ss second
#define pb push_back
#define in insert
#define f0(b) for(int i=0;i<(b);i++)
#define f00(b) for(int j=0;j<(b);j++)
#define f1(b) for(int i=1;i<=(b);i++)
#define f11(b) for(int j=1;j<=(b);j++)
#define f2(a,b) for(int i=(a);i<=(b);i++)
#define f22(a,b) for(int j=(a);j<=(b);j++)
#define sf(a) scanf("%lld",&a)
#define sff(a,b) scanf("%lld %lld", &a , &b)
#define pf(a) printf("%lld\n",a)
#define pff(a,b) printf("%lld %lld\n", a , b)
#define bug printf("**!\n")
#define mem(a , b) memset(a, b ,sizeof(a))
#define front_zero(n) __builtin_clzll(n)
#define back_zero(n) __builtin_ctzll(n)
#define total_one(n) __builtin_popcount(n)
#define clean fflush(stdout)
 
//const ll mod =  (ll) 998244353;
const ll mod =  (ll) 1e9 + 7;
const ll maxn = (ll)1e8 + 5;
const int nnn = 1048590;
const int inf = numeric_limits<int>::max()-1;
//const ll INF = numeric_limits<ll>::max()-1;
const ll INF = (ll)1e18;
 
ll dx[]={0,1,0,-1};
ll dy[]={1,0,-1,0};
ll dxx[]={0,1,0,-1,1,1,-1,-1};
ll dyy[]={1,0,-1,0,1,-1,1,-1};
 
bool USACO = 0;
 
mt19937 rng(chrono::system_clock::now().time_since_epoch().count());
 
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
 
template <typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

const ll N = 1e5 + 5;

struct cht{
  
  vector < ll > m, b, idx;
  ll sz = 0, ptr = 0;

  bool bad(ll f1, ll f2, ll f3){
    return __int128((b[f1] - b[f3]) * (m[f2] - m[f1])) <= 
           __int128((b[f1] - b[f2]) * (m[f3] - m[f1]));
  }

  void add(ll _m, ll _b, ll _i){
    if(sz && m.back() == _m){
      if(b.back() > _b) return;
      m.pop_back();
      b.pop_back();
      idx.pop_back();
      sz--;
    }
    m.pb(_m);
    b.pb(_b);
    idx.pb(_i);
    sz++;

    while(sz >= 3 && bad(sz - 3, sz - 2, sz - 1)){
      m.erase(m.end()-2);
      b.erase(b.end()-2);
      idx.erase(idx.end()-2);
      sz--;
    }
  }
  ll f(ll x, ll i){
    return m[i] * x + b[i];
  }
  ii query(ll x){
    
    ptr = min(ptr, sz-1);
    while(ptr + 1 < sz && f(x, ptr) <= f(x, ptr + 1)) ptr++;
    
    return {f(x, ptr), idx[ptr]};
  }
};
int par[204][N];
bool ok[204][N];
ll dp[2][N];
ll a[N] , sum[N];

ll s(ll i,ll j){
  return sum[j] - sum[i - 1];
}

void solve(){

  mem(dp, 0);
  mem(par, -1);
  ll n, k; cin >> n >> k;

  sum[0] = 0;

  for(ll i = 1; i <= n; i++){
    cin >> a[i];
    sum[i] = sum[i - 1] + a[i];
  }
  ll row = 0;
  mem(ok, 0);

  for(ll c = 1; c <= k; c++){
    cht T;
    T.add(0, 0, -1);
    row ^= 1;
    for(ll i = 1; i < n; i++){
      if(i < c){
        T.add(s(1, i) , -(s(1, i)* s(1, n)) + dp[row^1][i], i);
        continue;
      }
      auto [v, j] = T.query(s(1, i));
      dp[row][i] = s(1, i) * s(1, n) - s(1, i) * s(1, i) + v;
      T.add(s(1, i) , -(s(1, i)* s(1, n)) + dp[row^1][i], i);
      if(dp[row][i - 1] > dp[row][i]){
        dp[row][i] = dp[row][i-1];
        ok[c][i] = 0;
        if(ok[c][i-1] == 1) par[c][i] = i-1;
        else par[c][i] = par[c][i-1];
      }else par[c][i] = j, ok[c][i] = 1;
    }
  }

  cout << dp[row][n-1] << '\n';
  ll cur = n-1;
  for(ll c = k; c >= 1; c--){
    if(ok[c][cur] == 0) cur = par[c][cur];
    cout << cur << ' '; cur = par[c][cur];
  }


  return;
}
 
int main() {
    
    
    #ifdef LOCAL
        freopen("in", "r", stdin);
        freopen("out", "w", stdout);
        auto start_time = clock();
    #else 
       ios_base::sync_with_stdio(0); cin.tie(NULL); cout.tie(NULL);
    #endif
 
    //pre(N);
 
    ll T = 1, CT = 0;  //cin >> T; 
 
    while(T--){
        solve();
    }
    #ifdef LOCAL
        auto end_time = clock();
        cerr<< "Execution time: "<<(end_time - start_time)*(int)1e3/CLOCKS_PER_SEC<<" ms\n";
    #endif
 
    return 0;
}

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:178:15: warning: unused variable 'CT' [-Wunused-variable]
  178 |     ll T = 1, CT = 0;  //cin >> T;
      |               ^~

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 29 / 29