| # | Time | Username | Problem | Language | Result | Execution time | Memory |
|---|---|---|---|---|---|---|---|
| 851596 | treap_enjoyer | Split the sequence (APIO14_sequence) | C++14 | 0 ms | 0 KiB |
This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#pragma GCC optimize("Ofast,unroll-loops")
#define ll long long
#define int long long
#define all(x) x.begin(), x.end()
using namespace std;
using namespace __gnu_pbds;
template<class T> using oset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
const ll INF = 1e18;
const int MAXN = 1e5 + 5;
struct line{
ll k;
ll c;
ll num;
ll calc(ll x){
return k * x + c;
}
ll intersec(line b){
if(k == b.k){
if(c == b.c) return INF;
else return -INF;
}
else return (c - b.c) / (b.k - k);
}
};
vector<pair<line, ll> > st;
vector<ll> seg;
vector<line> seglines;
int cur;
int pos;
void add(line a){
if(st.size() == 0){
st.push_back({a, INF});
//cout << st[st.size() - 1].first.c << " " << st[st.size() - 1].first.k << endl;
seg[st.size()] = INF;
seglines[st.size()] = a;
pos = 1;
return;
}
if(st.size() == 1){
if(a.k == st.back().first.k){
if(a.c > st.back().first.c){
seglines[1] = a;
st.back().first = a;
//cout << st.back().first.k << " " << st.back().first.c << endl;
return;
}
}
else{
ll x = a.intersec(st.back().first);
st.back().second = x;
seg[st.size()] = x;
st.push_back({a, INF});
seg[st.size()] = INF;
seglines[st.size()] = a;
if(seg[pos] < x) pos++;
//cout << st[st.size() - 1].first.k << " " << st[st.size() - 1].first.c << endl;
return;
}
}
line b = st[st.size() - 1].first;
if(a.k == b.k){
if(a.c <= b.c) return;
else{
if(pos == st.size()){
pos--;
}
st.pop_back();
st.back().second = INF;
seg[st.size()] = INF;
add(a);
return;
}
}
else{
st.pop_back();
line c = st.back().first;
if(a.intersec(c) <= st.back().second){
//cout << a.k << " " << a.c << " -- " << b.k << " " << b.c << " --- " << c.k << " " << c.c << " " << a.intersec(c) << " " << st.back().second << endl;
if(pos == st.size() + 1){
pos--;
}
seg[st.size()] = INF;
st.back().second = INF;
add(a);
return;
}
else{
ll x = a.intersec(b);
if(pos == st.size() && x < cur){
pos++;
}
st.push_back({b, x});
seg[st.size()] = x;
st.push_back({a, INF});
seg[st.size()] = INF;
seglines[st.size()] = a;
return;
}
}
}
void upd(int x){
while(seg[pos] < x){
pos++;
}
cur = x;
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
//ifstream cin("input.txt");
//ofstream cout("output.txt");
int n, k;
cin >> n >> k;
vector<ll> a(n + 1);
for(int i = 1; i <= n; i++){
cin >> a[i];
}
vector<vector<ll> > dp(k + 2, vector<ll>(n + 2, -INF));
vector<vector<int> > p(k + 2, vector<int>(n + 2, 0));
dp[0][0] = 0;
vector<ll> pref(n + 2, 0);
for(int i = 1; i <= n; i++){
pref[i] += pref[i - 1];
pref[i] += a[i];
}
for(int i = 1; i <= k + 1; i++){
st.clear();
seg.clear();
seglines.clear();
seg.resize(n + 1, INF);
seglines.resize(n + 1);
cur = pref[1];
pos = 1;
// cout << i << ": " << endl;
for(int j = 1; j <= n; j++){
// cout << pref[j - 1] << " <> " << dp[i - 1][j - 1] - pref[j - 1] * pref[j - 1] << endl;
if(dp[i - 1][j - 1] != -INF){
add({pref[j - 1], dp[i - 1][j - 1] - pref[j - 1] * pref[j - 1], j - 1});
}
upd(pref[j]);
if(st.size() && seglines[pos].calc(pref[j]) > dp[i][j]){
dp[i][j] = seglines[pos].calc(pref[j]);
p[i][j] = seglines[pos].num;
}
/*for(int k = 0; k < st.size(); k++){
cout << "(" << st[k].first.k << " + " << st[k].first.c << ")" << endl;
}
cout << "---------" << endl;*/
}
}
vector<int> ans;
/*for(int i = 0; i <= k + 1; i++){
for(int j = 0; j <= n; j++){
cout << dp[i][j] << " ";
}
cout << endl;
}*/
int cur = n;
for(int i = k; i > 0; i--){
ans.push_back(p[i + 1][cur]);
cur = p[i + 1][cur];
}
cout << dp[k + 1][n] << endl;
reverse(all(ans));
for(auto i: ans){
cout << i << " ";
}
}