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>
using namespace std;
using ll = long long;
const int mxN = 2e5 + 5, mod = 1e9 + 7, LOG = 20;
int n, a[mxN];
ll p[mxN], res[mxN];
pair <ll, int> dp[mxN];
void solve(int l, int r) {
vector <int> arr;
arr.push_back(0);
for (int i = l; i <= r; ++i) arr.push_back(a[i]);
int m = (r - l + 1);
dp[1] = {a[1], 1ll};
for (int i = 2; i <= m; ++i) {
if (dp[i - 1].first >= dp[i - 2].first + arr[i]) {
p[i] = dp[i - 1].second;
dp[i] = dp[i - 1];
}
else {
p[i] = dp[i - 2].second;
dp[i] = {dp[i - 2].first + arr[i], i};
}
}
int now = dp[m].second;
multiset <int> lmao;
ll ans = 0;
while (now) {
ans += arr[now];
lmao.insert(arr[now]);
now = p[now];
}
if (m & 1) {
if ((int)lmao.size() < (m + 1) / 2) {
ll bruh = 0;
for (int i = 1; i <= m; i += 2) bruh += arr[i];
res[(m + 1) / 2] = max(res[(m + 1) / 2], bruh);
for (int i = m / 2; i > 0; i--) {
res[i] = max(res[i], ans);
ans -= *lmao.begin();
lmao.erase(lmao.begin());
}
return;
}
}
for (int i = (m + 1) / 2; i > 0; i--) {
res[i] = max(res[i], ans);
ans -= *lmao.begin();
lmao.erase(lmao.begin());
}
return;
}
int main() {
ios :: sync_with_stdio(false), cin.tie(nullptr);
cin >> n;
for (int i = 1; i <= n; ++i) cin >> a[i];
solve(1, n);
if (n != 1) solve(2, n), solve(1, n - 1);
for (int i = 1; i <= (n + 1) / 2; ++i) cout << res[i] << '\n';
return 0;
}
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