제출 #1340723

#제출 시각아이디문제언어결과실행 시간메모리
1340723justfadyFeast (NOI19_feast)C++20
100 / 100
425 ms40340 KiB
#include <bits/stdc++.h> //  +
using namespace std;     // +++
#define inf 1e18         //  +
#define int long long
#define all(a) a.begin(), a.end()
void files() {
// #ifndef ONLINE_JUDGE
//     freopen("input.txt", "r", stdin), freopen("output.txt", "w", stdout);
// #endif
}

int const N = 3e5 + 5;
pair<int, int> dp[N][2];
int vis[N][2], id;
int n, k, a[N];
int lamda;
pair<int, int> rec(int i, bool lst) {
    if (i == n) return {0, 0};
    auto &ret = dp[i][lst];
    if (vis[i][lst] == id) return ret;
    vis[i][lst] = id;
    auto leave = rec(i + 1, 0);
    auto take = rec(i + 1, 1);
    take.first += a[i];
    if (!lst) {
        take.first -= lamda;
        take.second--;
    }

    return ret = max(leave, take);
}

void solve() {
    cin >> n >> k;

    for (int i = 0; i < n; ++i) cin >> a[i];

    // st = 0       "AT MOST K" (empty allowed).
    // st = -1e15   "EXACTLY K" (must force bad choices).
    // en = 1e15     Always. It forces the DP to pick 0 items.
    
    int st = 0, en = 1e15, md; 
    __int128_t ans = 0;
    while (st <= en) {
        md = st + (en - st) / 2;
        lamda = md;
        
        ++id;
        auto [cur_ans, cnt] = rec(0, 0); 
        
        int used = -cnt; // cnt that you take (neg in dp)
        
        if (used > k) {
            // We used too many items. The penalty is too weak.
            st = md + 1; 
        } else {
            // We used <= k items. This is a valid configuration!
            // Refund the penalty for exactly K items to get the true score.
            ans = cur_ans + (__int128_t)md * k; 
            
            // Try to find a smaller valid penalty to handle collinear points
            en = md - 1; 
        }
    }

    cout << (int)ans << '\n';
}

signed main() {
    ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0), files();
    int tc = 1;
    // cin >> tc;
    while (tc--)
        solve();
}
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