Submission #970423

#	Time	Username	Problem	Language	Result	Execution time	Memory
970423		AisteS	Feast (NOI19_feast)	C++14	100 / 100	148 ms	15216 KiB

feast

//2019 NOI (National Olympiad of Singapore)

//Lagrangian Relaxation algorithm
#include<bits/stdc++.h>
using namespace std;
#define int int64_t
#define pii pair<int, int>
#define f first
#define s second

const int maxn = 3e5 + 5;
pii dp[maxn][2];
int A[maxn];
int N, K;

pii check(int lambda)
{
    dp[0][0] = {0, 0};
    dp[0][1] = {A[0] - lambda, 1};
    for (int i = 1; i < N; i++)
    {
        dp[i][0] = max(dp[i - 1][0], dp[i - 1][1]);
        dp[i][1] = max(make_pair(dp[i - 1][1].first + A[i], dp[i - 1][1].s),
                       make_pair(dp[i - 1][0].f - lambda + A[i], dp[i - 1][0].s + 1));
        //cout << i << " " << dp[i][0].f << " " << dp[i][1].f << endl;
    }
    return max(dp[N - 1][0], dp[N - 1][1]);
}

int32_t main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cin >> N >> K;
    for (int i = 0; i < N; i++)
        cin >> A[i];
    //cout << check(2).f << " bum\n";
    //find lambda
    int lo = 0, hi = 1e18;
    while(lo < hi)
    {
        int mid = (hi + lo + 1) / 2;
        //cout << mid <<endl;
        auto smth = check(mid);
        //cout << smth.f << " " << smth.s <<endl;
        if (smth.s >= K)
            lo = mid;
        else
            hi = mid - 1;
    }
    //cout << lo <<endl;
    cout << check(lo).f + lo * K;
}
/*
6 1
1 -2 3 -1 5 -6
ans: 7

6 2
1 2 3 -10 5 6
ans: 17


6 4
-1 -2 -1 0 -5 -1
ans: 0
*/

• Subtask 1: 4 / 4
• Subtask 2: 8 / 8
• Subtask 3: 18 / 18
• Subtask 4: 10 / 10
• Subtask 5: 11 / 11
• Subtask 6: 20 / 20
• Subtask 7: 29 / 29