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Submission #970423

# Submission time Handle Problem Language Result Execution time Memory
970423 2024-04-26T13:54:55 Z AisteS Feast (NOI19_feast) C++14
100 / 100
 148 ms 15216 KB 
//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
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 74 ms 14676 KB Output is correct
2 Correct 72 ms 14676 KB Output is correct
3 Correct 73 ms 15052 KB Output is correct
4 Correct 74 ms 14960 KB Output is correct
5 Correct 75 ms 14900 KB Output is correct
6 Correct 71 ms 14672 KB Output is correct
7 Correct 72 ms 14696 KB Output is correct
8 Correct 87 ms 14936 KB Output is correct
9 Correct 71 ms 14672 KB Output is correct
10 Correct 72 ms 14700 KB Output is correct

Subtask #2
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 63 ms 12892 KB Output is correct
2 Correct 66 ms 13292 KB Output is correct
3 Correct 66 ms 12888 KB Output is correct
4 Correct 65 ms 13148 KB Output is correct
5 Correct 75 ms 14704 KB Output is correct
6 Correct 62 ms 12888 KB Output is correct
7 Correct 68 ms 13144 KB Output is correct
8 Correct 79 ms 14984 KB Output is correct
9 Correct 74 ms 14664 KB Output is correct
10 Correct 67 ms 13032 KB Output is correct

Subtask #3
18.0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 95 ms 15088 KB Output is correct
2 Correct 95 ms 14928 KB Output is correct
3 Correct 95 ms 15056 KB Output is correct
4 Correct 109 ms 14944 KB Output is correct
5 Correct 96 ms 14960 KB Output is correct
6 Correct 96 ms 15132 KB Output is correct
7 Correct 96 ms 15176 KB Output is correct
8 Correct 98 ms 14964 KB Output is correct
9 Correct 106 ms 15208 KB Output is correct
10 Correct 94 ms 15192 KB Output is correct

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB Output is correct
2 Correct 1 ms 2396 KB Output is correct
3 Correct 1 ms 2512 KB Output is correct
4 Correct 1 ms 2652 KB Output is correct
5 Correct 1 ms 2516 KB Output is correct
6 Correct 1 ms 2392 KB Output is correct
7 Correct 1 ms 2396 KB Output is correct
8 Correct 1 ms 2396 KB Output is correct
9 Correct 1 ms 2396 KB Output is correct
10 Correct 1 ms 2396 KB Output is correct

Subtask #5
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB Output is correct
2 Correct 1 ms 2396 KB Output is correct
3 Correct 1 ms 2512 KB Output is correct
4 Correct 1 ms 2652 KB Output is correct
5 Correct 1 ms 2516 KB Output is correct
6 Correct 1 ms 2392 KB Output is correct
7 Correct 1 ms 2396 KB Output is correct
8 Correct 1 ms 2396 KB Output is correct
9 Correct 1 ms 2396 KB Output is correct
10 Correct 1 ms 2396 KB Output is correct
11 Correct 1 ms 2648 KB Output is correct
12 Correct 1 ms 2396 KB Output is correct
13 Correct 1 ms 2396 KB Output is correct
14 Correct 1 ms 2396 KB Output is correct
15 Correct 1 ms 2392 KB Output is correct
16 Correct 1 ms 2396 KB Output is correct
17 Correct 1 ms 2508 KB Output is correct
18 Correct 1 ms 2396 KB Output is correct
19 Correct 1 ms 2396 KB Output is correct
20 Correct 1 ms 2396 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB Output is correct
2 Correct 1 ms 2396 KB Output is correct
3 Correct 1 ms 2512 KB Output is correct
4 Correct 1 ms 2652 KB Output is correct
5 Correct 1 ms 2516 KB Output is correct
6 Correct 1 ms 2392 KB Output is correct
7 Correct 1 ms 2396 KB Output is correct
8 Correct 1 ms 2396 KB Output is correct
9 Correct 1 ms 2396 KB Output is correct
10 Correct 1 ms 2396 KB Output is correct
11 Correct 1 ms 2648 KB Output is correct
12 Correct 1 ms 2396 KB Output is correct
13 Correct 1 ms 2396 KB Output is correct
14 Correct 1 ms 2396 KB Output is correct
15 Correct 1 ms 2392 KB Output is correct
16 Correct 1 ms 2396 KB Output is correct
17 Correct 1 ms 2508 KB Output is correct
18 Correct 1 ms 2396 KB Output is correct
19 Correct 1 ms 2396 KB Output is correct
20 Correct 1 ms 2396 KB Output is correct
21 Correct 1 ms 2396 KB Output is correct
22 Correct 1 ms 2396 KB Output is correct
23 Correct 1 ms 2396 KB Output is correct
24 Correct 1 ms 2396 KB Output is correct
25 Correct 1 ms 2392 KB Output is correct
26 Correct 2 ms 2392 KB Output is correct
27 Correct 1 ms 2396 KB Output is correct
28 Correct 1 ms 2396 KB Output is correct
29 Correct 1 ms 2396 KB Output is correct
30 Correct 2 ms 2396 KB Output is correct

Subtask #7
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 74 ms 14676 KB Output is correct
2 Correct 72 ms 14676 KB Output is correct
3 Correct 73 ms 15052 KB Output is correct
4 Correct 74 ms 14960 KB Output is correct
5 Correct 75 ms 14900 KB Output is correct
6 Correct 71 ms 14672 KB Output is correct
7 Correct 72 ms 14696 KB Output is correct
8 Correct 87 ms 14936 KB Output is correct
9 Correct 71 ms 14672 KB Output is correct
10 Correct 72 ms 14700 KB Output is correct
11 Correct 63 ms 12892 KB Output is correct
12 Correct 66 ms 13292 KB Output is correct
13 Correct 66 ms 12888 KB Output is correct
14 Correct 65 ms 13148 KB Output is correct
15 Correct 75 ms 14704 KB Output is correct
16 Correct 62 ms 12888 KB Output is correct
17 Correct 68 ms 13144 KB Output is correct
18 Correct 79 ms 14984 KB Output is correct
19 Correct 74 ms 14664 KB Output is correct
20 Correct 67 ms 13032 KB Output is correct
21 Correct 95 ms 15088 KB Output is correct
22 Correct 95 ms 14928 KB Output is correct
23 Correct 95 ms 15056 KB Output is correct
24 Correct 109 ms 14944 KB Output is correct
25 Correct 96 ms 14960 KB Output is correct
26 Correct 96 ms 15132 KB Output is correct
27 Correct 96 ms 15176 KB Output is correct
28 Correct 98 ms 14964 KB Output is correct
29 Correct 106 ms 15208 KB Output is correct
30 Correct 94 ms 15192 KB Output is correct
31 Correct 1 ms 2396 KB Output is correct
32 Correct 1 ms 2396 KB Output is correct
33 Correct 1 ms 2512 KB Output is correct
34 Correct 1 ms 2652 KB Output is correct
35 Correct 1 ms 2516 KB Output is correct
36 Correct 1 ms 2392 KB Output is correct
37 Correct 1 ms 2396 KB Output is correct
38 Correct 1 ms 2396 KB Output is correct
39 Correct 1 ms 2396 KB Output is correct
40 Correct 1 ms 2396 KB Output is correct
41 Correct 1 ms 2648 KB Output is correct
42 Correct 1 ms 2396 KB Output is correct
43 Correct 1 ms 2396 KB Output is correct
44 Correct 1 ms 2396 KB Output is correct
45 Correct 1 ms 2392 KB Output is correct
46 Correct 1 ms 2396 KB Output is correct
47 Correct 1 ms 2508 KB Output is correct
48 Correct 1 ms 2396 KB Output is correct
49 Correct 1 ms 2396 KB Output is correct
50 Correct 1 ms 2396 KB Output is correct
51 Correct 1 ms 2396 KB Output is correct
52 Correct 1 ms 2396 KB Output is correct
53 Correct 1 ms 2396 KB Output is correct
54 Correct 1 ms 2396 KB Output is correct
55 Correct 1 ms 2392 KB Output is correct
56 Correct 2 ms 2392 KB Output is correct
57 Correct 1 ms 2396 KB Output is correct
58 Correct 1 ms 2396 KB Output is correct
59 Correct 1 ms 2396 KB Output is correct
60 Correct 2 ms 2396 KB Output is correct
61 Correct 138 ms 14812 KB Output is correct
62 Correct 130 ms 15216 KB Output is correct
63 Correct 114 ms 14900 KB Output is correct
64 Correct 137 ms 15136 KB Output is correct
65 Correct 134 ms 15080 KB Output is correct
66 Correct 144 ms 15104 KB Output is correct
67 Correct 148 ms 14912 KB Output is correct
68 Correct 96 ms 15152 KB Output is correct
69 Correct 95 ms 14672 KB Output is correct
70 Correct 98 ms 14840 KB Output is correct