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Submission #494815

# Submission time Handle Problem Language Result Execution time Memory
494815 2021-12-16T15:37:50 Z blue Discharging (NOI20_discharging) C++17
100 / 100
 155 ms 21828 KB 
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

using ll = long long;
using vll = vector<ll>;
using pll = pair<ll, ll>;
#define sz(x) int(x.size())

const ll INF = 1'000'000'000'000'000'000LL;

struct line
{
    double a;
    double b;
};

double intersect(line A, line B)
{
    return (B.b-A.b)/(A.a-B.a);
}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int N;
    cin >> N;

    int TS = N;

    vector<pll> T;

    T.push_back({0, 0});
    for(int i = 1; i <= N; i++)
    {
        ll t;
        cin >> t;
        if(t <= T.back().first)
            T.back().second++;
        else
            T.push_back({t, 1});
    }

    N = sz(T)-1;

    vll suff(1+N, 0);
    suff[0] = TS;
    for(int i = 1; i <= N; i++) suff[i] = suff[i-1] - T[i].second;


    vll dp(1+N, INF);

    dp[0] = 0;

    vector<line> L;
    L.push_back(line{double(suff[0]), double(dp[0])});

    for(int i = 1; i <= N; i++)
    {
        int lo = 0;
        int hi = sz(L) - 1;

        double x = T[i].first;

        while(lo != hi)
        {
            int mid = (lo+hi)/2;
            if(intersect(L[mid], L[mid+1]) <= x)
                lo = mid+1;
            else
                hi = mid;
        }

        dp[i] = ll(L[lo].a) * T[i].first  +  ll(L[lo].b);

        if(i < N)
        {
            line new_line{double(suff[i]), double(dp[i])};
            while(sz(L) >= 2 && intersect(L[sz(L)-2], L[sz(L)-1]) >= intersect(L[sz(L)-1], new_line))
                L.pop_back();

            L.push_back(new_line);
        }
    }
    cout << dp[N] << '\n';
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 204 KB Output is correct
3 Correct 0 ms 312 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 0 ms 204 KB Output is correct
6 Correct 0 ms 204 KB Output is correct
7 Correct 0 ms 312 KB Output is correct
8 Correct 0 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 0 ms 204 KB Output is correct
11 Correct 0 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 0 ms 204 KB Output is correct
14 Correct 0 ms 204 KB Output is correct

Subtask #2
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB Output is correct
2 Correct 1 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 1 ms 332 KB Output is correct
5 Correct 1 ms 320 KB Output is correct
6 Correct 1 ms 332 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 1 ms 332 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 1 ms 332 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 1 ms 332 KB Output is correct
13 Correct 1 ms 332 KB Output is correct
14 Correct 1 ms 332 KB Output is correct
15 Correct 1 ms 332 KB Output is correct

Subtask #3
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB Output is correct
2 Correct 1 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 1 ms 332 KB Output is correct
5 Correct 1 ms 320 KB Output is correct
6 Correct 1 ms 332 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 1 ms 332 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 1 ms 332 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 1 ms 332 KB Output is correct
13 Correct 1 ms 332 KB Output is correct
14 Correct 1 ms 332 KB Output is correct
15 Correct 1 ms 332 KB Output is correct
16 Correct 121 ms 14324 KB Output is correct
17 Correct 127 ms 15420 KB Output is correct
18 Correct 94 ms 10308 KB Output is correct
19 Correct 125 ms 15400 KB Output is correct
20 Correct 121 ms 16804 KB Output is correct
21 Correct 120 ms 15508 KB Output is correct
22 Correct 110 ms 14116 KB Output is correct
23 Correct 139 ms 20260 KB Output is correct
24 Correct 133 ms 18176 KB Output is correct
25 Correct 136 ms 18064 KB Output is correct
26 Correct 155 ms 21828 KB Output is correct
27 Correct 102 ms 12472 KB Output is correct
28 Correct 119 ms 16148 KB Output is correct
29 Correct 133 ms 18680 KB Output is correct
30 Correct 142 ms 21024 KB Output is correct

Subtask #4
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 100 ms 1968 KB Output is correct
2 Correct 95 ms 2324 KB Output is correct
3 Correct 94 ms 2328 KB Output is correct
4 Correct 95 ms 2364 KB Output is correct
5 Correct 93 ms 2372 KB Output is correct
6 Correct 91 ms 2388 KB Output is correct
7 Correct 97 ms 2524 KB Output is correct
8 Correct 105 ms 2336 KB Output is correct
9 Correct 94 ms 2372 KB Output is correct
10 Correct 97 ms 2420 KB Output is correct

Subtask #5
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 204 KB Output is correct
3 Correct 0 ms 312 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 0 ms 204 KB Output is correct
6 Correct 0 ms 204 KB Output is correct
7 Correct 0 ms 312 KB Output is correct
8 Correct 0 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 0 ms 204 KB Output is correct
11 Correct 0 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 0 ms 204 KB Output is correct
14 Correct 0 ms 204 KB Output is correct
15 Correct 1 ms 332 KB Output is correct
16 Correct 1 ms 332 KB Output is correct
17 Correct 1 ms 332 KB Output is correct
18 Correct 1 ms 332 KB Output is correct
19 Correct 1 ms 320 KB Output is correct
20 Correct 1 ms 332 KB Output is correct
21 Correct 1 ms 332 KB Output is correct
22 Correct 1 ms 332 KB Output is correct
23 Correct 1 ms 332 KB Output is correct
24 Correct 1 ms 332 KB Output is correct
25 Correct 1 ms 332 KB Output is correct
26 Correct 1 ms 332 KB Output is correct
27 Correct 1 ms 332 KB Output is correct
28 Correct 1 ms 332 KB Output is correct
29 Correct 1 ms 332 KB Output is correct
30 Correct 1 ms 204 KB Output is correct
31 Correct 1 ms 204 KB Output is correct
32 Correct 1 ms 204 KB Output is correct
33 Correct 1 ms 204 KB Output is correct
34 Correct 1 ms 316 KB Output is correct
35 Correct 1 ms 204 KB Output is correct
36 Correct 1 ms 332 KB Output is correct
37 Correct 1 ms 204 KB Output is correct
38 Correct 0 ms 204 KB Output is correct
39 Correct 0 ms 204 KB Output is correct
40 Correct 1 ms 204 KB Output is correct
41 Correct 1 ms 204 KB Output is correct
42 Correct 1 ms 332 KB Output is correct
43 Correct 1 ms 332 KB Output is correct
44 Correct 1 ms 204 KB Output is correct
45 Correct 1 ms 204 KB Output is correct
46 Correct 1 ms 204 KB Output is correct
47 Correct 1 ms 204 KB Output is correct
48 Correct 1 ms 204 KB Output is correct
49 Correct 1 ms 320 KB Output is correct
50 Correct 1 ms 204 KB Output is correct

Subtask #6
28.0 / 28.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 204 KB Output is correct
3 Correct 0 ms 312 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 0 ms 204 KB Output is correct
6 Correct 0 ms 204 KB Output is correct
7 Correct 0 ms 312 KB Output is correct
8 Correct 0 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 0 ms 204 KB Output is correct
11 Correct 0 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 0 ms 204 KB Output is correct
14 Correct 0 ms 204 KB Output is correct
15 Correct 1 ms 332 KB Output is correct
16 Correct 1 ms 332 KB Output is correct
17 Correct 1 ms 332 KB Output is correct
18 Correct 1 ms 332 KB Output is correct
19 Correct 1 ms 320 KB Output is correct
20 Correct 1 ms 332 KB Output is correct
21 Correct 1 ms 332 KB Output is correct
22 Correct 1 ms 332 KB Output is correct
23 Correct 1 ms 332 KB Output is correct
24 Correct 1 ms 332 KB Output is correct
25 Correct 1 ms 332 KB Output is correct
26 Correct 1 ms 332 KB Output is correct
27 Correct 1 ms 332 KB Output is correct
28 Correct 1 ms 332 KB Output is correct
29 Correct 1 ms 332 KB Output is correct
30 Correct 121 ms 14324 KB Output is correct
31 Correct 127 ms 15420 KB Output is correct
32 Correct 94 ms 10308 KB Output is correct
33 Correct 125 ms 15400 KB Output is correct
34 Correct 121 ms 16804 KB Output is correct
35 Correct 120 ms 15508 KB Output is correct
36 Correct 110 ms 14116 KB Output is correct
37 Correct 139 ms 20260 KB Output is correct
38 Correct 133 ms 18176 KB Output is correct
39 Correct 136 ms 18064 KB Output is correct
40 Correct 155 ms 21828 KB Output is correct
41 Correct 102 ms 12472 KB Output is correct
42 Correct 119 ms 16148 KB Output is correct
43 Correct 133 ms 18680 KB Output is correct
44 Correct 142 ms 21024 KB Output is correct
45 Correct 100 ms 1968 KB Output is correct
46 Correct 95 ms 2324 KB Output is correct
47 Correct 94 ms 2328 KB Output is correct
48 Correct 95 ms 2364 KB Output is correct
49 Correct 93 ms 2372 KB Output is correct
50 Correct 91 ms 2388 KB Output is correct
51 Correct 97 ms 2524 KB Output is correct
52 Correct 105 ms 2336 KB Output is correct
53 Correct 94 ms 2372 KB Output is correct
54 Correct 97 ms 2420 KB Output is correct
55 Correct 1 ms 204 KB Output is correct
56 Correct 1 ms 204 KB Output is correct
57 Correct 1 ms 204 KB Output is correct
58 Correct 1 ms 204 KB Output is correct
59 Correct 1 ms 316 KB Output is correct
60 Correct 1 ms 204 KB Output is correct
61 Correct 1 ms 332 KB Output is correct
62 Correct 1 ms 204 KB Output is correct
63 Correct 0 ms 204 KB Output is correct
64 Correct 0 ms 204 KB Output is correct
65 Correct 1 ms 204 KB Output is correct
66 Correct 1 ms 204 KB Output is correct
67 Correct 1 ms 332 KB Output is correct
68 Correct 1 ms 332 KB Output is correct
69 Correct 1 ms 204 KB Output is correct
70 Correct 1 ms 204 KB Output is correct
71 Correct 1 ms 204 KB Output is correct
72 Correct 1 ms 204 KB Output is correct
73 Correct 1 ms 204 KB Output is correct
74 Correct 1 ms 320 KB Output is correct
75 Correct 1 ms 204 KB Output is correct
76 Correct 76 ms 1660 KB Output is correct
77 Correct 74 ms 1712 KB Output is correct
78 Correct 69 ms 1604 KB Output is correct
79 Correct 71 ms 1720 KB Output is correct
80 Correct 75 ms 1688 KB Output is correct
81 Correct 72 ms 1736 KB Output is correct
82 Correct 67 ms 1808 KB Output is correct
83 Correct 70 ms 1704 KB Output is correct
84 Correct 73 ms 1788 KB Output is correct
85 Correct 78 ms 1696 KB Output is correct
86 Correct 68 ms 1568 KB Output is correct
87 Correct 74 ms 1572 KB Output is correct
88 Correct 73 ms 1568 KB Output is correct
89 Correct 73 ms 1668 KB Output is correct
90 Correct 69 ms 1476 KB Output is correct
91 Correct 68 ms 1604 KB Output is correct
92 Correct 135 ms 17700 KB Output is correct
93 Correct 126 ms 15780 KB Output is correct
94 Correct 66 ms 1300 KB Output is correct
95 Correct 75 ms 1316 KB Output is correct
96 Correct 67 ms 1348 KB Output is correct
97 Correct 69 ms 1352 KB Output is correct
98 Correct 78 ms 1464 KB Output is correct
99 Correct 74 ms 1304 KB Output is correct
100 Correct 70 ms 1152 KB Output is correct