oj.uz

Submission #321051

# Submission time Handle Problem Language Result Execution time Memory
321051 2020-11-10T18:34:35 Z saarang123 Discharging (NOI20_discharging) C++14
100 / 100
 159 ms 19684 KB 
#include <bits/stdc++.h>
using namespace std;
#define int long long

const int inf = 1e15;
const int N = 1502;

struct CHT {
    struct Line {
        int slope, c; //slope, yIntercept
        Line(int slope, int c) : slope(slope), c(c) {}
        int val(int xCoordinate) { return slope * xCoordinate + c; }  //y coordinate
        int intersect(Line other) {  //ceiling of x coordinate of intersection
            return (other.c - c + slope - other.slope - 1) / (slope - other.slope);
        }
    };
    //Similar to monotonic queue
    deque<pair<Line, int>> dq;   //used to maintain the CHT
    void add(int slope, int yIntersect) { //add new line
        Line newLine(slope, yIntersect);
        while(!dq.empty() && dq.back().second >= dq.back().first.intersect(newLine)) // <= if max is optimal
            dq.pop_back();  //pop redundant(not optimal) lines
        if(dq.empty())
            dq.push_back(make_pair(newLine, 0)); //set 0 to -inf if -ve
        else
            dq.push_back(make_pair(newLine, dq.back().first.intersect(newLine)));
    }
    int qry(int xCoordinate) { //only if queries are monotonic - O(1) on average
        while(dq.size() > 1) {
            if(dq[1].second <= xCoordinate) dq.pop_front(); //finding optimal range for xCoord
            else break;
        }
        return dq[0].first.val(xCoordinate);
    }
    int query(int xCoordinate) { //works when queries are not monotonic by using binsearch
        auto ans = *lower_bound(dq.begin(), dq.end(),  //because min is in front and max at back
                                make_pair(Line(0, 0), xCoordinate),
                                [&] (const pair<Line, int> &a, const pair<Line, int> &b) {
                                    return a.second < b.second;  //custom comparator for the pair
                                });
        return ans.first.val(xCoordinate);
    }
};

signed main() {
    std::ios::sync_with_stdio(0);
    std::cout.tie(0);
    std::cin.tie(0);
    int n; cin >> n;
    vector<int> a(n + 1), dp(n + 1);
    for(int i = 1; i <= n; i++) cin >> a[i];
    CHT cht;
    dp[1] = a[1] * n;
    cht.add(n, 0);
    int mx = a[1];
    for(int i = 2; i <= n; i++) {
        mx = max(mx, a[i]);
        cht.add(n - i + 1, dp[i - 1]);
        dp[i] = cht.qry(mx);
    }
    cout << dp[n] << '\n';
    return 0;
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 364 KB Output is correct
2 Correct 1 ms 384 KB Output is correct
3 Correct 1 ms 376 KB Output is correct
4 Correct 1 ms 384 KB Output is correct
5 Correct 1 ms 364 KB Output is correct
6 Correct 0 ms 364 KB Output is correct
7 Correct 0 ms 364 KB Output is correct
8 Correct 1 ms 364 KB Output is correct
9 Correct 1 ms 492 KB Output is correct
10 Correct 0 ms 364 KB Output is correct
11 Correct 1 ms 364 KB Output is correct
12 Correct 0 ms 364 KB Output is correct
13 Correct 0 ms 364 KB Output is correct
14 Correct 0 ms 364 KB Output is correct

Subtask #2
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 492 KB Output is correct
2 Correct 1 ms 364 KB Output is correct
3 Correct 1 ms 364 KB Output is correct
4 Correct 1 ms 364 KB Output is correct
5 Correct 1 ms 364 KB Output is correct
6 Correct 1 ms 364 KB Output is correct
7 Correct 1 ms 364 KB Output is correct
8 Correct 1 ms 364 KB Output is correct
9 Correct 1 ms 364 KB Output is correct
10 Correct 1 ms 364 KB Output is correct
11 Correct 1 ms 364 KB Output is correct
12 Correct 1 ms 364 KB Output is correct
13 Correct 1 ms 364 KB Output is correct
14 Correct 1 ms 364 KB Output is correct
15 Correct 1 ms 364 KB Output is correct

Subtask #3
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 492 KB Output is correct
2 Correct 1 ms 364 KB Output is correct
3 Correct 1 ms 364 KB Output is correct
4 Correct 1 ms 364 KB Output is correct
5 Correct 1 ms 364 KB Output is correct
6 Correct 1 ms 364 KB Output is correct
7 Correct 1 ms 364 KB Output is correct
8 Correct 1 ms 364 KB Output is correct
9 Correct 1 ms 364 KB Output is correct
10 Correct 1 ms 364 KB Output is correct
11 Correct 1 ms 364 KB Output is correct
12 Correct 1 ms 364 KB Output is correct
13 Correct 1 ms 364 KB Output is correct
14 Correct 1 ms 364 KB Output is correct
15 Correct 1 ms 364 KB Output is correct
16 Correct 135 ms 19556 KB Output is correct
17 Correct 127 ms 19044 KB Output is correct
18 Correct 115 ms 19684 KB Output is correct
19 Correct 128 ms 19172 KB Output is correct
20 Correct 128 ms 19300 KB Output is correct
21 Correct 125 ms 19044 KB Output is correct
22 Correct 127 ms 19324 KB Output is correct
23 Correct 133 ms 19044 KB Output is correct
24 Correct 127 ms 19044 KB Output is correct
25 Correct 130 ms 19044 KB Output is correct
26 Correct 136 ms 19044 KB Output is correct
27 Correct 120 ms 19428 KB Output is correct
28 Correct 129 ms 19172 KB Output is correct
29 Correct 131 ms 19044 KB Output is correct
30 Correct 130 ms 19044 KB Output is correct

Subtask #4
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 149 ms 18176 KB Output is correct
2 Correct 154 ms 18148 KB Output is correct
3 Correct 153 ms 18148 KB Output is correct
4 Correct 148 ms 18020 KB Output is correct
5 Correct 151 ms 18028 KB Output is correct
6 Correct 151 ms 18020 KB Output is correct
7 Correct 150 ms 18024 KB Output is correct
8 Correct 159 ms 18052 KB Output is correct
9 Correct 148 ms 18020 KB Output is correct
10 Correct 149 ms 18020 KB Output is correct

Subtask #5
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 364 KB Output is correct
2 Correct 1 ms 384 KB Output is correct
3 Correct 1 ms 376 KB Output is correct
4 Correct 1 ms 384 KB Output is correct
5 Correct 1 ms 364 KB Output is correct
6 Correct 0 ms 364 KB Output is correct
7 Correct 0 ms 364 KB Output is correct
8 Correct 1 ms 364 KB Output is correct
9 Correct 1 ms 492 KB Output is correct
10 Correct 0 ms 364 KB Output is correct
11 Correct 1 ms 364 KB Output is correct
12 Correct 0 ms 364 KB Output is correct
13 Correct 0 ms 364 KB Output is correct
14 Correct 0 ms 364 KB Output is correct
15 Correct 1 ms 492 KB Output is correct
16 Correct 1 ms 364 KB Output is correct
17 Correct 1 ms 364 KB Output is correct
18 Correct 1 ms 364 KB Output is correct
19 Correct 1 ms 364 KB Output is correct
20 Correct 1 ms 364 KB Output is correct
21 Correct 1 ms 364 KB Output is correct
22 Correct 1 ms 364 KB Output is correct
23 Correct 1 ms 364 KB Output is correct
24 Correct 1 ms 364 KB Output is correct
25 Correct 1 ms 364 KB Output is correct
26 Correct 1 ms 364 KB Output is correct
27 Correct 1 ms 364 KB Output is correct
28 Correct 1 ms 364 KB Output is correct
29 Correct 1 ms 364 KB Output is correct
30 Correct 1 ms 364 KB Output is correct
31 Correct 1 ms 364 KB Output is correct
32 Correct 1 ms 364 KB Output is correct
33 Correct 1 ms 364 KB Output is correct
34 Correct 1 ms 364 KB Output is correct
35 Correct 1 ms 380 KB Output is correct
36 Correct 1 ms 364 KB Output is correct
37 Correct 1 ms 364 KB Output is correct
38 Correct 1 ms 364 KB Output is correct
39 Correct 1 ms 364 KB Output is correct
40 Correct 1 ms 364 KB Output is correct
41 Correct 1 ms 364 KB Output is correct
42 Correct 1 ms 364 KB Output is correct
43 Correct 1 ms 364 KB Output is correct
44 Correct 1 ms 364 KB Output is correct
45 Correct 1 ms 364 KB Output is correct
46 Correct 1 ms 364 KB Output is correct
47 Correct 1 ms 364 KB Output is correct
48 Correct 1 ms 364 KB Output is correct
49 Correct 1 ms 364 KB Output is correct
50 Correct 1 ms 364 KB Output is correct

Subtask #6
28.0 / 28.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 364 KB Output is correct
2 Correct 1 ms 384 KB Output is correct
3 Correct 1 ms 376 KB Output is correct
4 Correct 1 ms 384 KB Output is correct
5 Correct 1 ms 364 KB Output is correct
6 Correct 0 ms 364 KB Output is correct
7 Correct 0 ms 364 KB Output is correct
8 Correct 1 ms 364 KB Output is correct
9 Correct 1 ms 492 KB Output is correct
10 Correct 0 ms 364 KB Output is correct
11 Correct 1 ms 364 KB Output is correct
12 Correct 0 ms 364 KB Output is correct
13 Correct 0 ms 364 KB Output is correct
14 Correct 0 ms 364 KB Output is correct
15 Correct 1 ms 492 KB Output is correct
16 Correct 1 ms 364 KB Output is correct
17 Correct 1 ms 364 KB Output is correct
18 Correct 1 ms 364 KB Output is correct
19 Correct 1 ms 364 KB Output is correct
20 Correct 1 ms 364 KB Output is correct
21 Correct 1 ms 364 KB Output is correct
22 Correct 1 ms 364 KB Output is correct
23 Correct 1 ms 364 KB Output is correct
24 Correct 1 ms 364 KB Output is correct
25 Correct 1 ms 364 KB Output is correct
26 Correct 1 ms 364 KB Output is correct
27 Correct 1 ms 364 KB Output is correct
28 Correct 1 ms 364 KB Output is correct
29 Correct 1 ms 364 KB Output is correct
30 Correct 135 ms 19556 KB Output is correct
31 Correct 127 ms 19044 KB Output is correct
32 Correct 115 ms 19684 KB Output is correct
33 Correct 128 ms 19172 KB Output is correct
34 Correct 128 ms 19300 KB Output is correct
35 Correct 125 ms 19044 KB Output is correct
36 Correct 127 ms 19324 KB Output is correct
37 Correct 133 ms 19044 KB Output is correct
38 Correct 127 ms 19044 KB Output is correct
39 Correct 130 ms 19044 KB Output is correct
40 Correct 136 ms 19044 KB Output is correct
41 Correct 120 ms 19428 KB Output is correct
42 Correct 129 ms 19172 KB Output is correct
43 Correct 131 ms 19044 KB Output is correct
44 Correct 130 ms 19044 KB Output is correct
45 Correct 149 ms 18176 KB Output is correct
46 Correct 154 ms 18148 KB Output is correct
47 Correct 153 ms 18148 KB Output is correct
48 Correct 148 ms 18020 KB Output is correct
49 Correct 151 ms 18028 KB Output is correct
50 Correct 151 ms 18020 KB Output is correct
51 Correct 150 ms 18024 KB Output is correct
52 Correct 159 ms 18052 KB Output is correct
53 Correct 148 ms 18020 KB Output is correct
54 Correct 149 ms 18020 KB Output is correct
55 Correct 1 ms 364 KB Output is correct
56 Correct 1 ms 364 KB Output is correct
57 Correct 1 ms 364 KB Output is correct
58 Correct 1 ms 364 KB Output is correct
59 Correct 1 ms 364 KB Output is correct
60 Correct 1 ms 380 KB Output is correct
61 Correct 1 ms 364 KB Output is correct
62 Correct 1 ms 364 KB Output is correct
63 Correct 1 ms 364 KB Output is correct
64 Correct 1 ms 364 KB Output is correct
65 Correct 1 ms 364 KB Output is correct
66 Correct 1 ms 364 KB Output is correct
67 Correct 1 ms 364 KB Output is correct
68 Correct 1 ms 364 KB Output is correct
69 Correct 1 ms 364 KB Output is correct
70 Correct 1 ms 364 KB Output is correct
71 Correct 1 ms 364 KB Output is correct
72 Correct 1 ms 364 KB Output is correct
73 Correct 1 ms 364 KB Output is correct
74 Correct 1 ms 364 KB Output is correct
75 Correct 1 ms 364 KB Output is correct
76 Correct 126 ms 18912 KB Output is correct
77 Correct 127 ms 18860 KB Output is correct
78 Correct 122 ms 18916 KB Output is correct
79 Correct 123 ms 18884 KB Output is correct
80 Correct 130 ms 18660 KB Output is correct
81 Correct 125 ms 18660 KB Output is correct
82 Correct 123 ms 18532 KB Output is correct
83 Correct 131 ms 18752 KB Output is correct
84 Correct 127 ms 18532 KB Output is correct
85 Correct 128 ms 18148 KB Output is correct
86 Correct 121 ms 18276 KB Output is correct
87 Correct 120 ms 18276 KB Output is correct
88 Correct 122 ms 18276 KB Output is correct
89 Correct 124 ms 18276 KB Output is correct
90 Correct 121 ms 18276 KB Output is correct
91 Correct 120 ms 18020 KB Output is correct
92 Correct 132 ms 17900 KB Output is correct
93 Correct 127 ms 17892 KB Output is correct
94 Correct 118 ms 18108 KB Output is correct
95 Correct 132 ms 17792 KB Output is correct
96 Correct 122 ms 17636 KB Output is correct
97 Correct 124 ms 17636 KB Output is correct
98 Correct 126 ms 17764 KB Output is correct
99 Correct 120 ms 17636 KB Output is correct
100 Correct 124 ms 17508 KB Output is correct