oj.uz

Submission #321052

# Submission time Handle Problem Language Result Execution time Memory
321052 2020-11-10T18:37:46 Z saarang123 Discharging (NOI20_discharging) C++14
100 / 100
 175 ms 17380 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.rbegin(), dq.rend(),  //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.query(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 364 KB Output is correct
3 Correct 0 ms 364 KB Output is correct
4 Correct 0 ms 364 KB Output is correct
5 Correct 0 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 0 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 0 ms 364 KB Output is correct

Subtask #2
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 364 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 364 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 154 ms 16996 KB Output is correct
17 Correct 163 ms 17092 KB Output is correct
18 Correct 145 ms 17380 KB Output is correct
19 Correct 162 ms 16996 KB Output is correct
20 Correct 159 ms 16996 KB Output is correct
21 Correct 166 ms 17124 KB Output is correct
22 Correct 158 ms 16996 KB Output is correct
23 Correct 174 ms 17252 KB Output is correct
24 Correct 163 ms 16996 KB Output is correct
25 Correct 172 ms 17252 KB Output is correct
26 Correct 172 ms 17084 KB Output is correct
27 Correct 152 ms 17124 KB Output is correct
28 Correct 162 ms 17120 KB Output is correct
29 Correct 167 ms 17000 KB Output is correct
30 Correct 169 ms 16996 KB Output is correct

Subtask #4
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 175 ms 16868 KB Output is correct
2 Correct 175 ms 16996 KB Output is correct
3 Correct 170 ms 16868 KB Output is correct
4 Correct 170 ms 16868 KB Output is correct
5 Correct 170 ms 16996 KB Output is correct
6 Correct 173 ms 16996 KB Output is correct
7 Correct 173 ms 17000 KB Output is correct
8 Correct 170 ms 16868 KB Output is correct
9 Correct 169 ms 16868 KB Output is correct
10 Correct 168 ms 16872 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 364 KB Output is correct
3 Correct 0 ms 364 KB Output is correct
4 Correct 0 ms 364 KB Output is correct
5 Correct 0 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 0 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 0 ms 364 KB Output is correct
15 Correct 1 ms 364 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 364 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 508 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 364 KB Output is correct
3 Correct 0 ms 364 KB Output is correct
4 Correct 0 ms 364 KB Output is correct
5 Correct 0 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 0 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 0 ms 364 KB Output is correct
15 Correct 1 ms 364 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 154 ms 16996 KB Output is correct
31 Correct 163 ms 17092 KB Output is correct
32 Correct 145 ms 17380 KB Output is correct
33 Correct 162 ms 16996 KB Output is correct
34 Correct 159 ms 16996 KB Output is correct
35 Correct 166 ms 17124 KB Output is correct
36 Correct 158 ms 16996 KB Output is correct
37 Correct 174 ms 17252 KB Output is correct
38 Correct 163 ms 16996 KB Output is correct
39 Correct 172 ms 17252 KB Output is correct
40 Correct 172 ms 17084 KB Output is correct
41 Correct 152 ms 17124 KB Output is correct
42 Correct 162 ms 17120 KB Output is correct
43 Correct 167 ms 17000 KB Output is correct
44 Correct 169 ms 16996 KB Output is correct
45 Correct 175 ms 16868 KB Output is correct
46 Correct 175 ms 16996 KB Output is correct
47 Correct 170 ms 16868 KB Output is correct
48 Correct 170 ms 16868 KB Output is correct
49 Correct 170 ms 16996 KB Output is correct
50 Correct 173 ms 16996 KB Output is correct
51 Correct 173 ms 17000 KB Output is correct
52 Correct 170 ms 16868 KB Output is correct
53 Correct 169 ms 16868 KB Output is correct
54 Correct 168 ms 16872 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 364 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 508 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 155 ms 17156 KB Output is correct
77 Correct 149 ms 16996 KB Output is correct
78 Correct 146 ms 17092 KB Output is correct
79 Correct 148 ms 16996 KB Output is correct
80 Correct 157 ms 16996 KB Output is correct
81 Correct 150 ms 17124 KB Output is correct
82 Correct 145 ms 16996 KB Output is correct
83 Correct 149 ms 16996 KB Output is correct
84 Correct 149 ms 16996 KB Output is correct
85 Correct 155 ms 16996 KB Output is correct
86 Correct 143 ms 16996 KB Output is correct
87 Correct 144 ms 16996 KB Output is correct
88 Correct 147 ms 16996 KB Output is correct
89 Correct 154 ms 17124 KB Output is correct
90 Correct 147 ms 16996 KB Output is correct
91 Correct 144 ms 16996 KB Output is correct
92 Correct 171 ms 16996 KB Output is correct
93 Correct 163 ms 16996 KB Output is correct
94 Correct 147 ms 17148 KB Output is correct
95 Correct 150 ms 16996 KB Output is correct
96 Correct 147 ms 16996 KB Output is correct
97 Correct 145 ms 16996 KB Output is correct
98 Correct 148 ms 17124 KB Output is correct
99 Correct 148 ms 17124 KB Output is correct
100 Correct 147 ms 17124 KB Output is correct