oj.uz

Submission #321055

# Submission time Handle Problem Language Result Execution time Memory
321055 2020-11-10T19:14:40 Z saarang123 Discharging (NOI20_discharging) C++14
100 / 100
 149 ms 17508 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.size() > 1 && 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
        //doing it in reverse as u can use lowerbound directly then (otherwise ull have to do --)
        auto ans = *lower_bound(dq.rbegin(), dq.rend(),
                                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); //querying all n at one time
    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);
        //we can qry for mx cuz the x coordinate has to be atleast mx (all under same time 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 0 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 0 ms 364 KB Output is correct
13 Correct 0 ms 364 KB Output is correct
14 Correct 1 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 360 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 360 KB Output is correct
15 Correct 1 ms 364 KB Output is correct
16 Correct 120 ms 17504 KB Output is correct
17 Correct 127 ms 17380 KB Output is correct
18 Correct 113 ms 17124 KB Output is correct
19 Correct 130 ms 17380 KB Output is correct
20 Correct 124 ms 17380 KB Output is correct
21 Correct 143 ms 17508 KB Output is correct
22 Correct 141 ms 17508 KB Output is correct
23 Correct 130 ms 17380 KB Output is correct
24 Correct 140 ms 17380 KB Output is correct
25 Correct 130 ms 17508 KB Output is correct
26 Correct 133 ms 17508 KB Output is correct
27 Correct 119 ms 17380 KB Output is correct
28 Correct 129 ms 17472 KB Output is correct
29 Correct 129 ms 17380 KB Output is correct
30 Correct 132 ms 17380 KB Output is correct

Subtask #4
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 145 ms 17380 KB Output is correct
2 Correct 145 ms 17384 KB Output is correct
3 Correct 145 ms 17388 KB Output is correct
4 Correct 146 ms 17380 KB Output is correct
5 Correct 146 ms 17508 KB Output is correct
6 Correct 143 ms 17376 KB Output is correct
7 Correct 144 ms 17380 KB Output is correct
8 Correct 149 ms 17420 KB Output is correct
9 Correct 148 ms 17508 KB Output is correct
10 Correct 145 ms 17380 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 0 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 0 ms 364 KB Output is correct
13 Correct 0 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 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 360 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 360 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 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 0 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 0 ms 364 KB Output is correct
13 Correct 0 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 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 360 KB Output is correct
29 Correct 1 ms 364 KB Output is correct
30 Correct 120 ms 17504 KB Output is correct
31 Correct 127 ms 17380 KB Output is correct
32 Correct 113 ms 17124 KB Output is correct
33 Correct 130 ms 17380 KB Output is correct
34 Correct 124 ms 17380 KB Output is correct
35 Correct 143 ms 17508 KB Output is correct
36 Correct 141 ms 17508 KB Output is correct
37 Correct 130 ms 17380 KB Output is correct
38 Correct 140 ms 17380 KB Output is correct
39 Correct 130 ms 17508 KB Output is correct
40 Correct 133 ms 17508 KB Output is correct
41 Correct 119 ms 17380 KB Output is correct
42 Correct 129 ms 17472 KB Output is correct
43 Correct 129 ms 17380 KB Output is correct
44 Correct 132 ms 17380 KB Output is correct
45 Correct 145 ms 17380 KB Output is correct
46 Correct 145 ms 17384 KB Output is correct
47 Correct 145 ms 17388 KB Output is correct
48 Correct 146 ms 17380 KB Output is correct
49 Correct 146 ms 17508 KB Output is correct
50 Correct 143 ms 17376 KB Output is correct
51 Correct 144 ms 17380 KB Output is correct
52 Correct 149 ms 17420 KB Output is correct
53 Correct 148 ms 17508 KB Output is correct
54 Correct 145 ms 17380 KB Output is correct
55 Correct 1 ms 364 KB Output is correct
56 Correct 1 ms 360 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 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 124 ms 17380 KB Output is correct
77 Correct 127 ms 17380 KB Output is correct
78 Correct 120 ms 17380 KB Output is correct
79 Correct 123 ms 17380 KB Output is correct
80 Correct 132 ms 17380 KB Output is correct
81 Correct 120 ms 17380 KB Output is correct
82 Correct 120 ms 17380 KB Output is correct
83 Correct 123 ms 17380 KB Output is correct
84 Correct 123 ms 17380 KB Output is correct
85 Correct 127 ms 17448 KB Output is correct
86 Correct 119 ms 17376 KB Output is correct
87 Correct 119 ms 17380 KB Output is correct
88 Correct 122 ms 17480 KB Output is correct
89 Correct 120 ms 17380 KB Output is correct
90 Correct 122 ms 17380 KB Output is correct
91 Correct 117 ms 17508 KB Output is correct
92 Correct 134 ms 17508 KB Output is correct
93 Correct 129 ms 17380 KB Output is correct
94 Correct 118 ms 17508 KB Output is correct
95 Correct 126 ms 17380 KB Output is correct
96 Correct 126 ms 17380 KB Output is correct
97 Correct 123 ms 17508 KB Output is correct
98 Correct 124 ms 17380 KB Output is correct
99 Correct 126 ms 17508 KB Output is correct
100 Correct 121 ms 17380 KB Output is correct