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Submission #389127

# Submission time Handle Problem Language Result Execution time Memory
389127 2021-04-13T17:06:32 Z solaimanope Safety (NOI18_safety) C++17
100 / 100
 62 ms 5188 KB 
#include<bits/stdc++.h>
using namespace std;
typedef long long LL;

/**
 * @brief Slope-Trick
 * @see https://maspypy.com/slope-trick-1-%E8%A7%A3%E8%AA%AC%E7%B7%A8
 */
template< typename T >
struct SlopeTrick {

    const T INF = numeric_limits< T >::max() / 3;

    T min_f;
    priority_queue< T, vector< T >, less<> > L;
    priority_queue< T, vector< T >, greater<> > R;
    T add_l, add_r;


private:
    void push_R(const T &a) {
        R.push(a - add_r);
    }

    T top_R() const {
        return R.top() + add_r;
    }

    T pop_R() {
        T val = top_R();
        R.pop();
        return val;
    }

    void push_L(const T &a) {
        L.push(a - add_l);
    }

    T top_L() const {
        return L.top() + add_l;
    }

    T pop_L() {
        T val = top_L();
        L.pop();
        return val;
    }

public:
    SlopeTrick() : min_f(0), add_l(0), add_r(0) {
        L.push(-INF);
        R.push(INF);
    }

    struct Query {
        T lx, rx, min_f;
    };

    // return min f(x)
    Query query() const {
        return (Query) {top_L(), top_R(), min_f};
    }

    // f(x) += a
    void add_all(const T &a) {
        min_f += a;
    }

    // add \_
    // f(x) += max(a - x, 0)
    void add_a_minus_x(const T &a) {
        min_f += max(T(0), a - top_R());
        push_R(a);
        push_L(pop_R());
    }

    // add _/
    // f(x) += max(x - a, 0)
    void add_x_minus_a(const T &a) {
        min_f += max(T(0), top_L() - a);
        push_L(a);
        push_R(pop_L());
    }

    // add \/
    // f(x) += abs(x - a)
//    void add_abs(const T &a) {
//        add_a_minus_x(a);
//        add_x_minus_a(a);
//    }

    void add_abs(const T &a) {
        if (a < top_L()) {
            min_f += top_L() - a;
            push_L(a);
            push_L(a);
            push_R(pop_L());
        } else if (top_R() < a) {
            min_f += a - top_R();
            push_R(a);
            push_R(a);
            push_L(pop_R());
        } else {
            push_L(a);
            push_R(a);
        }
    }

    // \/ -> \_
    // f_{new} (x) = min f(y) (y <= x)
    void clear_right() {
        while(R.size() >= 2) R.pop();
    }

    // \/ -> _/
    // f_{new} (x) = min f(y) (y >= x)
    void clear_left() {
        while(L.size() >= 2) L.pop();
    }

    // \/. -> .\/
    // f_{new} (x) = f(x - a)
    void shift(const T &a) {
        add_l += a;
        add_r += a;
    }


    T get(const T &x) {
        T ret = min_f;

        if (!L.empty() && x < top_L()) {
            while(!L.empty()) {
                ret += max(T(0), pop_L() - x);
            }
        }
        if (!R.empty() && top_R() < x) {
            while(!R.empty()) {
                ret += max(T(0), x - pop_R());
            }
        }
        return ret;
    }

};

const int MAXN = 2e5+7;
LL S[MAXN];


int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);

    int n; LL H;
    cin >> n >> H;
    for (int i = 1; i <= n; i++) cin >> S[i];

    SlopeTrick<LL>trick;
    trick.add_abs(0);

    for (int i = 2; i <= n; i++) {
        trick.add_r -= S[i]-S[i-1]-H;
        trick.add_l -= S[i]-S[i-1]+H;
        trick.add_abs(0);
    }

    cout << trick.min_f << "\n";


    return 0;
}

Subtask #1
3.0 / 3.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 0 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 0 ms 204 KB Output is correct
7 Correct 0 ms 204 KB Output is correct

Subtask #2
4.0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 0 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 0 ms 204 KB Output is correct

Subtask #3
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 0 ms 204 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 1 ms 204 KB Output is correct

Subtask #4
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 39 ms 4552 KB Output is correct
2 Correct 55 ms 4932 KB Output is correct
3 Correct 57 ms 4956 KB Output is correct

Subtask #5
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 0 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 0 ms 204 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 0 ms 204 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 0 ms 204 KB Output is correct
12 Correct 0 ms 204 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 1 ms 332 KB Output is correct
17 Correct 0 ms 332 KB Output is correct
18 Correct 1 ms 332 KB Output is correct
19 Correct 1 ms 332 KB Output is correct

Subtask #6
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 0 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 0 ms 204 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 0 ms 204 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 0 ms 204 KB Output is correct
12 Correct 0 ms 204 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 1 ms 332 KB Output is correct
17 Correct 0 ms 332 KB Output is correct
18 Correct 1 ms 332 KB Output is correct
19 Correct 1 ms 332 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 0 ms 332 KB Output is correct
26 Correct 1 ms 332 KB Output is correct
27 Correct 1 ms 332 KB Output is correct

Subtask #7
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 0 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 0 ms 204 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 0 ms 204 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 0 ms 204 KB Output is correct
12 Correct 0 ms 204 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 1 ms 332 KB Output is correct
17 Correct 0 ms 332 KB Output is correct
18 Correct 1 ms 332 KB Output is correct
19 Correct 1 ms 332 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 0 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 2 ms 460 KB Output is correct
29 Correct 1 ms 460 KB Output is correct
30 Correct 2 ms 460 KB Output is correct
31 Correct 1 ms 332 KB Output is correct
32 Correct 1 ms 460 KB Output is correct
33 Correct 1 ms 460 KB Output is correct
34 Correct 1 ms 460 KB Output is correct

Subtask #8
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 0 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 0 ms 204 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 0 ms 204 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 0 ms 204 KB Output is correct
12 Correct 0 ms 204 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 0 ms 204 KB Output is correct
16 Correct 0 ms 204 KB Output is correct
17 Correct 1 ms 204 KB Output is correct
18 Correct 1 ms 204 KB Output is correct
19 Correct 1 ms 332 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 0 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 332 KB Output is correct
31 Correct 0 ms 332 KB Output is correct
32 Correct 1 ms 332 KB Output is correct
33 Correct 1 ms 332 KB Output is correct
34 Correct 2 ms 460 KB Output is correct
35 Correct 1 ms 460 KB Output is correct
36 Correct 2 ms 460 KB Output is correct
37 Correct 1 ms 332 KB Output is correct
38 Correct 1 ms 460 KB Output is correct
39 Correct 1 ms 460 KB Output is correct
40 Correct 1 ms 460 KB Output is correct
41 Correct 2 ms 460 KB Output is correct
42 Correct 2 ms 460 KB Output is correct
43 Correct 2 ms 460 KB Output is correct
44 Correct 2 ms 460 KB Output is correct
45 Correct 1 ms 460 KB Output is correct
46 Correct 2 ms 464 KB Output is correct

Subtask #9
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 0 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 0 ms 204 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 0 ms 204 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 0 ms 204 KB Output is correct
12 Correct 0 ms 204 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 0 ms 204 KB Output is correct
16 Correct 0 ms 204 KB Output is correct
17 Correct 1 ms 204 KB Output is correct
18 Correct 1 ms 204 KB Output is correct
19 Correct 39 ms 4552 KB Output is correct
20 Correct 55 ms 4932 KB Output is correct
21 Correct 57 ms 4956 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 0 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 332 KB Output is correct
31 Correct 1 ms 332 KB Output is correct
32 Correct 1 ms 332 KB Output is correct
33 Correct 1 ms 332 KB Output is correct
34 Correct 0 ms 332 KB Output is correct
35 Correct 1 ms 332 KB Output is correct
36 Correct 1 ms 332 KB Output is correct
37 Correct 2 ms 460 KB Output is correct
38 Correct 1 ms 460 KB Output is correct
39 Correct 2 ms 460 KB Output is correct
40 Correct 1 ms 332 KB Output is correct
41 Correct 1 ms 460 KB Output is correct
42 Correct 1 ms 460 KB Output is correct
43 Correct 1 ms 460 KB Output is correct
44 Correct 2 ms 460 KB Output is correct
45 Correct 2 ms 460 KB Output is correct
46 Correct 2 ms 460 KB Output is correct
47 Correct 2 ms 460 KB Output is correct
48 Correct 1 ms 460 KB Output is correct
49 Correct 2 ms 464 KB Output is correct
50 Correct 62 ms 5168 KB Output is correct
51 Correct 51 ms 4760 KB Output is correct
52 Correct 33 ms 4792 KB Output is correct
53 Correct 39 ms 5116 KB Output is correct
54 Correct 57 ms 5188 KB Output is correct
55 Correct 34 ms 4832 KB Output is correct
56 Correct 37 ms 4916 KB Output is correct
57 Correct 46 ms 4784 KB Output is correct
58 Correct 35 ms 4632 KB Output is correct
59 Correct 45 ms 4964 KB Output is correct