oj.uz

Submission #600465

# Submission time Handle Problem Language Result Execution time Memory
600465 2022-07-20T22:07:27 Z verngutz Discharging (NOI20_discharging) C++17
100 / 100
 183 ms 37104 KB 
#include <bits/stdc++.h>
#define err(args...) {}
#ifdef DEBUG
#include "_debug.cpp"
#endif
using namespace std;
using ll = long long;
using ld = long double;
template <typename T> using lim = numeric_limits<T>;
template <typename T> istream& operator>>(istream& is, vector<T>& a) { for(T& x : a) { is >> x; } return is; }
template <typename X, typename Y> istream& operator>>(istream& is, pair<X, Y>& p) { return is >> p.first >> p.second; }
template <typename Iter, typename T> int gt(Iter L, Iter R, T v) { return upper_bound(L, R, v) - L; }
template <typename Iter, typename T> int ge(Iter L, Iter R, T v) { return lower_bound(L, R, v) - L; }
template <typename Iter, typename T> int lt(Iter L, Iter R, T v) { return lower_bound(L, R, v) - L - 1; }
template <typename Iter, typename T> int le(Iter L, Iter R, T v) { return upper_bound(L, R, v) - L - 1; }
template <typename Bst, typename T> typename Bst::const_iterator gt(const Bst& bst, T v) { return bst.upper_bound(v); }
template <typename Bst, typename T> typename Bst::const_iterator ge(const Bst& bst, T v) { return bst.lower_bound(v); }
template <typename Bst, typename T> typename Bst::const_iterator lt(const Bst& bst, T v) { return bst.lower_bound(v) == bst.begin() ? bst.end() : --bst.lower_bound(v); }
template <typename Bst, typename T> typename Bst::const_iterator le(const Bst& bst, T v) { return bst.upper_bound(v) == bst.begin() ? bst.end() : --bst.upper_bound(v); }
// maintain an upper/lower hull L of lines y = mx + b
// query for y(x) such that y(x) is minimum/maximum over all lines y in L
// assumes lines are inserted in non-increasing/non-decreasing order of m
// minimization by default, call constructor with greater<ll>() for maximization
struct cht {
    struct line {
        ll m, b, intersection;
        ll eval(ll x) const { return m * x + b; }
        ll cross(const line& l) const { return (l.b - b) / (m - l.m); }
        bool operator<(const line& l) const { return m > l.m; }
        bool operator<(const ll x) const { return intersection < x; }
        friend bool operator<(const ll x, const line& l) { return x < l.intersection; }
    };
    multiset<line, less<>> h;
    const function<bool(ll, ll)> cmp;
    cht(const function<bool(ll, ll)>& cmp = less<ll>()) : cmp(cmp) {}
    const line& l1() { return *h.rbegin(); }
    const line& l2() { return *++h.rbegin(); }
    void pop() { h.erase(--h.end()); }
    void add(ll m, ll b) {
        if(h.empty()) {
            h.insert({m, b, numeric_limits<ll>::min()});
        } else if(m != l1().m or cmp(b, l1().b)) {
            if(m == l1().m) pop();
            while(h.size() >= 2 and l1().cross({m, b}) <= l1().cross(l2())) pop();
            h.insert({m, b, l1().cross({m, b})});
        }
    }
    ll opt(ll x) {
        assert(!h.empty());
        ll y1 = lt(h, x)->eval(x), y2 = le(h, x)->eval(x);
        return cmp(y1, y2) ? y1 : y2;
    }
};
template <typename T, typename Cmp = decltype(less<T>())>
vector<int> nsv(const vector<T>& a, int L, int R, int d, Cmp&& cmp = less<T>()) {
    static_assert(is_convertible<decltype(cmp), function<bool(T, T)>>::value);
    vector<int> s, nearest_smaller_to(a.size());
    for(int i = L; i != R; i += d) {
        while(not s.empty() and not cmp(a[s.back()], a[i])) {
            s.pop_back();
        }
        nearest_smaller_to[i] = s.empty() ? L - d : s.back();
        s.push_back(i);
    }
    return nearest_smaller_to;
}
template <typename T, typename Cmp = decltype(less<T>())>
vector<int> lnsv(const vector<T>& a, Cmp&& cmp = less<T>()) {
    return nsv(a, 0, a.size(), 1, cmp);
}
template <typename T, typename Cmp = decltype(less<T>())>
vector<int> rnsv(const vector<T>& a, Cmp&& cmp = less<T>()) {
    return nsv(a, a.size() - 1, -1, -1, cmp);
}
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    int n;
    cin >> n;
    vector<ll> t(n);
    cin >> t;
    auto lsv = lnsv(t);
    auto rgv = rnsv(t, greater<ll>());
    vector<ll> opt(n + 1);
    cht hull;
    vector<int> I;
    for(int i = 0; i < n; i = rgv[i]) {
        I.push_back(i);
    }
    I.push_back(n);
    for(int ii = I.size() - 1; ii >= 0; ii--) {
        int i = I[ii];
        if(i == n) {
            opt[i] = 0;
        } else {
            opt[i] = min(
                t[i] * (n - i) + opt[rgv[i]],
                hull.h.empty() ? lim<ll>::max() : hull.opt(n - i)
            );
        }    
        if(ii > 0) {
            hull.add(t[I[ii - 1]], opt[i]);
        }
    }
    cout << opt[0] << endl;
    return 0;
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 0 ms 320 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 1 ms 324 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 1 ms 212 KB Output is correct

Subtask #2
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 2 ms 340 KB Output is correct
3 Correct 1 ms 328 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 ms 332 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 340 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 384 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 1 ms 340 KB Output is correct

Subtask #3
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 2 ms 340 KB Output is correct
3 Correct 1 ms 328 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 ms 332 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 340 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 384 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 1 ms 340 KB Output is correct
16 Correct 148 ms 32380 KB Output is correct
17 Correct 145 ms 33508 KB Output is correct
18 Correct 113 ms 31380 KB Output is correct
19 Correct 145 ms 33304 KB Output is correct
20 Correct 143 ms 33456 KB Output is correct
21 Correct 153 ms 33396 KB Output is correct
22 Correct 166 ms 32840 KB Output is correct
23 Correct 161 ms 36704 KB Output is correct
24 Correct 153 ms 35844 KB Output is correct
25 Correct 166 ms 36236 KB Output is correct
26 Correct 183 ms 37104 KB Output is correct
27 Correct 130 ms 32380 KB Output is correct
28 Correct 139 ms 33556 KB Output is correct
29 Correct 158 ms 36092 KB Output is correct
30 Correct 168 ms 36656 KB Output is correct

Subtask #4
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 106 ms 33468 KB Output is correct
2 Correct 134 ms 33484 KB Output is correct
3 Correct 111 ms 33608 KB Output is correct
4 Correct 112 ms 33480 KB Output is correct
5 Correct 114 ms 33484 KB Output is correct
6 Correct 111 ms 33480 KB Output is correct
7 Correct 109 ms 33484 KB Output is correct
8 Correct 114 ms 33492 KB Output is correct
9 Correct 124 ms 33364 KB Output is correct
10 Correct 110 ms 33480 KB Output is correct

Subtask #5
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 0 ms 320 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 1 ms 324 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 1 ms 212 KB Output is correct
15 Correct 1 ms 340 KB Output is correct
16 Correct 2 ms 340 KB Output is correct
17 Correct 1 ms 328 KB Output is correct
18 Correct 1 ms 340 KB Output is correct
19 Correct 1 ms 340 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 332 KB Output is correct
23 Correct 1 ms 340 KB Output is correct
24 Correct 1 ms 340 KB Output is correct
25 Correct 1 ms 340 KB Output is correct
26 Correct 1 ms 340 KB Output is correct
27 Correct 1 ms 384 KB Output is correct
28 Correct 1 ms 340 KB Output is correct
29 Correct 1 ms 340 KB Output is correct
30 Correct 1 ms 324 KB Output is correct
31 Correct 1 ms 340 KB Output is correct
32 Correct 1 ms 340 KB Output is correct
33 Correct 1 ms 340 KB Output is correct
34 Correct 1 ms 340 KB Output is correct
35 Correct 1 ms 340 KB Output is correct
36 Correct 1 ms 340 KB Output is correct
37 Correct 1 ms 352 KB Output is correct
38 Correct 1 ms 340 KB Output is correct
39 Correct 1 ms 340 KB Output is correct
40 Correct 1 ms 340 KB Output is correct
41 Correct 1 ms 340 KB Output is correct
42 Correct 1 ms 328 KB Output is correct
43 Correct 1 ms 340 KB Output is correct
44 Correct 1 ms 340 KB Output is correct
45 Correct 1 ms 340 KB Output is correct
46 Correct 1 ms 340 KB Output is correct
47 Correct 1 ms 340 KB Output is correct
48 Correct 1 ms 328 KB Output is correct
49 Correct 1 ms 340 KB Output is correct
50 Correct 1 ms 324 KB Output is correct

Subtask #6
28.0 / 28.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 0 ms 320 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 0 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 1 ms 324 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 1 ms 212 KB Output is correct
15 Correct 1 ms 340 KB Output is correct
16 Correct 2 ms 340 KB Output is correct
17 Correct 1 ms 328 KB Output is correct
18 Correct 1 ms 340 KB Output is correct
19 Correct 1 ms 340 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 332 KB Output is correct
23 Correct 1 ms 340 KB Output is correct
24 Correct 1 ms 340 KB Output is correct
25 Correct 1 ms 340 KB Output is correct
26 Correct 1 ms 340 KB Output is correct
27 Correct 1 ms 384 KB Output is correct
28 Correct 1 ms 340 KB Output is correct
29 Correct 1 ms 340 KB Output is correct
30 Correct 148 ms 32380 KB Output is correct
31 Correct 145 ms 33508 KB Output is correct
32 Correct 113 ms 31380 KB Output is correct
33 Correct 145 ms 33304 KB Output is correct
34 Correct 143 ms 33456 KB Output is correct
35 Correct 153 ms 33396 KB Output is correct
36 Correct 166 ms 32840 KB Output is correct
37 Correct 161 ms 36704 KB Output is correct
38 Correct 153 ms 35844 KB Output is correct
39 Correct 166 ms 36236 KB Output is correct
40 Correct 183 ms 37104 KB Output is correct
41 Correct 130 ms 32380 KB Output is correct
42 Correct 139 ms 33556 KB Output is correct
43 Correct 158 ms 36092 KB Output is correct
44 Correct 168 ms 36656 KB Output is correct
45 Correct 106 ms 33468 KB Output is correct
46 Correct 134 ms 33484 KB Output is correct
47 Correct 111 ms 33608 KB Output is correct
48 Correct 112 ms 33480 KB Output is correct
49 Correct 114 ms 33484 KB Output is correct
50 Correct 111 ms 33480 KB Output is correct
51 Correct 109 ms 33484 KB Output is correct
52 Correct 114 ms 33492 KB Output is correct
53 Correct 124 ms 33364 KB Output is correct
54 Correct 110 ms 33480 KB Output is correct
55 Correct 1 ms 324 KB Output is correct
56 Correct 1 ms 340 KB Output is correct
57 Correct 1 ms 340 KB Output is correct
58 Correct 1 ms 340 KB Output is correct
59 Correct 1 ms 340 KB Output is correct
60 Correct 1 ms 340 KB Output is correct
61 Correct 1 ms 340 KB Output is correct
62 Correct 1 ms 352 KB Output is correct
63 Correct 1 ms 340 KB Output is correct
64 Correct 1 ms 340 KB Output is correct
65 Correct 1 ms 340 KB Output is correct
66 Correct 1 ms 340 KB Output is correct
67 Correct 1 ms 328 KB Output is correct
68 Correct 1 ms 340 KB Output is correct
69 Correct 1 ms 340 KB Output is correct
70 Correct 1 ms 340 KB Output is correct
71 Correct 1 ms 340 KB Output is correct
72 Correct 1 ms 340 KB Output is correct
73 Correct 1 ms 328 KB Output is correct
74 Correct 1 ms 340 KB Output is correct
75 Correct 1 ms 324 KB Output is correct
76 Correct 101 ms 29804 KB Output is correct
77 Correct 103 ms 29772 KB Output is correct
78 Correct 100 ms 29248 KB Output is correct
79 Correct 111 ms 29468 KB Output is correct
80 Correct 138 ms 30040 KB Output is correct
81 Correct 98 ms 29256 KB Output is correct
82 Correct 100 ms 29284 KB Output is correct
83 Correct 115 ms 29768 KB Output is correct
84 Correct 114 ms 29712 KB Output is correct
85 Correct 110 ms 29768 KB Output is correct
86 Correct 97 ms 29256 KB Output is correct
87 Correct 98 ms 29132 KB Output is correct
88 Correct 101 ms 29512 KB Output is correct
89 Correct 115 ms 29372 KB Output is correct
90 Correct 131 ms 29264 KB Output is correct
91 Correct 95 ms 29000 KB Output is correct
92 Correct 161 ms 34408 KB Output is correct
93 Correct 144 ms 33428 KB Output is correct
94 Correct 99 ms 28736 KB Output is correct
95 Correct 120 ms 30148 KB Output is correct
96 Correct 99 ms 28964 KB Output is correct
97 Correct 112 ms 29392 KB Output is correct
98 Correct 110 ms 29516 KB Output is correct
99 Correct 115 ms 29208 KB Output is correct
100 Correct 102 ms 29260 KB Output is correct