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Submission #1029263

# Submission time Handle Problem Language Result Execution time Memory
1029263 2024-07-20T14:27:11 Z avighna Discharging (NOI20_discharging) C++17
100 / 100
 194 ms 196440 KB 
#include <bits/stdc++.h>

typedef long long ll;

class SparseTable {
public:
  ll maxPow;
  std::vector<ll> orig;
  std::vector<std::vector<ll>> table_max;

  SparseTable(const std::vector<ll> &x) : orig(x) {
    const ll n = x.size();
    maxPow = std::floor(std::log2(n));
    table_max = std::vector<std::vector<ll>>(maxPow + 1, std::vector<ll>(n));
    for (ll i = 0; i < n; ++i) {
      table_max[0][i] = x[i];
    }
    for (ll power = 1; power <= maxPow; ++power) {
      for (ll i = 0; i < n - (1 << (power - 1)); ++i) {
        table_max[power][i] =
            std::max(table_max[power - 1][i],
                     table_max[power - 1][i + (1 << (power - 1))]);
      }
    }
  }

  ll query_max(ll a, ll b) {
    if (a == b) {
      return orig[a];
    }
    ll pow_to_use = std::ceil(std::log2(b - a + 1)) - 1;
    return std::max(table_max[pow_to_use][a],
                    table_max[pow_to_use][b - (1 << pow_to_use) + 1]);
  }
};

struct Line {
  ll m, b;

  Line() {}
  Line(ll m, ll b) : m(m), b(b) {}

  ll operator()(ll x) { return m * x + b; }
};

class CHT {
private:
  long double x_intersect(const Line &l1, const Line &l2) {
    return -(l1.b - l2.b) / ((long double)(l1.m - l2.m));
  }

public:
  std::deque<Line> dq;

  void insert(Line l) {
    while (dq.size() > 1 &&
           x_intersect(dq[0], dq[1]) <= x_intersect(dq[0], l)) {
      dq.pop_front();
    }
    dq.push_front(l);
  }

  ll query(ll x) {
    while (dq.size() > 1 && dq[dq.size() - 1](x) <= dq[dq.size() - 2](x)) {
      dq.pop_back();
    }
    return dq.back()(x);
  }
};

int main() {
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(nullptr);

  ll n;
  std::cin >> n;
  std::vector<ll> a(n), val(n);
  std::vector<bool> active(n);
  for (ll i = 0, mx = 0, prev = -1; i < n; ++i) {
    std::cin >> a[i];
    if (a[i] > mx) {
      mx = a[i];
      val[i] = prev;
      active[i] = true;
      prev = mx;
    }
  }

  std::vector<ll> dp(n);
  SparseTable table(a);
  CHT convex_hull;
  for (ll i = n - 1, j = -1, suff_max = 0; i >= 0; --i) {
    suff_max = std::max(suff_max, a[i]);
    dp[i] = suff_max * (n - i);
    if (!convex_hull.dq.empty()) {
      dp[i] = std::min(dp[i], -convex_hull.query(i));
    }
    if (j != -1) {
      dp[i] = std::min(dp[i], table.query_max(i, j - 1) * (n - i) + dp[j]);
    }
    if (active[i]) {
      if (j != -1) {
        convex_hull.insert({val[j], -dp[j] - val[j] * n});
      }
      j = i;
    }
  }
  std::cout << dp[0] << '\n';
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 344 KB Output is correct
3 Correct 0 ms 344 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 344 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct

Subtask #2
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 604 KB Output is correct
2 Correct 1 ms 604 KB Output is correct
3 Correct 0 ms 604 KB Output is correct
4 Correct 0 ms 604 KB Output is correct
5 Correct 1 ms 600 KB Output is correct
6 Correct 0 ms 604 KB Output is correct
7 Correct 0 ms 604 KB Output is correct
8 Correct 0 ms 604 KB Output is correct
9 Correct 0 ms 604 KB Output is correct
10 Correct 1 ms 604 KB Output is correct
11 Correct 0 ms 604 KB Output is correct
12 Correct 0 ms 604 KB Output is correct
13 Correct 0 ms 604 KB Output is correct
14 Correct 1 ms 604 KB Output is correct
15 Correct 0 ms 604 KB Output is correct

Subtask #3
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 604 KB Output is correct
2 Correct 1 ms 604 KB Output is correct
3 Correct 0 ms 604 KB Output is correct
4 Correct 0 ms 604 KB Output is correct
5 Correct 1 ms 600 KB Output is correct
6 Correct 0 ms 604 KB Output is correct
7 Correct 0 ms 604 KB Output is correct
8 Correct 0 ms 604 KB Output is correct
9 Correct 0 ms 604 KB Output is correct
10 Correct 1 ms 604 KB Output is correct
11 Correct 0 ms 604 KB Output is correct
12 Correct 0 ms 604 KB Output is correct
13 Correct 0 ms 604 KB Output is correct
14 Correct 1 ms 604 KB Output is correct
15 Correct 0 ms 604 KB Output is correct
16 Correct 152 ms 196320 KB Output is correct
17 Correct 161 ms 196180 KB Output is correct
18 Correct 161 ms 196212 KB Output is correct
19 Correct 178 ms 196180 KB Output is correct
20 Correct 151 ms 196204 KB Output is correct
21 Correct 161 ms 196212 KB Output is correct
22 Correct 161 ms 196180 KB Output is correct
23 Correct 151 ms 196176 KB Output is correct
24 Correct 161 ms 196200 KB Output is correct
25 Correct 180 ms 196220 KB Output is correct
26 Correct 163 ms 196180 KB Output is correct
27 Correct 151 ms 196192 KB Output is correct
28 Correct 152 ms 196180 KB Output is correct
29 Correct 158 ms 196200 KB Output is correct
30 Correct 160 ms 196176 KB Output is correct

Subtask #4
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 143 ms 196212 KB Output is correct
2 Correct 150 ms 196212 KB Output is correct
3 Correct 133 ms 196176 KB Output is correct
4 Correct 150 ms 196192 KB Output is correct
5 Correct 152 ms 196440 KB Output is correct
6 Correct 144 ms 196180 KB Output is correct
7 Correct 194 ms 196180 KB Output is correct
8 Correct 146 ms 196200 KB Output is correct
9 Correct 138 ms 196204 KB Output is correct
10 Correct 144 ms 196180 KB Output is correct

Subtask #5
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 344 KB Output is correct
3 Correct 0 ms 344 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 344 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 1 ms 604 KB Output is correct
16 Correct 1 ms 604 KB Output is correct
17 Correct 0 ms 604 KB Output is correct
18 Correct 0 ms 604 KB Output is correct
19 Correct 1 ms 600 KB Output is correct
20 Correct 0 ms 604 KB Output is correct
21 Correct 0 ms 604 KB Output is correct
22 Correct 0 ms 604 KB Output is correct
23 Correct 0 ms 604 KB Output is correct
24 Correct 1 ms 604 KB Output is correct
25 Correct 0 ms 604 KB Output is correct
26 Correct 0 ms 604 KB Output is correct
27 Correct 0 ms 604 KB Output is correct
28 Correct 1 ms 604 KB Output is correct
29 Correct 0 ms 604 KB Output is correct
30 Correct 0 ms 604 KB Output is correct
31 Correct 0 ms 604 KB Output is correct
32 Correct 0 ms 604 KB Output is correct
33 Correct 0 ms 604 KB Output is correct
34 Correct 0 ms 604 KB Output is correct
35 Correct 1 ms 604 KB Output is correct
36 Correct 0 ms 604 KB Output is correct
37 Correct 0 ms 600 KB Output is correct
38 Correct 0 ms 604 KB Output is correct
39 Correct 1 ms 604 KB Output is correct
40 Correct 0 ms 604 KB Output is correct
41 Correct 1 ms 604 KB Output is correct
42 Correct 0 ms 640 KB Output is correct
43 Correct 1 ms 604 KB Output is correct
44 Correct 1 ms 604 KB Output is correct
45 Correct 0 ms 604 KB Output is correct
46 Correct 0 ms 604 KB Output is correct
47 Correct 1 ms 604 KB Output is correct
48 Correct 0 ms 604 KB Output is correct
49 Correct 0 ms 604 KB Output is correct
50 Correct 0 ms 604 KB Output is correct

Subtask #6
28.0 / 28.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 344 KB Output is correct
3 Correct 0 ms 344 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 344 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 0 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 1 ms 604 KB Output is correct
16 Correct 1 ms 604 KB Output is correct
17 Correct 0 ms 604 KB Output is correct
18 Correct 0 ms 604 KB Output is correct
19 Correct 1 ms 600 KB Output is correct
20 Correct 0 ms 604 KB Output is correct
21 Correct 0 ms 604 KB Output is correct
22 Correct 0 ms 604 KB Output is correct
23 Correct 0 ms 604 KB Output is correct
24 Correct 1 ms 604 KB Output is correct
25 Correct 0 ms 604 KB Output is correct
26 Correct 0 ms 604 KB Output is correct
27 Correct 0 ms 604 KB Output is correct
28 Correct 1 ms 604 KB Output is correct
29 Correct 0 ms 604 KB Output is correct
30 Correct 152 ms 196320 KB Output is correct
31 Correct 161 ms 196180 KB Output is correct
32 Correct 161 ms 196212 KB Output is correct
33 Correct 178 ms 196180 KB Output is correct
34 Correct 151 ms 196204 KB Output is correct
35 Correct 161 ms 196212 KB Output is correct
36 Correct 161 ms 196180 KB Output is correct
37 Correct 151 ms 196176 KB Output is correct
38 Correct 161 ms 196200 KB Output is correct
39 Correct 180 ms 196220 KB Output is correct
40 Correct 163 ms 196180 KB Output is correct
41 Correct 151 ms 196192 KB Output is correct
42 Correct 152 ms 196180 KB Output is correct
43 Correct 158 ms 196200 KB Output is correct
44 Correct 160 ms 196176 KB Output is correct
45 Correct 143 ms 196212 KB Output is correct
46 Correct 150 ms 196212 KB Output is correct
47 Correct 133 ms 196176 KB Output is correct
48 Correct 150 ms 196192 KB Output is correct
49 Correct 152 ms 196440 KB Output is correct
50 Correct 144 ms 196180 KB Output is correct
51 Correct 194 ms 196180 KB Output is correct
52 Correct 146 ms 196200 KB Output is correct
53 Correct 138 ms 196204 KB Output is correct
54 Correct 144 ms 196180 KB Output is correct
55 Correct 0 ms 604 KB Output is correct
56 Correct 0 ms 604 KB Output is correct
57 Correct 0 ms 604 KB Output is correct
58 Correct 0 ms 604 KB Output is correct
59 Correct 0 ms 604 KB Output is correct
60 Correct 1 ms 604 KB Output is correct
61 Correct 0 ms 604 KB Output is correct
62 Correct 0 ms 600 KB Output is correct
63 Correct 0 ms 604 KB Output is correct
64 Correct 1 ms 604 KB Output is correct
65 Correct 0 ms 604 KB Output is correct
66 Correct 1 ms 604 KB Output is correct
67 Correct 0 ms 640 KB Output is correct
68 Correct 1 ms 604 KB Output is correct
69 Correct 1 ms 604 KB Output is correct
70 Correct 0 ms 604 KB Output is correct
71 Correct 0 ms 604 KB Output is correct
72 Correct 1 ms 604 KB Output is correct
73 Correct 0 ms 604 KB Output is correct
74 Correct 0 ms 604 KB Output is correct
75 Correct 0 ms 604 KB Output is correct
76 Correct 149 ms 196208 KB Output is correct
77 Correct 158 ms 196436 KB Output is correct
78 Correct 148 ms 196180 KB Output is correct
79 Correct 146 ms 196204 KB Output is correct
80 Correct 161 ms 196180 KB Output is correct
81 Correct 158 ms 196176 KB Output is correct
82 Correct 177 ms 196176 KB Output is correct
83 Correct 149 ms 196176 KB Output is correct
84 Correct 159 ms 196020 KB Output is correct
85 Correct 148 ms 196212 KB Output is correct
86 Correct 151 ms 196108 KB Output is correct
87 Correct 159 ms 196180 KB Output is correct
88 Correct 140 ms 196196 KB Output is correct
89 Correct 140 ms 196180 KB Output is correct
90 Correct 136 ms 196212 KB Output is correct
91 Correct 138 ms 196176 KB Output is correct
92 Correct 164 ms 196216 KB Output is correct
93 Correct 162 ms 196180 KB Output is correct
94 Correct 147 ms 196008 KB Output is correct
95 Correct 143 ms 196180 KB Output is correct
96 Correct 137 ms 196180 KB Output is correct
97 Correct 135 ms 196180 KB Output is correct
98 Correct 134 ms 196176 KB Output is correct
99 Correct 141 ms 196032 KB Output is correct
100 Correct 137 ms 196208 KB Output is correct