oj.uz

Submission #1029258

# Submission time Handle Problem Language Result Execution time Memory
1029258 2024-07-20T14:21:27 Z avighna Discharging (NOI20_discharging) C++17
100 / 100
 201 ms 202832 KB 
#include <bits/stdc++.h>

typedef long long ll;

struct Line {
  ll m, b;

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

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

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 powToUse = std::ceil(std::log2(b - a + 1)) - 1;
    return std::max(table_max[powToUse][a],
                    table_max[powToUse][b - (1 << powToUse) + 1]);
  }
};

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);
  for (auto &i : a) {
    std::cin >> i;
  }

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

  std::vector<ll> dp(n);
  ll suff_max = 0;
  ll j = -1;
  SparseTable table(a);
  CHT convex_hull;
  for (ll i = n - 1; 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) {
        // = (-val) * i + dp[j] + val * n
        ll m = -val[j];
        ll b = dp[j] + val[j] * n;
        // insertion is now largest to smallest based on slope
        convex_hull.insert({-m, -b});
      }
      j = i;
    }
  }
  std::cout << dp[0] << '\n';
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 448 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 344 KB Output is correct
8 Correct 0 ms 344 KB Output is correct
9 Correct 1 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 0 ms 604 KB Output is correct
3 Correct 1 ms 604 KB Output is correct
4 Correct 0 ms 468 KB Output is correct
5 Correct 1 ms 604 KB Output is correct
6 Correct 0 ms 604 KB Output is correct
7 Correct 0 ms 604 KB Output is correct
8 Correct 1 ms 856 KB Output is correct
9 Correct 1 ms 604 KB Output is correct
10 Correct 1 ms 604 KB Output is correct
11 Correct 1 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 600 KB Output is correct
15 Correct 1 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 0 ms 604 KB Output is correct
3 Correct 1 ms 604 KB Output is correct
4 Correct 0 ms 468 KB Output is correct
5 Correct 1 ms 604 KB Output is correct
6 Correct 0 ms 604 KB Output is correct
7 Correct 0 ms 604 KB Output is correct
8 Correct 1 ms 856 KB Output is correct
9 Correct 1 ms 604 KB Output is correct
10 Correct 1 ms 604 KB Output is correct
11 Correct 1 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 600 KB Output is correct
15 Correct 1 ms 604 KB Output is correct
16 Correct 201 ms 201148 KB Output is correct
17 Correct 167 ms 202200 KB Output is correct
18 Correct 166 ms 200524 KB Output is correct
19 Correct 166 ms 202016 KB Output is correct
20 Correct 190 ms 201804 KB Output is correct
21 Correct 169 ms 202068 KB Output is correct
22 Correct 170 ms 201548 KB Output is correct
23 Correct 168 ms 202580 KB Output is correct
24 Correct 172 ms 202196 KB Output is correct
25 Correct 167 ms 202572 KB Output is correct
26 Correct 173 ms 202832 KB Output is correct
27 Correct 160 ms 201292 KB Output is correct
28 Correct 169 ms 202068 KB Output is correct
29 Correct 160 ms 202308 KB Output is correct
30 Correct 165 ms 202580 KB Output is correct

Subtask #4
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 146 ms 196188 KB Output is correct
2 Correct 147 ms 196180 KB Output is correct
3 Correct 184 ms 196180 KB Output is correct
4 Correct 149 ms 196176 KB Output is correct
5 Correct 148 ms 196184 KB Output is correct
6 Correct 144 ms 196176 KB Output is correct
7 Correct 155 ms 196436 KB Output is correct
8 Correct 143 ms 196176 KB Output is correct
9 Correct 150 ms 196176 KB Output is correct
10 Correct 149 ms 196176 KB Output is correct

Subtask #5
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 448 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 344 KB Output is correct
8 Correct 0 ms 344 KB Output is correct
9 Correct 1 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 0 ms 604 KB Output is correct
17 Correct 1 ms 604 KB Output is correct
18 Correct 0 ms 468 KB Output is correct
19 Correct 1 ms 604 KB Output is correct
20 Correct 0 ms 604 KB Output is correct
21 Correct 0 ms 604 KB Output is correct
22 Correct 1 ms 856 KB Output is correct
23 Correct 1 ms 604 KB Output is correct
24 Correct 1 ms 604 KB Output is correct
25 Correct 1 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 600 KB Output is correct
29 Correct 1 ms 604 KB Output is correct
30 Correct 1 ms 600 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 460 KB Output is correct
35 Correct 0 ms 604 KB Output is correct
36 Correct 0 ms 604 KB Output is correct
37 Correct 1 ms 604 KB Output is correct
38 Correct 0 ms 600 KB Output is correct
39 Correct 0 ms 604 KB Output is correct
40 Correct 0 ms 604 KB Output is correct
41 Correct 0 ms 604 KB Output is correct
42 Correct 0 ms 604 KB Output is correct
43 Correct 0 ms 604 KB Output is correct
44 Correct 0 ms 460 KB Output is correct
45 Correct 1 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 1 ms 604 KB Output is correct
49 Correct 0 ms 612 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 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 448 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 344 KB Output is correct
8 Correct 0 ms 344 KB Output is correct
9 Correct 1 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 0 ms 604 KB Output is correct
17 Correct 1 ms 604 KB Output is correct
18 Correct 0 ms 468 KB Output is correct
19 Correct 1 ms 604 KB Output is correct
20 Correct 0 ms 604 KB Output is correct
21 Correct 0 ms 604 KB Output is correct
22 Correct 1 ms 856 KB Output is correct
23 Correct 1 ms 604 KB Output is correct
24 Correct 1 ms 604 KB Output is correct
25 Correct 1 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 600 KB Output is correct
29 Correct 1 ms 604 KB Output is correct
30 Correct 201 ms 201148 KB Output is correct
31 Correct 167 ms 202200 KB Output is correct
32 Correct 166 ms 200524 KB Output is correct
33 Correct 166 ms 202016 KB Output is correct
34 Correct 190 ms 201804 KB Output is correct
35 Correct 169 ms 202068 KB Output is correct
36 Correct 170 ms 201548 KB Output is correct
37 Correct 168 ms 202580 KB Output is correct
38 Correct 172 ms 202196 KB Output is correct
39 Correct 167 ms 202572 KB Output is correct
40 Correct 173 ms 202832 KB Output is correct
41 Correct 160 ms 201292 KB Output is correct
42 Correct 169 ms 202068 KB Output is correct
43 Correct 160 ms 202308 KB Output is correct
44 Correct 165 ms 202580 KB Output is correct
45 Correct 146 ms 196188 KB Output is correct
46 Correct 147 ms 196180 KB Output is correct
47 Correct 184 ms 196180 KB Output is correct
48 Correct 149 ms 196176 KB Output is correct
49 Correct 148 ms 196184 KB Output is correct
50 Correct 144 ms 196176 KB Output is correct
51 Correct 155 ms 196436 KB Output is correct
52 Correct 143 ms 196176 KB Output is correct
53 Correct 150 ms 196176 KB Output is correct
54 Correct 149 ms 196176 KB Output is correct
55 Correct 1 ms 600 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 460 KB Output is correct
60 Correct 0 ms 604 KB Output is correct
61 Correct 0 ms 604 KB Output is correct
62 Correct 1 ms 604 KB Output is correct
63 Correct 0 ms 600 KB Output is correct
64 Correct 0 ms 604 KB Output is correct
65 Correct 0 ms 604 KB Output is correct
66 Correct 0 ms 604 KB Output is correct
67 Correct 0 ms 604 KB Output is correct
68 Correct 0 ms 604 KB Output is correct
69 Correct 0 ms 460 KB Output is correct
70 Correct 1 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 1 ms 604 KB Output is correct
74 Correct 0 ms 612 KB Output is correct
75 Correct 0 ms 604 KB Output is correct
76 Correct 177 ms 202068 KB Output is correct
77 Correct 152 ms 202236 KB Output is correct
78 Correct 149 ms 201904 KB Output is correct
79 Correct 189 ms 201940 KB Output is correct
80 Correct 156 ms 202580 KB Output is correct
81 Correct 148 ms 201812 KB Output is correct
82 Correct 165 ms 201684 KB Output is correct
83 Correct 174 ms 202200 KB Output is correct
84 Correct 156 ms 202060 KB Output is correct
85 Correct 164 ms 202312 KB Output is correct
86 Correct 160 ms 201660 KB Output is correct
87 Correct 176 ms 201540 KB Output is correct
88 Correct 179 ms 202064 KB Output is correct
89 Correct 153 ms 201676 KB Output is correct
90 Correct 155 ms 201808 KB Output is correct
91 Correct 190 ms 201556 KB Output is correct
92 Correct 171 ms 202776 KB Output is correct
93 Correct 160 ms 201940 KB Output is correct
94 Correct 151 ms 201044 KB Output is correct
95 Correct 161 ms 202700 KB Output is correct
96 Correct 185 ms 201424 KB Output is correct
97 Correct 194 ms 201796 KB Output is correct
98 Correct 151 ms 202068 KB Output is correct
99 Correct 158 ms 201556 KB Output is correct
100 Correct 155 ms 201812 KB Output is correct