oj.uz

Submission #396489

# Submission time Handle Problem Language Result Execution time Memory
396489 2021-04-30T04:02:43 Z rama_pang Bigger segments (IZhO19_segments) C++17
100 / 100
 232 ms 28796 KB 
#include <bits/stdc++.h>
using namespace std;

class SegTree {
 public:
  int sz;
  vector<long long> coords;
  vector<pair<int, int>> tree;

  SegTree(int sz, vector<long long> coords) : sz(sz), coords(coords), tree(2 * sz, {-1e9, -1e9}) {}

  void Update(long long p, pair<int, int> x) {
    p = lower_bound(begin(coords), end(coords), p) - begin(coords);
    if (p == sz) return;
    for (p += sz; p > 0; p /= 2) tree[p] = max(tree[p], x);
  }

  pair<int, int> Query(long long l, long long r) {
    l = lower_bound(begin(coords), end(coords), l) - begin(coords);
    r = upper_bound(begin(coords), end(coords), r) - begin(coords);
    pair<int, int> res = {-1e9, -1e9};
    for (l += sz, r += sz; l < r; l /= 2, r /= 2) {
      if (l & 1) res = max(res, tree[l++]);
      if (r & 1) res = max(res, tree[--r]);
    }
    return res;
  }
};

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

  int N;
  cin >> N;

  vector<long long> A(N + 1);
  for (int i = 1; i <= N; i++) {
    cin >> A[i];
    A[i] += A[i - 1];
  }

  // dp[i] = (max_segments, last_segment_sum)
  // it is always optimal to maximize max_segments first, since
  // the more segments, the smaller the last_sum.
  //
  // dp[i] = j < i: (dp[j].seg + 1, prefix[i] - prefix[j]) if prefix[i] - prefix[j] >= dp[j].sum
  // criteria: prefix[i] >= dp[j].sum + prefix[j]
  // put (dp[j]) on position (dp[j].sum + prefix[j]), then:
  // We want max in position <= prefix[i]; find maximum possible j with maximum possible seg
  //   (since we want to minimize prefix[i] - prefix[j])
  // Just use segment tree. Time complexity: O(N log N).

  SegTree seg(N + 1, A);
  vector<pair<int, long long>> dp(N + 1);
  dp[0] = {0, 0};
  seg.Update(0, {0, 0});
  for (int i = 1; i <= N; i++) {
    auto q = seg.Query(0, A[i]);
    dp[i] = {q.first + 1, A[i] - A[q.second]};
    seg.Update(dp[i].second + A[i], {dp[i].first, i});
  }

  cout << dp[N].first << '\n';
  return 0;
}

Subtask #1
13.0 / 13.0

# 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 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 1 ms 204 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 1 ms 312 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 204 KB Output is correct

Subtask #2
14.0 / 14.0

# 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 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 1 ms 204 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 1 ms 312 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 1 ms 312 KB Output is correct
17 Correct 1 ms 332 KB Output is correct
18 Correct 1 ms 320 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 1 ms 332 KB Output is correct
26 Correct 1 ms 316 KB Output is correct
27 Correct 1 ms 332 KB Output is correct
28 Correct 1 ms 316 KB Output is correct
29 Correct 1 ms 316 KB Output is correct
30 Correct 1 ms 332 KB Output is correct

Subtask #3
10.0 / 10.0

# 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 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 1 ms 204 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 1 ms 312 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 1 ms 312 KB Output is correct
17 Correct 1 ms 332 KB Output is correct
18 Correct 1 ms 320 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 1 ms 332 KB Output is correct
26 Correct 1 ms 316 KB Output is correct
27 Correct 1 ms 332 KB Output is correct
28 Correct 1 ms 316 KB Output is correct
29 Correct 1 ms 316 KB Output is correct
30 Correct 1 ms 332 KB Output is correct
31 Correct 1 ms 456 KB Output is correct
32 Correct 2 ms 460 KB Output is correct
33 Correct 2 ms 460 KB Output is correct
34 Correct 2 ms 460 KB Output is correct
35 Correct 2 ms 460 KB Output is correct
36 Correct 2 ms 460 KB Output is correct
37 Correct 2 ms 460 KB Output is correct
38 Correct 1 ms 328 KB Output is correct
39 Correct 2 ms 460 KB Output is correct
40 Correct 2 ms 460 KB Output is correct
41 Correct 2 ms 460 KB Output is correct
42 Correct 2 ms 464 KB Output is correct
43 Correct 2 ms 460 KB Output is correct
44 Correct 2 ms 460 KB Output is correct
45 Correct 2 ms 460 KB Output is correct

Subtask #4
36.0 / 36.0

# 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 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 1 ms 204 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 1 ms 312 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 1 ms 312 KB Output is correct
17 Correct 1 ms 332 KB Output is correct
18 Correct 1 ms 320 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 1 ms 332 KB Output is correct
26 Correct 1 ms 316 KB Output is correct
27 Correct 1 ms 332 KB Output is correct
28 Correct 1 ms 316 KB Output is correct
29 Correct 1 ms 316 KB Output is correct
30 Correct 1 ms 332 KB Output is correct
31 Correct 1 ms 456 KB Output is correct
32 Correct 2 ms 460 KB Output is correct
33 Correct 2 ms 460 KB Output is correct
34 Correct 2 ms 460 KB Output is correct
35 Correct 2 ms 460 KB Output is correct
36 Correct 2 ms 460 KB Output is correct
37 Correct 2 ms 460 KB Output is correct
38 Correct 1 ms 328 KB Output is correct
39 Correct 2 ms 460 KB Output is correct
40 Correct 2 ms 460 KB Output is correct
41 Correct 2 ms 460 KB Output is correct
42 Correct 2 ms 464 KB Output is correct
43 Correct 2 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 28 ms 5160 KB Output is correct
47 Correct 34 ms 5436 KB Output is correct
48 Correct 40 ms 5824 KB Output is correct
49 Correct 39 ms 5944 KB Output is correct
50 Correct 40 ms 5948 KB Output is correct
51 Correct 40 ms 5948 KB Output is correct
52 Correct 20 ms 3140 KB Output is correct
53 Correct 12 ms 2016 KB Output is correct
54 Correct 37 ms 5156 KB Output is correct
55 Correct 40 ms 5948 KB Output is correct
56 Correct 35 ms 5436 KB Output is correct
57 Correct 33 ms 5444 KB Output is correct
58 Correct 34 ms 5396 KB Output is correct
59 Correct 36 ms 5632 KB Output is correct
60 Correct 37 ms 5564 KB Output is correct

Subtask #5
27.0 / 27.0

# 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 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 1 ms 204 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 1 ms 312 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 1 ms 312 KB Output is correct
17 Correct 1 ms 332 KB Output is correct
18 Correct 1 ms 320 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 1 ms 332 KB Output is correct
26 Correct 1 ms 316 KB Output is correct
27 Correct 1 ms 332 KB Output is correct
28 Correct 1 ms 316 KB Output is correct
29 Correct 1 ms 316 KB Output is correct
30 Correct 1 ms 332 KB Output is correct
31 Correct 1 ms 456 KB Output is correct
32 Correct 2 ms 460 KB Output is correct
33 Correct 2 ms 460 KB Output is correct
34 Correct 2 ms 460 KB Output is correct
35 Correct 2 ms 460 KB Output is correct
36 Correct 2 ms 460 KB Output is correct
37 Correct 2 ms 460 KB Output is correct
38 Correct 1 ms 328 KB Output is correct
39 Correct 2 ms 460 KB Output is correct
40 Correct 2 ms 460 KB Output is correct
41 Correct 2 ms 460 KB Output is correct
42 Correct 2 ms 464 KB Output is correct
43 Correct 2 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 28 ms 5160 KB Output is correct
47 Correct 34 ms 5436 KB Output is correct
48 Correct 40 ms 5824 KB Output is correct
49 Correct 39 ms 5944 KB Output is correct
50 Correct 40 ms 5948 KB Output is correct
51 Correct 40 ms 5948 KB Output is correct
52 Correct 20 ms 3140 KB Output is correct
53 Correct 12 ms 2016 KB Output is correct
54 Correct 37 ms 5156 KB Output is correct
55 Correct 40 ms 5948 KB Output is correct
56 Correct 35 ms 5436 KB Output is correct
57 Correct 33 ms 5444 KB Output is correct
58 Correct 34 ms 5396 KB Output is correct
59 Correct 36 ms 5632 KB Output is correct
60 Correct 37 ms 5564 KB Output is correct
61 Correct 153 ms 25764 KB Output is correct
62 Correct 167 ms 25768 KB Output is correct
63 Correct 224 ms 26236 KB Output is correct
64 Correct 217 ms 28468 KB Output is correct
65 Correct 202 ms 28796 KB Output is correct
66 Correct 222 ms 28732 KB Output is correct
67 Correct 176 ms 22984 KB Output is correct
68 Correct 81 ms 11584 KB Output is correct
69 Correct 210 ms 24856 KB Output is correct
70 Correct 217 ms 28724 KB Output is correct
71 Correct 187 ms 25664 KB Output is correct
72 Correct 180 ms 26156 KB Output is correct
73 Correct 223 ms 26752 KB Output is correct
74 Correct 232 ms 27008 KB Output is correct
75 Correct 193 ms 27132 KB Output is correct