답안 #630796

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
630796	2022-08-17T03:57:46 Z	hltk	송신탑 (IOI22_towers)	C++17	11 / 100	4000 ms	4928 KB

towers

#include "towers.h"

#include <vector>
#include <set>
#include <iostream>
#include <queue>

using namespace std;

// The key observation.
//  - All towers have a 'banned region' that spans some elements
//    on both sides of the tower. It ends to either to the end
//    of the array, or to the next element with height larger
//    by at least D.
//
// Some further observations on 'banned regions'.
//  - If a tower is selected, no other towers from its banned
//    region may be selected. Thus, we need to select the
//    maximum amount of towers such that none of their banned
//    regions overlap.
//  - A region may be completely contained in a another. Let us
//    ignore this case from now on.
//  - Any two regions, that are not contained in each other, will not
//    intersect at any point other than an optional shared endpoint,
//    and because regions with a shared endpoint may be selected,
//    we will have to find the amount of regions when completely
//    contained regions are removed.
//  - If a region is contained inside another, it is optimal to remove
//    the larger only of them. If the ranges are exactly the same,
//    we will remove the one with a lower value of h[i].
//
// Ideas for the full solution.
//  - Let us first try to solve the problem for a fixed
//    value of D.
//  - We need to be able to efficiently answer range
//    queries, that is, we need to be able find the maximum amount
//    non-contained regions in a range.
//     - One solution, that is also easily made persistent, is
//       to use two segments trees. One for finding the first range,
//       and the other for finding the amount of ranges (by for example,
//       counting endpoints of ranges in the tree).
//  - Now it's pretty easy to generalize this for all values of D.
//  - Let us sweep through values of D.
//  - An increase in the value of D, can cause some ranges to lengthen.
//  - It may happen that when a range lengthens it 'eats' another range
//    inside of it, which makes it redundant.
//  - Let us start with D = 1 and the largest possible set of
//    non-contained ranges.
//  - We have to account for the 'eating' of regions, while keeping
//    track of the ranges.
//  - At any point, the amount of regions in a query range, is the answer
//    to the range query.
//  - One more important observation. The optimal set of regions forms
//    a continuous chain, which makes it easy to maintain as any
//    lengthening will cause ranges to 'eat' each other, and thus
//    cause a removal.

int n;
vector<int> h;

void init(int n, vector<int> h) {
  ::n = n;
  ::h = h;
}

int max_towers(int l, int r, int d) {
  r++;
  vector<int> region_start(n), region_end(n);
  for (int i = l; i < r; ++i) {
    region_start[i] = i;
    while (region_start[i] >= 0 && h[region_start[i]] < h[i] + d) {
      region_start[i]--;
    }
    region_start[i] = max(region_start[i], l);
    region_end[i] = i;
    while (region_end[i] < r && h[region_end[i]] < h[i] + d) {
      region_end[i]++;
    }
    region_end[i] = min(region_end[i], r - 1);
  }
  priority_queue<pair<int, int>> ranges;
  for (int i = l; i < r; ++i) {
    ranges.emplace(region_start[i] - region_end[i], i);
  }
  set<pair<int, int>> added;
  while (!ranges.empty()) {
    int i = ranges.top().second;
    ranges.pop();
    int l = region_start[i], r = region_end[i];
    auto it = added.lower_bound({l, 0});
    if (!(it != added.end() && it->second <= r)) {
      added.emplace(l, r);
    }
  }
  return added.size();
}

Subtask #1
0 / 4.0

#	결과	실행 시간	메모리	Grader output
1	Execution timed out	4088 ms	2224 KB	Time limit exceeded
2	Halted	0 ms	0 KB	-

Subtask #2
11.0 / 11.0

#	결과	실행 시간	메모리	Grader output
1	Correct	0 ms	208 KB	Output is correct
2	Correct	1 ms	336 KB	Output is correct
3	Correct	2 ms	336 KB	Output is correct
4	Correct	1 ms	336 KB	Output is correct
5	Correct	1 ms	336 KB	Output is correct
6	Correct	1 ms	208 KB	Output is correct
7	Correct	1 ms	336 KB	Output is correct
8	Correct	1 ms	208 KB	Output is correct
9	Correct	1 ms	208 KB	Output is correct
10	Correct	1 ms	208 KB	Output is correct
11	Correct	1 ms	208 KB	Output is correct
12	Correct	0 ms	208 KB	Output is correct
13	Correct	1 ms	336 KB	Output is correct
14	Correct	1 ms	336 KB	Output is correct
15	Correct	1 ms	208 KB	Output is correct
16	Correct	1 ms	336 KB	Output is correct
17	Correct	1 ms	336 KB	Output is correct
18	Correct	1 ms	208 KB	Output is correct
19	Correct	1 ms	336 KB	Output is correct
20	Correct	1 ms	336 KB	Output is correct
21	Correct	1 ms	336 KB	Output is correct
22	Correct	1 ms	336 KB	Output is correct
23	Correct	2 ms	336 KB	Output is correct
24	Correct	2 ms	344 KB	Output is correct
25	Correct	1 ms	208 KB	Output is correct
26	Correct	3 ms	336 KB	Output is correct
27	Correct	2 ms	336 KB	Output is correct
28	Correct	3 ms	336 KB	Output is correct
29	Correct	2 ms	336 KB	Output is correct
30	Correct	3 ms	336 KB	Output is correct
31	Correct	3 ms	336 KB	Output is correct
32	Correct	3 ms	336 KB	Output is correct
33	Correct	3 ms	336 KB	Output is correct
34	Correct	3 ms	336 KB	Output is correct
35	Correct	2 ms	336 KB	Output is correct

Subtask #3
0 / 12.0

#	결과	실행 시간	메모리	Grader output
1	Correct	0 ms	208 KB	Output is correct
2	Correct	1 ms	336 KB	Output is correct
3	Correct	2 ms	336 KB	Output is correct
4	Correct	1 ms	336 KB	Output is correct
5	Correct	1 ms	336 KB	Output is correct
6	Correct	1 ms	208 KB	Output is correct
7	Correct	1 ms	336 KB	Output is correct
8	Correct	1 ms	208 KB	Output is correct
9	Correct	1 ms	208 KB	Output is correct
10	Correct	1 ms	208 KB	Output is correct
11	Correct	1 ms	208 KB	Output is correct
12	Correct	0 ms	208 KB	Output is correct
13	Correct	1 ms	336 KB	Output is correct
14	Correct	1 ms	336 KB	Output is correct
15	Correct	1 ms	208 KB	Output is correct
16	Correct	1 ms	336 KB	Output is correct
17	Correct	1 ms	336 KB	Output is correct
18	Correct	1 ms	208 KB	Output is correct
19	Correct	1 ms	336 KB	Output is correct
20	Correct	1 ms	336 KB	Output is correct
21	Correct	1 ms	336 KB	Output is correct
22	Correct	1 ms	336 KB	Output is correct
23	Correct	2 ms	336 KB	Output is correct
24	Correct	2 ms	344 KB	Output is correct
25	Correct	1 ms	208 KB	Output is correct
26	Correct	3 ms	336 KB	Output is correct
27	Correct	2 ms	336 KB	Output is correct
28	Correct	3 ms	336 KB	Output is correct
29	Correct	2 ms	336 KB	Output is correct
30	Correct	3 ms	336 KB	Output is correct
31	Correct	3 ms	336 KB	Output is correct
32	Correct	3 ms	336 KB	Output is correct
33	Correct	3 ms	336 KB	Output is correct
34	Correct	3 ms	336 KB	Output is correct
35	Correct	2 ms	336 KB	Output is correct
36	Correct	30 ms	1696 KB	Output is correct
37	Correct	1431 ms	2616 KB	Output is correct
38	Correct	245 ms	2108 KB	Output is correct
39	Correct	868 ms	2364 KB	Output is correct
40	Correct	66 ms	2112 KB	Output is correct
41	Correct	2644 ms	3396 KB	Output is correct
42	Correct	15 ms	1808 KB	Output is correct
43	Correct	2708 ms	2752 KB	Output is correct
44	Correct	301 ms	1984 KB	Output is correct
45	Correct	40 ms	1852 KB	Output is correct
46	Correct	29 ms	1852 KB	Output is correct
47	Correct	20 ms	2584 KB	Output is correct
48	Correct	26 ms	2412 KB	Output is correct
49	Correct	13 ms	2068 KB	Output is correct
50	Correct	165 ms	2240 KB	Output is correct
51	Correct	1804 ms	2624 KB	Output is correct
52	Correct	52 ms	4120 KB	Output is correct
53	Correct	58 ms	4880 KB	Output is correct
54	Correct	43 ms	4928 KB	Output is correct
55	Correct	3333 ms	3480 KB	Output is correct
56	Correct	2706 ms	3380 KB	Output is correct
57	Correct	3818 ms	3340 KB	Output is correct
58	Correct	2811 ms	3508 KB	Output is correct
59	Correct	1696 ms	3800 KB	Output is correct
60	Correct	107 ms	4872 KB	Output is correct
61	Correct	1507 ms	4536 KB	Output is correct
62	Correct	2612 ms	4028 KB	Output is correct
63	Correct	1378 ms	4628 KB	Output is correct
64	Execution timed out	4059 ms	1820 KB	Time limit exceeded
65	Halted	0 ms	0 KB	-

Subtask #4
0 / 14.0

#	결과	실행 시간	메모리	Grader output
1	Execution timed out	4022 ms	4256 KB	Time limit exceeded
2	Halted	0 ms	0 KB	-

Subtask #5
0 / 17.0

#	결과	실행 시간	메모리	Grader output
1	Execution timed out	4061 ms	1596 KB	Time limit exceeded
2	Halted	0 ms	0 KB	-

Subtask #6
0 / 19.0

#	결과	실행 시간	메모리	Grader output
1	Correct	0 ms	208 KB	Output is correct
2	Correct	1 ms	336 KB	Output is correct
3	Correct	2 ms	336 KB	Output is correct
4	Correct	1 ms	336 KB	Output is correct
5	Correct	1 ms	336 KB	Output is correct
6	Correct	1 ms	208 KB	Output is correct
7	Correct	1 ms	336 KB	Output is correct
8	Correct	1 ms	208 KB	Output is correct
9	Correct	1 ms	208 KB	Output is correct
10	Correct	1 ms	208 KB	Output is correct
11	Correct	1 ms	208 KB	Output is correct
12	Correct	0 ms	208 KB	Output is correct
13	Correct	1 ms	336 KB	Output is correct
14	Correct	1 ms	336 KB	Output is correct
15	Correct	1 ms	208 KB	Output is correct
16	Correct	1 ms	336 KB	Output is correct
17	Correct	1 ms	336 KB	Output is correct
18	Correct	1 ms	208 KB	Output is correct
19	Correct	1 ms	336 KB	Output is correct
20	Correct	1 ms	336 KB	Output is correct
21	Correct	1 ms	336 KB	Output is correct
22	Correct	1 ms	336 KB	Output is correct
23	Correct	2 ms	336 KB	Output is correct
24	Correct	2 ms	344 KB	Output is correct
25	Correct	1 ms	208 KB	Output is correct
26	Correct	3 ms	336 KB	Output is correct
27	Correct	2 ms	336 KB	Output is correct
28	Correct	3 ms	336 KB	Output is correct
29	Correct	2 ms	336 KB	Output is correct
30	Correct	3 ms	336 KB	Output is correct
31	Correct	3 ms	336 KB	Output is correct
32	Correct	3 ms	336 KB	Output is correct
33	Correct	3 ms	336 KB	Output is correct
34	Correct	3 ms	336 KB	Output is correct
35	Correct	2 ms	336 KB	Output is correct
36	Correct	30 ms	1696 KB	Output is correct
37	Correct	1431 ms	2616 KB	Output is correct
38	Correct	245 ms	2108 KB	Output is correct
39	Correct	868 ms	2364 KB	Output is correct
40	Correct	66 ms	2112 KB	Output is correct
41	Correct	2644 ms	3396 KB	Output is correct
42	Correct	15 ms	1808 KB	Output is correct
43	Correct	2708 ms	2752 KB	Output is correct
44	Correct	301 ms	1984 KB	Output is correct
45	Correct	40 ms	1852 KB	Output is correct
46	Correct	29 ms	1852 KB	Output is correct
47	Correct	20 ms	2584 KB	Output is correct
48	Correct	26 ms	2412 KB	Output is correct
49	Correct	13 ms	2068 KB	Output is correct
50	Correct	165 ms	2240 KB	Output is correct
51	Correct	1804 ms	2624 KB	Output is correct
52	Correct	52 ms	4120 KB	Output is correct
53	Correct	58 ms	4880 KB	Output is correct
54	Correct	43 ms	4928 KB	Output is correct
55	Correct	3333 ms	3480 KB	Output is correct
56	Correct	2706 ms	3380 KB	Output is correct
57	Correct	3818 ms	3340 KB	Output is correct
58	Correct	2811 ms	3508 KB	Output is correct
59	Correct	1696 ms	3800 KB	Output is correct
60	Correct	107 ms	4872 KB	Output is correct
61	Correct	1507 ms	4536 KB	Output is correct
62	Correct	2612 ms	4028 KB	Output is correct
63	Correct	1378 ms	4628 KB	Output is correct
64	Execution timed out	4059 ms	1820 KB	Time limit exceeded
65	Halted	0 ms	0 KB	-

Subtask #7
0 / 23.0

#	결과	실행 시간	메모리	Grader output
1	Execution timed out	4088 ms	2224 KB	Time limit exceeded
2	Halted	0 ms	0 KB	-

답안 #630796

Compilation message

Subtask #1 0 / 4.0

Subtask #2 11.0 / 11.0

Subtask #3 0 / 12.0

Subtask #4 0 / 14.0

Subtask #5 0 / 17.0

Subtask #6 0 / 19.0

Subtask #7 0 / 23.0

Subtask #1
0 / 4.0

Subtask #2
11.0 / 11.0

Subtask #3
0 / 12.0

Subtask #4
0 / 14.0

Subtask #5
0 / 17.0

Subtask #6
0 / 19.0

Subtask #7
0 / 23.0