/**
* It's not that hard to come up with a almost-full solution. First, let non-lollipop
* be any prize with val < v. The number of non-lollipops is O(sqrt(n)), and there're
* at most 5 types of prizes.
*
* One can also notice that if two prizes u, v have the same value, then the sum of
* reponse for u and v is the same. Therefore, query any O(sqrt(n)) positions and we
* will find the number of non-lollipops. Finally, we know that lollipops account for
* most of the prizes, and their "left response" is increasing from left to right. We
* can treat (a[0]) from lollipops as an increasing sequence, and apply binary search
* to find all non-lollipops. Naturally, we will find the diamond.
* Doing O(sqrt(n)) separate binary searches require about 7000-9000 steps. In impl1,
* I optimize my search by applying those binary searches simultaneously. Namely, for
* each range [l,r] we're working with, query pos (l+r)/2 first. The monotonicity
* helps us determine the range of values for [l,(l+r)/2) and ((l+r)/2,r]. The
* approach is analogous to the well-known divide-and-conquer optimization. I know
* that this method has the same complexity, yet the constant, though I don't know,
* is smaller.
*
* I scored 95.56 points with impl1, with the max query count being 5444. This means
* we're quite close~ Indeed, "parallel binary search" takes less queries than
* O(sqrt(n)) instances of binary search. In impl1.5, I lowered the num of searches
* to find a lollipop: it turns out that my computation was incorrect (yielding a
* suboptimal bound). By using a python script, I brute-forced the max num of
* non-lollipops - 472, achieved with (1, 4, 21, 446, 199528).
*
* Queries needed: sqrt(n) * log(n) (unsure about the const)
* Implementation 1.5
*/
#include <bits/stdc++.h>
#include "prize.h"
typedef std::vector<int> vec;
const int MAX_TYPES = 5;
const int MAX_LOL = 472; // max num of non-lollipops
int non_lol; // number of non-lollipops
int search(int l, int r, int val_lower, int val_upper) {
if (l > r || val_lower == val_upper)
return -1;
int mid = (l + r) / 2, pt = mid, t = -1;
for (; l <= pt; pt--) {
vec res = ask(pt);
if (res[0] + res[1] == 0) // diamond found
return pt;
if (res[0] + res[1] == non_lol) {
t = res[0];
break;
}
}
return std::max(search(l, pt - 1, val_lower, t),
search(mid + 1, r, t + (mid - pt), val_upper));
}
int find_best(int n) {
non_lol = 0;
std::set<int> distinct_sum;
for (int k = 0; k <= MAX_LOL; k++) {
int pos = std::min(n / MAX_LOL * k, n - 1); // roughly evenly-spaced
vec res = ask(pos);
int s = res[0] + res[1];
if (s == 0)
return pos;
non_lol = std::max(non_lol, s);
distinct_sum.emplace(s);
if (int(distinct_sum.size()) >= MAX_TYPES)
break;
}
return search(0, n - 1, 0, MAX_LOL);
}
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
4 ms |
208 KB |
Output is correct |
| 2 |
Correct |
2 ms |
288 KB |
Output is correct |
| 3 |
Correct |
5 ms |
208 KB |
Output is correct |
| 4 |
Correct |
3 ms |
336 KB |
Output is correct |
| 5 |
Correct |
6 ms |
208 KB |
Output is correct |
| 6 |
Correct |
1 ms |
208 KB |
Output is correct |
| 7 |
Correct |
2 ms |
208 KB |
Output is correct |
| 8 |
Correct |
4 ms |
208 KB |
Output is correct |
| 9 |
Correct |
4 ms |
208 KB |
Output is correct |
| 10 |
Correct |
5 ms |
208 KB |
Output is correct |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
6 ms |
272 KB |
Output is correct |
| 2 |
Correct |
2 ms |
288 KB |
Output is correct |
| 3 |
Correct |
3 ms |
208 KB |
Output is correct |
| 4 |
Correct |
5 ms |
292 KB |
Output is correct |
| 5 |
Correct |
3 ms |
208 KB |
Output is correct |
| 6 |
Correct |
1 ms |
208 KB |
Output is correct |
| 7 |
Correct |
5 ms |
268 KB |
Output is correct |
| 8 |
Correct |
5 ms |
208 KB |
Output is correct |
| 9 |
Correct |
2 ms |
296 KB |
Output is correct |
| 10 |
Correct |
6 ms |
208 KB |
Output is correct |
| 11 |
Correct |
7 ms |
208 KB |
Output is correct |
| 12 |
Correct |
7 ms |
208 KB |
Output is correct |
| 13 |
Correct |
10 ms |
208 KB |
Output is correct |
| 14 |
Correct |
11 ms |
208 KB |
Output is correct |
| 15 |
Correct |
30 ms |
288 KB |
Output is correct |
| 16 |
Correct |
48 ms |
208 KB |
Output is correct |
| 17 |
Correct |
37 ms |
292 KB |
Output is correct |
| 18 |
Correct |
34 ms |
208 KB |
Output is correct |
| 19 |
Correct |
46 ms |
288 KB |
Output is correct |
| 20 |
Correct |
36 ms |
208 KB |
Output is correct |
| 21 |
Correct |
46 ms |
292 KB |
Output is correct |
| 22 |
Correct |
37 ms |
208 KB |
Output is correct |
| 23 |
Correct |
6 ms |
208 KB |
Output is correct |
| 24 |
Correct |
10 ms |
296 KB |
Output is correct |
| 25 |
Correct |
45 ms |
208 KB |
Output is correct |
| 26 |
Correct |
18 ms |
288 KB |
Output is correct |
| 27 |
Correct |
6 ms |
292 KB |
Output is correct |
| 28 |
Correct |
43 ms |
272 KB |
Output is correct |
| 29 |
Correct |
40 ms |
292 KB |
Output is correct |
| 30 |
Correct |
23 ms |
208 KB |
Output is correct |
| 31 |
Correct |
48 ms |
292 KB |
Output is correct |
| 32 |
Correct |
4 ms |
292 KB |
Output is correct |
| 33 |
Correct |
5 ms |
208 KB |
Output is correct |
| 34 |
Correct |
39 ms |
208 KB |
Output is correct |
| 35 |
Correct |
6 ms |
296 KB |
Output is correct |
| 36 |
Correct |
42 ms |
288 KB |
Output is correct |
| 37 |
Correct |
11 ms |
208 KB |
Output is correct |
| 38 |
Correct |
7 ms |
208 KB |
Output is correct |
| 39 |
Correct |
30 ms |
208 KB |
Output is correct |
| 40 |
Correct |
45 ms |
296 KB |
Output is correct |
| 41 |
Correct |
38 ms |
208 KB |
Output is correct |
| 42 |
Correct |
44 ms |
288 KB |
Output is correct |
| 43 |
Correct |
33 ms |
208 KB |
Output is correct |
| 44 |
Correct |
20 ms |
280 KB |
Output is correct |
| 45 |
Correct |
37 ms |
292 KB |
Output is correct |
| 46 |
Correct |
47 ms |
288 KB |
Output is correct |
| 47 |
Correct |
34 ms |
208 KB |
Output is correct |
| 48 |
Correct |
36 ms |
208 KB |
Output is correct |
| 49 |
Correct |
43 ms |
288 KB |
Output is correct |
| 50 |
Correct |
35 ms |
208 KB |
Output is correct |
| 51 |
Correct |
42 ms |
208 KB |
Output is correct |
| 52 |
Correct |
33 ms |
208 KB |
Output is correct |
| 53 |
Correct |
5 ms |
208 KB |
Output is correct |
| 54 |
Correct |
40 ms |
208 KB |
Output is correct |
| 55 |
Correct |
32 ms |
272 KB |
Output is correct |
| 56 |
Correct |
40 ms |
208 KB |
Output is correct |
| 57 |
Correct |
20 ms |
296 KB |
Output is correct |
| 58 |
Correct |
40 ms |
208 KB |
Output is correct |
| 59 |
Correct |
38 ms |
288 KB |
Output is correct |
| 60 |
Correct |
28 ms |
208 KB |
Output is correct |
| 61 |
Correct |
7 ms |
208 KB |
Output is correct |
| 62 |
Correct |
8 ms |
208 KB |
Output is correct |
| 63 |
Correct |
3 ms |
288 KB |
Output is correct |
| 64 |
Correct |
6 ms |
208 KB |
Output is correct |
| 65 |
Correct |
7 ms |
296 KB |
Output is correct |
| 66 |
Correct |
4 ms |
272 KB |
Output is correct |
| 67 |
Correct |
3 ms |
208 KB |
Output is correct |
| 68 |
Correct |
9 ms |
292 KB |
Output is correct |
| 69 |
Correct |
9 ms |
284 KB |
Output is correct |
| 70 |
Correct |
6 ms |
208 KB |
Output is correct |
| 71 |
Partially correct |
40 ms |
208 KB |
Partially correct - number of queries: 5232 |
| 72 |
Correct |
6 ms |
208 KB |
Output is correct |
| 73 |
Partially correct |
21 ms |
292 KB |
Partially correct - number of queries: 5177 |
| 74 |
Partially correct |
36 ms |
208 KB |
Partially correct - number of queries: 5204 |
| 75 |
Correct |
5 ms |
208 KB |
Output is correct |
| 76 |
Correct |
45 ms |
208 KB |
Output is correct |
| 77 |
Correct |
42 ms |
208 KB |
Output is correct |
| 78 |
Correct |
9 ms |
208 KB |
Output is correct |
| 79 |
Correct |
21 ms |
208 KB |
Output is correct |
| 80 |
Correct |
21 ms |
288 KB |
Output is correct |
| 81 |
Correct |
20 ms |
336 KB |
Output is correct |
| 82 |
Correct |
37 ms |
208 KB |
Output is correct |
| 83 |
Correct |
4 ms |
208 KB |
Output is correct |
| 84 |
Correct |
39 ms |
208 KB |
Output is correct |
| 85 |
Correct |
51 ms |
208 KB |
Output is correct |
| 86 |
Correct |
16 ms |
292 KB |
Output is correct |
| 87 |
Correct |
10 ms |
208 KB |
Output is correct |
| 88 |
Correct |
25 ms |
208 KB |
Output is correct |
| 89 |
Correct |
26 ms |
208 KB |
Output is correct |
| 90 |
Correct |
6 ms |
208 KB |
Output is correct |
| 91 |
Correct |
29 ms |
208 KB |
Output is correct |
| 92 |
Correct |
28 ms |
292 KB |
Output is correct |
| 93 |
Correct |
36 ms |
208 KB |
Output is correct |
| 94 |
Correct |
39 ms |
208 KB |
Output is correct |
| 95 |
Correct |
37 ms |
208 KB |
Output is correct |
| 96 |
Correct |
28 ms |
208 KB |
Output is correct |
| 97 |
Correct |
42 ms |
208 KB |
Output is correct |
