| # |
Submission time |
Handle |
Problem |
Language |
Result |
Execution time |
Memory |
| 991231 |
2024-06-01T15:32:35 Z |
model_code |
Trains (BOI24_trains) |
C++17 |
|
346 ms |
159444 KB |
/* TASK: Train Journey (trains)
* Task proposal by: Bohdan Feysa (UKR)
* Task prepared by: Bohdan Feysa (UKR), Zigmas Bitinas (LTU SC), Aldas Lenkšas (LTU SC)
*
* Task can be solved by square root decomposition. Let's choose a constant C = sqrt(N).
* Now we do the Dynamic Programming solution, where dp[i] represents how many journies
* can be made if we would end the journey at the i-th city.
*
* If d[i] >= C, then each dp[j] is increased by dp[i], where j = i + t * d[i]. This takes
* O(N/C) time.
*
* If d[i] < C, then we store the value in the array, so that we can add this value later.
*
*/
#include <bits/stdc++.h>
using namespace std;
const int MOD = 1e9+7;
const int MAXN = 1e5;
const int C = 400; // ~sqrt(MAXN)
int n;
long long d[MAXN], x[MAXN];
int dp[MAXN];
int acc[C][C]; // the value to add to dp
int addToAcc[MAXN][C]; // the value to add to accumulator
void addToAccumulator(long long i, int jump, int a) {
// a is the value to add
if (i >= n)
return; // not interested
if (a < 0) // deal with subtractions
a = (a + MOD) % MOD;
addToAcc[i][jump] = (addToAcc[i][jump] + a) % MOD;
}
int main() {
// read input
cin >> n;
for (int i = 0; i < n; i++)
cin >> d[i] >> x[i];
dp[0] = 1; // base case
for (int i = 0; i < n; i++) {
for (int jump = 1; jump < C; jump++) {
int m = i % jump;
acc[jump][m] = (acc[jump][m] + addToAcc[i][jump]) % MOD;
dp[i] = (dp[i] + acc[jump][m]) % MOD;
}
if (d[i] == 0) continue; // not working teleporter
// sqrt decomposition
if (d[i] < C) {
int jump = d[i];
addToAccumulator(i + jump, jump, dp[i]);
addToAccumulator(i + jump * x[i] + jump, jump, -dp[i]);
} else {
for (int j = i + d[i], xu = 1; xu <= x[i] && j < n; xu++, j += d[i]) {
dp[j] = (dp[j] + dp[i]) % MOD;
}
}
}
// ans = dp[0] + dp[1] + ... + dp[n-1]
int ans = 0;
for (int i = 0; i < n; i++)
ans = (ans + dp[i]) % MOD;
cout << (ans % MOD) << endl;
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
860 KB |
Output is correct |
| 2 |
Correct |
0 ms |
860 KB |
Output is correct |
| 3 |
Correct |
1 ms |
860 KB |
Output is correct |
| 4 |
Correct |
0 ms |
860 KB |
Output is correct |
| 5 |
Correct |
1 ms |
860 KB |
Output is correct |
| 6 |
Correct |
0 ms |
860 KB |
Output is correct |
| 7 |
Correct |
1 ms |
860 KB |
Output is correct |
| 8 |
Correct |
0 ms |
860 KB |
Output is correct |
| 9 |
Correct |
0 ms |
860 KB |
Output is correct |
| 10 |
Correct |
0 ms |
860 KB |
Output is correct |
| 11 |
Correct |
0 ms |
860 KB |
Output is correct |
| 12 |
Correct |
0 ms |
860 KB |
Output is correct |
| 13 |
Correct |
0 ms |
860 KB |
Output is correct |
| 14 |
Correct |
0 ms |
860 KB |
Output is correct |
| 15 |
Correct |
1 ms |
860 KB |
Output is correct |
| 16 |
Correct |
1 ms |
860 KB |
Output is correct |
| 17 |
Correct |
1 ms |
860 KB |
Output is correct |
| 18 |
Correct |
1 ms |
860 KB |
Output is correct |
| 19 |
Correct |
1 ms |
860 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
860 KB |
Output is correct |
| 2 |
Correct |
0 ms |
860 KB |
Output is correct |
| 3 |
Correct |
1 ms |
860 KB |
Output is correct |
| 4 |
Correct |
0 ms |
860 KB |
Output is correct |
| 5 |
Correct |
1 ms |
860 KB |
Output is correct |
| 6 |
Correct |
0 ms |
860 KB |
Output is correct |
| 7 |
Correct |
1 ms |
860 KB |
Output is correct |
| 8 |
Correct |
0 ms |
860 KB |
Output is correct |
| 9 |
Correct |
0 ms |
860 KB |
Output is correct |
| 10 |
Correct |
0 ms |
860 KB |
Output is correct |
| 11 |
Correct |
0 ms |
860 KB |
Output is correct |
| 12 |
Correct |
0 ms |
860 KB |
Output is correct |
| 13 |
Correct |
0 ms |
860 KB |
Output is correct |
| 14 |
Correct |
0 ms |
860 KB |
Output is correct |
| 15 |
Correct |
1 ms |
860 KB |
Output is correct |
| 16 |
Correct |
1 ms |
860 KB |
Output is correct |
| 17 |
Correct |
1 ms |
860 KB |
Output is correct |
| 18 |
Correct |
1 ms |
860 KB |
Output is correct |
| 19 |
Correct |
1 ms |
860 KB |
Output is correct |
| 20 |
Correct |
21 ms |
13660 KB |
Output is correct |
| 21 |
Correct |
7 ms |
3672 KB |
Output is correct |
| 22 |
Correct |
25 ms |
12124 KB |
Output is correct |
| 23 |
Correct |
18 ms |
11096 KB |
Output is correct |
| 24 |
Correct |
11 ms |
4444 KB |
Output is correct |
| 25 |
Correct |
25 ms |
13904 KB |
Output is correct |
| 26 |
Correct |
12 ms |
8024 KB |
Output is correct |
| 27 |
Correct |
22 ms |
14472 KB |
Output is correct |
| 28 |
Correct |
28 ms |
16824 KB |
Output is correct |
| 29 |
Correct |
27 ms |
16728 KB |
Output is correct |
| 30 |
Correct |
28 ms |
2536 KB |
Output is correct |
| 31 |
Correct |
27 ms |
13916 KB |
Output is correct |
| 32 |
Correct |
28 ms |
16916 KB |
Output is correct |
| 33 |
Correct |
26 ms |
16472 KB |
Output is correct |
| 34 |
Correct |
24 ms |
2640 KB |
Output is correct |
| 35 |
Correct |
22 ms |
3164 KB |
Output is correct |
| 36 |
Correct |
26 ms |
15676 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
860 KB |
Output is correct |
| 2 |
Correct |
17 ms |
11220 KB |
Output is correct |
| 3 |
Correct |
13 ms |
8016 KB |
Output is correct |
| 4 |
Correct |
24 ms |
14428 KB |
Output is correct |
| 5 |
Correct |
225 ms |
123376 KB |
Output is correct |
| 6 |
Correct |
287 ms |
159436 KB |
Output is correct |
| 7 |
Correct |
283 ms |
159388 KB |
Output is correct |
| 8 |
Correct |
1 ms |
856 KB |
Output is correct |
| 9 |
Correct |
1 ms |
860 KB |
Output is correct |
| 10 |
Correct |
1 ms |
860 KB |
Output is correct |
| 11 |
Correct |
27 ms |
16732 KB |
Output is correct |
| 12 |
Correct |
281 ms |
159444 KB |
Output is correct |
| 13 |
Correct |
1 ms |
856 KB |
Output is correct |
| 14 |
Correct |
27 ms |
16724 KB |
Output is correct |
| 15 |
Correct |
289 ms |
159308 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
133 ms |
72272 KB |
Output is correct |
| 2 |
Correct |
107 ms |
60240 KB |
Output is correct |
| 3 |
Correct |
314 ms |
159312 KB |
Output is correct |
| 4 |
Correct |
207 ms |
109392 KB |
Output is correct |
| 5 |
Correct |
1 ms |
856 KB |
Output is correct |
| 6 |
Correct |
1 ms |
860 KB |
Output is correct |
| 7 |
Correct |
28 ms |
16820 KB |
Output is correct |
| 8 |
Correct |
281 ms |
159316 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
860 KB |
Output is correct |
| 2 |
Correct |
0 ms |
860 KB |
Output is correct |
| 3 |
Correct |
1 ms |
860 KB |
Output is correct |
| 4 |
Correct |
0 ms |
860 KB |
Output is correct |
| 5 |
Correct |
1 ms |
860 KB |
Output is correct |
| 6 |
Correct |
0 ms |
860 KB |
Output is correct |
| 7 |
Correct |
1 ms |
860 KB |
Output is correct |
| 8 |
Correct |
0 ms |
860 KB |
Output is correct |
| 9 |
Correct |
0 ms |
860 KB |
Output is correct |
| 10 |
Correct |
0 ms |
860 KB |
Output is correct |
| 11 |
Correct |
0 ms |
860 KB |
Output is correct |
| 12 |
Correct |
0 ms |
860 KB |
Output is correct |
| 13 |
Correct |
0 ms |
860 KB |
Output is correct |
| 14 |
Correct |
0 ms |
860 KB |
Output is correct |
| 15 |
Correct |
1 ms |
860 KB |
Output is correct |
| 16 |
Correct |
1 ms |
860 KB |
Output is correct |
| 17 |
Correct |
1 ms |
860 KB |
Output is correct |
| 18 |
Correct |
1 ms |
860 KB |
Output is correct |
| 19 |
Correct |
1 ms |
860 KB |
Output is correct |
| 20 |
Correct |
21 ms |
13660 KB |
Output is correct |
| 21 |
Correct |
7 ms |
3672 KB |
Output is correct |
| 22 |
Correct |
25 ms |
12124 KB |
Output is correct |
| 23 |
Correct |
18 ms |
11096 KB |
Output is correct |
| 24 |
Correct |
11 ms |
4444 KB |
Output is correct |
| 25 |
Correct |
25 ms |
13904 KB |
Output is correct |
| 26 |
Correct |
12 ms |
8024 KB |
Output is correct |
| 27 |
Correct |
22 ms |
14472 KB |
Output is correct |
| 28 |
Correct |
28 ms |
16824 KB |
Output is correct |
| 29 |
Correct |
27 ms |
16728 KB |
Output is correct |
| 30 |
Correct |
28 ms |
2536 KB |
Output is correct |
| 31 |
Correct |
27 ms |
13916 KB |
Output is correct |
| 32 |
Correct |
28 ms |
16916 KB |
Output is correct |
| 33 |
Correct |
26 ms |
16472 KB |
Output is correct |
| 34 |
Correct |
24 ms |
2640 KB |
Output is correct |
| 35 |
Correct |
22 ms |
3164 KB |
Output is correct |
| 36 |
Correct |
26 ms |
15676 KB |
Output is correct |
| 37 |
Correct |
1 ms |
860 KB |
Output is correct |
| 38 |
Correct |
17 ms |
11220 KB |
Output is correct |
| 39 |
Correct |
13 ms |
8016 KB |
Output is correct |
| 40 |
Correct |
24 ms |
14428 KB |
Output is correct |
| 41 |
Correct |
225 ms |
123376 KB |
Output is correct |
| 42 |
Correct |
287 ms |
159436 KB |
Output is correct |
| 43 |
Correct |
283 ms |
159388 KB |
Output is correct |
| 44 |
Correct |
1 ms |
856 KB |
Output is correct |
| 45 |
Correct |
1 ms |
860 KB |
Output is correct |
| 46 |
Correct |
1 ms |
860 KB |
Output is correct |
| 47 |
Correct |
27 ms |
16732 KB |
Output is correct |
| 48 |
Correct |
281 ms |
159444 KB |
Output is correct |
| 49 |
Correct |
1 ms |
856 KB |
Output is correct |
| 50 |
Correct |
27 ms |
16724 KB |
Output is correct |
| 51 |
Correct |
289 ms |
159308 KB |
Output is correct |
| 52 |
Correct |
133 ms |
72272 KB |
Output is correct |
| 53 |
Correct |
107 ms |
60240 KB |
Output is correct |
| 54 |
Correct |
314 ms |
159312 KB |
Output is correct |
| 55 |
Correct |
207 ms |
109392 KB |
Output is correct |
| 56 |
Correct |
1 ms |
856 KB |
Output is correct |
| 57 |
Correct |
1 ms |
860 KB |
Output is correct |
| 58 |
Correct |
28 ms |
16820 KB |
Output is correct |
| 59 |
Correct |
281 ms |
159316 KB |
Output is correct |
| 60 |
Correct |
237 ms |
122908 KB |
Output is correct |
| 61 |
Correct |
265 ms |
155912 KB |
Output is correct |
| 62 |
Correct |
266 ms |
158036 KB |
Output is correct |
| 63 |
Correct |
265 ms |
156012 KB |
Output is correct |
| 64 |
Correct |
225 ms |
3148 KB |
Output is correct |
| 65 |
Correct |
284 ms |
103512 KB |
Output is correct |
| 66 |
Correct |
293 ms |
159308 KB |
Output is correct |
| 67 |
Correct |
246 ms |
4432 KB |
Output is correct |
| 68 |
Correct |
258 ms |
131668 KB |
Output is correct |
| 69 |
Correct |
266 ms |
156752 KB |
Output is correct |
| 70 |
Correct |
320 ms |
4828 KB |
Output is correct |
| 71 |
Correct |
221 ms |
5568 KB |
Output is correct |
| 72 |
Correct |
346 ms |
147080 KB |
Output is correct |
