| # |
Submission time |
Handle |
Problem |
Language |
Result |
Execution time |
Memory |
| 45550 |
2018-04-15T10:24:18 Z |
fallingstar |
Boat (APIO16_boat) |
C++17 |
|
1148 ms |
6464 KB |
/**
Problem: Boat
Source: APIO 2016 problem 1
*/
#include <iostream>
#include <algorithm>
#define long long long
using namespace std;
const int N = 500 + 2;
const int MOD = 1e9 + 7;
int Mul(int a, int b) { return (long) a * b % MOD; }
void Add(int &a, int b) { a += b; if (a >= MOD) a -= MOD; }
int Sum(int a, int b) { Add(a, b); return a; }
void Sub(int &a, int b) { a -= b; if (a < 0) a += MOD; }
int Pow(int x, int n)
{
if (n == 1) return x;
int t = Pow(x, n / 2); t = Mul(t, t);
return n & 1 ? Mul(t, x) : t;
}
int n, a[N], b[N];
int m, p[N * 2]; // left and right ends of ranges
int c[N][N]; // c[i][j] = choose j from i
int g[N * 2][N];
int inv[N]; // inv[i] = i^-1
int f[N][N * 2];
void Prep() // precalculate all g(i, j)
{
for (int i = 1; i <= n; ++i)
inv[i] = Pow(i, MOD - 2);
c[0][0] = 1;
for (int i = 1; i <= n; ++i) // calculate all c(i, j) with i, j <= n
{
c[i][0] = 1;
for (int j = 1; j <= i; ++j)
c[i][j] = Sum(c[i - 1][j], c[i - 1][j - 1]);
}
for (int i = 1; i < m; ++i)
{
int tmp[N] = {}, len = p[i] - p[i - 1]; // tmp[i] = c(len, i)
tmp[0] = 1;
for (int j = 1; j <= min(n, len); ++j)
tmp[j] = Mul(Mul(tmp[j - 1], len - j + 1), inv[j]);
for (int j = 1; j <= n; ++j) // j schools can send, including the current one
for (int k = 1; k <= min(j, len); ++k) // k schools actually sent, including the current one
Add(g[i][j], Mul(c[j - 1][k - 1], tmp[k]));
}
}
void Solve()
{
int res = 0;
fill(f[0], f[0] + m, 1);
for (int i = 1; i <= n; ++i)
for (int j = 1; j < m; ++j)
{
if (a[i] <= p[j - 1] + 1 && p[j] <= b[i])
{
int cnt = 0; // number of schools that contain range j
for (int k = i; k >= 1; --k)
{
cnt += (a[k] <= p[j - 1] + 1 && p[j] <= b[k]);
Add(f[i][j], Mul(f[k - 1][j - 1], g[j][cnt]));
}
// cerr << "f[" << i << "][" << j << "] = " << f[i][j] << '\n';
Add(res, f[i][j]);
}
Add(f[i][j], f[i][j - 1]);
}
cout << res;
}
int main()
{
cin >> n;
for (int i = 1; i <= n; ++i)
{
cin >> a[i] >> b[i];
p[m++] = a[i] - 1;
p[m++] = b[i];
}
sort(p, p + m);
m = unique(p, p + m) - p;
Prep();
Solve();
return 0;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
202 ms |
5368 KB |
Output is correct |
| 2 |
Correct |
209 ms |
5368 KB |
Output is correct |
| 3 |
Correct |
222 ms |
5512 KB |
Output is correct |
| 4 |
Correct |
202 ms |
5512 KB |
Output is correct |
| 5 |
Correct |
202 ms |
5512 KB |
Output is correct |
| 6 |
Correct |
209 ms |
5512 KB |
Output is correct |
| 7 |
Correct |
235 ms |
5512 KB |
Output is correct |
| 8 |
Correct |
207 ms |
5512 KB |
Output is correct |
| 9 |
Correct |
203 ms |
5512 KB |
Output is correct |
| 10 |
Correct |
288 ms |
5588 KB |
Output is correct |
| 11 |
Correct |
244 ms |
5588 KB |
Output is correct |
| 12 |
Correct |
231 ms |
5612 KB |
Output is correct |
| 13 |
Correct |
216 ms |
5612 KB |
Output is correct |
| 14 |
Correct |
203 ms |
5628 KB |
Output is correct |
| 15 |
Correct |
204 ms |
5628 KB |
Output is correct |
| 16 |
Correct |
42 ms |
5628 KB |
Output is correct |
| 17 |
Correct |
43 ms |
5628 KB |
Output is correct |
| 18 |
Correct |
43 ms |
5628 KB |
Output is correct |
| 19 |
Correct |
43 ms |
5628 KB |
Output is correct |
| 20 |
Correct |
42 ms |
5628 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
202 ms |
5368 KB |
Output is correct |
| 2 |
Correct |
209 ms |
5368 KB |
Output is correct |
| 3 |
Correct |
222 ms |
5512 KB |
Output is correct |
| 4 |
Correct |
202 ms |
5512 KB |
Output is correct |
| 5 |
Correct |
202 ms |
5512 KB |
Output is correct |
| 6 |
Correct |
209 ms |
5512 KB |
Output is correct |
| 7 |
Correct |
235 ms |
5512 KB |
Output is correct |
| 8 |
Correct |
207 ms |
5512 KB |
Output is correct |
| 9 |
Correct |
203 ms |
5512 KB |
Output is correct |
| 10 |
Correct |
288 ms |
5588 KB |
Output is correct |
| 11 |
Correct |
244 ms |
5588 KB |
Output is correct |
| 12 |
Correct |
231 ms |
5612 KB |
Output is correct |
| 13 |
Correct |
216 ms |
5612 KB |
Output is correct |
| 14 |
Correct |
203 ms |
5628 KB |
Output is correct |
| 15 |
Correct |
204 ms |
5628 KB |
Output is correct |
| 16 |
Correct |
42 ms |
5628 KB |
Output is correct |
| 17 |
Correct |
43 ms |
5628 KB |
Output is correct |
| 18 |
Correct |
43 ms |
5628 KB |
Output is correct |
| 19 |
Correct |
43 ms |
5628 KB |
Output is correct |
| 20 |
Correct |
42 ms |
5628 KB |
Output is correct |
| 21 |
Correct |
594 ms |
5628 KB |
Output is correct |
| 22 |
Correct |
580 ms |
5628 KB |
Output is correct |
| 23 |
Correct |
596 ms |
5628 KB |
Output is correct |
| 24 |
Correct |
568 ms |
5628 KB |
Output is correct |
| 25 |
Correct |
576 ms |
5628 KB |
Output is correct |
| 26 |
Correct |
620 ms |
5628 KB |
Output is correct |
| 27 |
Correct |
641 ms |
5628 KB |
Output is correct |
| 28 |
Correct |
650 ms |
5628 KB |
Output is correct |
| 29 |
Correct |
648 ms |
5716 KB |
Output is correct |
| 30 |
Correct |
249 ms |
5724 KB |
Output is correct |
| 31 |
Correct |
212 ms |
5864 KB |
Output is correct |
| 32 |
Correct |
207 ms |
5864 KB |
Output is correct |
| 33 |
Correct |
208 ms |
5864 KB |
Output is correct |
| 34 |
Correct |
211 ms |
5864 KB |
Output is correct |
| 35 |
Correct |
201 ms |
5864 KB |
Output is correct |
| 36 |
Correct |
207 ms |
5928 KB |
Output is correct |
| 37 |
Correct |
210 ms |
5928 KB |
Output is correct |
| 38 |
Correct |
263 ms |
5928 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
14 ms |
5928 KB |
Output is correct |
| 2 |
Correct |
10 ms |
5928 KB |
Output is correct |
| 3 |
Correct |
11 ms |
5928 KB |
Output is correct |
| 4 |
Correct |
11 ms |
5928 KB |
Output is correct |
| 5 |
Correct |
12 ms |
5928 KB |
Output is correct |
| 6 |
Correct |
13 ms |
5928 KB |
Output is correct |
| 7 |
Correct |
13 ms |
5928 KB |
Output is correct |
| 8 |
Correct |
13 ms |
5928 KB |
Output is correct |
| 9 |
Correct |
12 ms |
5928 KB |
Output is correct |
| 10 |
Correct |
12 ms |
5928 KB |
Output is correct |
| 11 |
Correct |
11 ms |
5928 KB |
Output is correct |
| 12 |
Correct |
10 ms |
5928 KB |
Output is correct |
| 13 |
Correct |
10 ms |
5928 KB |
Output is correct |
| 14 |
Correct |
10 ms |
5928 KB |
Output is correct |
| 15 |
Correct |
10 ms |
5928 KB |
Output is correct |
| 16 |
Correct |
7 ms |
5928 KB |
Output is correct |
| 17 |
Correct |
7 ms |
5928 KB |
Output is correct |
| 18 |
Correct |
7 ms |
5928 KB |
Output is correct |
| 19 |
Correct |
7 ms |
5928 KB |
Output is correct |
| 20 |
Correct |
8 ms |
5928 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
202 ms |
5368 KB |
Output is correct |
| 2 |
Correct |
209 ms |
5368 KB |
Output is correct |
| 3 |
Correct |
222 ms |
5512 KB |
Output is correct |
| 4 |
Correct |
202 ms |
5512 KB |
Output is correct |
| 5 |
Correct |
202 ms |
5512 KB |
Output is correct |
| 6 |
Correct |
209 ms |
5512 KB |
Output is correct |
| 7 |
Correct |
235 ms |
5512 KB |
Output is correct |
| 8 |
Correct |
207 ms |
5512 KB |
Output is correct |
| 9 |
Correct |
203 ms |
5512 KB |
Output is correct |
| 10 |
Correct |
288 ms |
5588 KB |
Output is correct |
| 11 |
Correct |
244 ms |
5588 KB |
Output is correct |
| 12 |
Correct |
231 ms |
5612 KB |
Output is correct |
| 13 |
Correct |
216 ms |
5612 KB |
Output is correct |
| 14 |
Correct |
203 ms |
5628 KB |
Output is correct |
| 15 |
Correct |
204 ms |
5628 KB |
Output is correct |
| 16 |
Correct |
42 ms |
5628 KB |
Output is correct |
| 17 |
Correct |
43 ms |
5628 KB |
Output is correct |
| 18 |
Correct |
43 ms |
5628 KB |
Output is correct |
| 19 |
Correct |
43 ms |
5628 KB |
Output is correct |
| 20 |
Correct |
42 ms |
5628 KB |
Output is correct |
| 21 |
Correct |
594 ms |
5628 KB |
Output is correct |
| 22 |
Correct |
580 ms |
5628 KB |
Output is correct |
| 23 |
Correct |
596 ms |
5628 KB |
Output is correct |
| 24 |
Correct |
568 ms |
5628 KB |
Output is correct |
| 25 |
Correct |
576 ms |
5628 KB |
Output is correct |
| 26 |
Correct |
620 ms |
5628 KB |
Output is correct |
| 27 |
Correct |
641 ms |
5628 KB |
Output is correct |
| 28 |
Correct |
650 ms |
5628 KB |
Output is correct |
| 29 |
Correct |
648 ms |
5716 KB |
Output is correct |
| 30 |
Correct |
249 ms |
5724 KB |
Output is correct |
| 31 |
Correct |
212 ms |
5864 KB |
Output is correct |
| 32 |
Correct |
207 ms |
5864 KB |
Output is correct |
| 33 |
Correct |
208 ms |
5864 KB |
Output is correct |
| 34 |
Correct |
211 ms |
5864 KB |
Output is correct |
| 35 |
Correct |
201 ms |
5864 KB |
Output is correct |
| 36 |
Correct |
207 ms |
5928 KB |
Output is correct |
| 37 |
Correct |
210 ms |
5928 KB |
Output is correct |
| 38 |
Correct |
263 ms |
5928 KB |
Output is correct |
| 39 |
Correct |
14 ms |
5928 KB |
Output is correct |
| 40 |
Correct |
10 ms |
5928 KB |
Output is correct |
| 41 |
Correct |
11 ms |
5928 KB |
Output is correct |
| 42 |
Correct |
11 ms |
5928 KB |
Output is correct |
| 43 |
Correct |
12 ms |
5928 KB |
Output is correct |
| 44 |
Correct |
13 ms |
5928 KB |
Output is correct |
| 45 |
Correct |
13 ms |
5928 KB |
Output is correct |
| 46 |
Correct |
13 ms |
5928 KB |
Output is correct |
| 47 |
Correct |
12 ms |
5928 KB |
Output is correct |
| 48 |
Correct |
12 ms |
5928 KB |
Output is correct |
| 49 |
Correct |
11 ms |
5928 KB |
Output is correct |
| 50 |
Correct |
10 ms |
5928 KB |
Output is correct |
| 51 |
Correct |
10 ms |
5928 KB |
Output is correct |
| 52 |
Correct |
10 ms |
5928 KB |
Output is correct |
| 53 |
Correct |
10 ms |
5928 KB |
Output is correct |
| 54 |
Correct |
7 ms |
5928 KB |
Output is correct |
| 55 |
Correct |
7 ms |
5928 KB |
Output is correct |
| 56 |
Correct |
7 ms |
5928 KB |
Output is correct |
| 57 |
Correct |
7 ms |
5928 KB |
Output is correct |
| 58 |
Correct |
8 ms |
5928 KB |
Output is correct |
| 59 |
Correct |
1016 ms |
6136 KB |
Output is correct |
| 60 |
Correct |
979 ms |
6136 KB |
Output is correct |
| 61 |
Correct |
947 ms |
6136 KB |
Output is correct |
| 62 |
Correct |
1002 ms |
6136 KB |
Output is correct |
| 63 |
Correct |
1030 ms |
6136 KB |
Output is correct |
| 64 |
Correct |
1085 ms |
6136 KB |
Output is correct |
| 65 |
Correct |
1110 ms |
6136 KB |
Output is correct |
| 66 |
Correct |
1148 ms |
6136 KB |
Output is correct |
| 67 |
Correct |
1138 ms |
6168 KB |
Output is correct |
| 68 |
Correct |
1090 ms |
6240 KB |
Output is correct |
| 69 |
Correct |
942 ms |
6240 KB |
Output is correct |
| 70 |
Correct |
900 ms |
6388 KB |
Output is correct |
| 71 |
Correct |
844 ms |
6388 KB |
Output is correct |
| 72 |
Correct |
906 ms |
6388 KB |
Output is correct |
| 73 |
Correct |
905 ms |
6464 KB |
Output is correct |
| 74 |
Correct |
163 ms |
6464 KB |
Output is correct |
| 75 |
Correct |
159 ms |
6464 KB |
Output is correct |
| 76 |
Correct |
164 ms |
6464 KB |
Output is correct |
| 77 |
Correct |
160 ms |
6464 KB |
Output is correct |
| 78 |
Correct |
167 ms |
6464 KB |
Output is correct |
