#include <bits/stdc++.h>
using namespace std;
#define debug(x) cout << #x << " = " << x << endl;
using ll = long long;
const int mod = 1e9 + 7;
ll qpow(ll b, ll p) {
ll ret = 1;
while(p) {
if(p & 1) ret = (ret * b) % mod;
b = (b * b) % mod, p >>= 1;
} return ret;
}
struct base {
ll x;
void fix() {
if(x < 0 or x >= mod) x %= mod;
if(x < 0) x += mod;
}
base() {x = 0;}
base(int _x) { x = _x; fix(); }
base(ll _x) { x = _x; fix(); }
base operator + (const base &o) const {
base ret;
ret.x = x + o.x;
if(ret.x >= mod) {
ret.x -= mod;
}
return ret;
}
base operator - (const base &o) const { return base(x - o.x); }
base operator * (const base &o) const { return base(x * o.x); }
base operator / (const base &o) const {
return base(x * qpow(o.x, mod - 2)); }
friend istream& operator >> (istream &in, base &o) {
return in >> o.x; }
friend ostream& operator << (ostream &out, const base &o) {
return out << o.x; }
void operator += (const base &o) { (*this) = (*this) + o; }
void operator -= (const base &o) { (*this) = (*this) - o; }
void operator *= (const base &o) { (*this) = (*this) * o; }
void operator /= (const base &o) { (*this) = (*this) / o; }
};
const int maxn = 505;
int n;
int a[maxn], b[maxn];
int N_rng;
int l[maxn << 1], r[maxn << 1];
// bool vis[maxn][maxn << 1];
base inv[maxn];
base dp[maxn << 1][maxn];
/* dp[rng][i] = # of ways to distribute [1..i] among [1..rng]
ranges s.t. i-th school sends positive amount of boats.
*/
base BC[maxn << 1][maxn]; /* BC = nCr for big N = range size, [range][r] */
base SC[maxn][maxn]; /* SC = nCr for small N, all pair (N, R) */
base g[maxn << 1][maxn];
/* g[range][k] = \sum{i = 1}^{k} \binom{k - 1}{i - 1} * \binom{range_size}{i} */
int main(int argc, char const *argv[])
{
cin >> n;
vector<int> tmp;
for(int i = 1; i <= n; i++) {
cin >> a[i] >> b[i];
a[i]--;
tmp.emplace_back(a[i]);
tmp.emplace_back(b[i]);
}
sort(tmp.begin(), tmp.end());
tmp.erase(unique(tmp.begin(), tmp.end()), tmp.end());
for(int i = 1; i < tmp.size(); i++) {
N_rng++;
l[N_rng] = tmp[i - 1];
r[N_rng] = tmp[i];
}
{ // precalc i^{-1}
inv[0] = 1;
for(int i = 1; i <= n; i++) {
inv[i] = base(1) / i;
}
}
{ // precalc SC[][]
for(int i = 0; i <= n; i++) {
SC[i][0] = 1;
}
for(int i = 1; i <= n; i++) {
for(int j = 1; j <= i; j++) {
SC[i][j] = SC[i - 1][j] + SC[i - 1][j - 1];
}
}
}
{ // precalc BC[][]
for(int i = 1; i <= N_rng; i++) {
BC[i][0] = 1;
for(int j = 1, sz = r[i] - l[i]; j <= n and sz; j++, sz--) {
BC[i][j] = BC[i][j - 1] * inv[j] * sz;
}
}
}
{ // precalc g[][]
for(int range = 1; range <= N_rng; range++) {
for(int k = 1; k <= n; k++) {
for(int i = 1; i <= k; i++) {
g[range][k] += SC[k - 1][i - 1] * BC[range][i];
}
}
}
}
for(int i = 0; i <= N_rng; i++) {
dp[i][0] = 1;
}
for(int rng = 1; rng <= N_rng; rng++) {
for(int i = 1; i <= n; i++) {
dp[rng][i] = dp[rng - 1][i];
if(a[i] <= l[rng] and r[rng] <= b[i]) {
int cnt = 0;
for(int k = i; k >= 1; k--) {
if(a[k] <= l[rng] and r[rng] <= b[k]) {
cnt++;
}
dp[rng][i] += dp[rng - 1][k - 1] * g[rng][cnt];
}
}
}
}
base ans = 0;
for(int i = 1; i <= n; i++) {
ans += dp[N_rng][i];
}
cout << ans << endl;
return 0;
}
Compilation message
boat.cpp: In function 'int main(int, const char**)':
boat.cpp:81:19: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for(int i = 1; i < tmp.size(); i++) {
~~^~~~~~~~~~~~
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
494 ms |
14328 KB |
Output is correct |
| 2 |
Correct |
494 ms |
14328 KB |
Output is correct |
| 3 |
Correct |
495 ms |
14456 KB |
Output is correct |
| 4 |
Correct |
495 ms |
14384 KB |
Output is correct |
| 5 |
Correct |
497 ms |
14364 KB |
Output is correct |
| 6 |
Correct |
495 ms |
14352 KB |
Output is correct |
| 7 |
Correct |
494 ms |
14456 KB |
Output is correct |
| 8 |
Correct |
494 ms |
14456 KB |
Output is correct |
| 9 |
Correct |
497 ms |
14328 KB |
Output is correct |
| 10 |
Correct |
494 ms |
14456 KB |
Output is correct |
| 11 |
Correct |
494 ms |
14456 KB |
Output is correct |
| 12 |
Correct |
495 ms |
14328 KB |
Output is correct |
| 13 |
Correct |
494 ms |
14456 KB |
Output is correct |
| 14 |
Correct |
494 ms |
14456 KB |
Output is correct |
| 15 |
Correct |
499 ms |
14328 KB |
Output is correct |
| 16 |
Correct |
99 ms |
14328 KB |
Output is correct |
| 17 |
Correct |
107 ms |
14428 KB |
Output is correct |
| 18 |
Correct |
102 ms |
14460 KB |
Output is correct |
| 19 |
Correct |
105 ms |
14332 KB |
Output is correct |
| 20 |
Correct |
103 ms |
14328 KB |
Output is correct |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
494 ms |
14328 KB |
Output is correct |
| 2 |
Correct |
494 ms |
14328 KB |
Output is correct |
| 3 |
Correct |
495 ms |
14456 KB |
Output is correct |
| 4 |
Correct |
495 ms |
14384 KB |
Output is correct |
| 5 |
Correct |
497 ms |
14364 KB |
Output is correct |
| 6 |
Correct |
495 ms |
14352 KB |
Output is correct |
| 7 |
Correct |
494 ms |
14456 KB |
Output is correct |
| 8 |
Correct |
494 ms |
14456 KB |
Output is correct |
| 9 |
Correct |
497 ms |
14328 KB |
Output is correct |
| 10 |
Correct |
494 ms |
14456 KB |
Output is correct |
| 11 |
Correct |
494 ms |
14456 KB |
Output is correct |
| 12 |
Correct |
495 ms |
14328 KB |
Output is correct |
| 13 |
Correct |
494 ms |
14456 KB |
Output is correct |
| 14 |
Correct |
494 ms |
14456 KB |
Output is correct |
| 15 |
Correct |
499 ms |
14328 KB |
Output is correct |
| 16 |
Correct |
99 ms |
14328 KB |
Output is correct |
| 17 |
Correct |
107 ms |
14428 KB |
Output is correct |
| 18 |
Correct |
102 ms |
14460 KB |
Output is correct |
| 19 |
Correct |
105 ms |
14332 KB |
Output is correct |
| 20 |
Correct |
103 ms |
14328 KB |
Output is correct |
| 21 |
Correct |
603 ms |
14356 KB |
Output is correct |
| 22 |
Correct |
606 ms |
14456 KB |
Output is correct |
| 23 |
Correct |
583 ms |
14456 KB |
Output is correct |
| 24 |
Correct |
589 ms |
14348 KB |
Output is correct |
| 25 |
Correct |
590 ms |
14456 KB |
Output is correct |
| 26 |
Correct |
663 ms |
14476 KB |
Output is correct |
| 27 |
Correct |
683 ms |
14352 KB |
Output is correct |
| 28 |
Correct |
663 ms |
14356 KB |
Output is correct |
| 29 |
Correct |
664 ms |
14388 KB |
Output is correct |
| 30 |
Correct |
492 ms |
14456 KB |
Output is correct |
| 31 |
Correct |
493 ms |
14480 KB |
Output is correct |
| 32 |
Correct |
499 ms |
14328 KB |
Output is correct |
| 33 |
Correct |
495 ms |
14456 KB |
Output is correct |
| 34 |
Correct |
493 ms |
14328 KB |
Output is correct |
| 35 |
Correct |
497 ms |
14384 KB |
Output is correct |
| 36 |
Correct |
492 ms |
14456 KB |
Output is correct |
| 37 |
Correct |
493 ms |
14356 KB |
Output is correct |
| 38 |
Correct |
492 ms |
14400 KB |
Output is correct |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
20 ms |
14328 KB |
Output is correct |
| 2 |
Correct |
19 ms |
14332 KB |
Output is correct |
| 3 |
Correct |
20 ms |
14328 KB |
Output is correct |
| 4 |
Correct |
20 ms |
14328 KB |
Output is correct |
| 5 |
Correct |
19 ms |
14328 KB |
Output is correct |
| 6 |
Correct |
21 ms |
14300 KB |
Output is correct |
| 7 |
Correct |
20 ms |
14328 KB |
Output is correct |
| 8 |
Correct |
21 ms |
14328 KB |
Output is correct |
| 9 |
Correct |
20 ms |
14328 KB |
Output is correct |
| 10 |
Correct |
21 ms |
14456 KB |
Output is correct |
| 11 |
Correct |
19 ms |
14328 KB |
Output is correct |
| 12 |
Correct |
19 ms |
14328 KB |
Output is correct |
| 13 |
Correct |
20 ms |
14328 KB |
Output is correct |
| 14 |
Correct |
20 ms |
14328 KB |
Output is correct |
| 15 |
Correct |
19 ms |
14328 KB |
Output is correct |
| 16 |
Correct |
17 ms |
14328 KB |
Output is correct |
| 17 |
Correct |
17 ms |
14328 KB |
Output is correct |
| 18 |
Correct |
17 ms |
14328 KB |
Output is correct |
| 19 |
Correct |
16 ms |
14328 KB |
Output is correct |
| 20 |
Correct |
17 ms |
14532 KB |
Output is correct |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
494 ms |
14328 KB |
Output is correct |
| 2 |
Correct |
494 ms |
14328 KB |
Output is correct |
| 3 |
Correct |
495 ms |
14456 KB |
Output is correct |
| 4 |
Correct |
495 ms |
14384 KB |
Output is correct |
| 5 |
Correct |
497 ms |
14364 KB |
Output is correct |
| 6 |
Correct |
495 ms |
14352 KB |
Output is correct |
| 7 |
Correct |
494 ms |
14456 KB |
Output is correct |
| 8 |
Correct |
494 ms |
14456 KB |
Output is correct |
| 9 |
Correct |
497 ms |
14328 KB |
Output is correct |
| 10 |
Correct |
494 ms |
14456 KB |
Output is correct |
| 11 |
Correct |
494 ms |
14456 KB |
Output is correct |
| 12 |
Correct |
495 ms |
14328 KB |
Output is correct |
| 13 |
Correct |
494 ms |
14456 KB |
Output is correct |
| 14 |
Correct |
494 ms |
14456 KB |
Output is correct |
| 15 |
Correct |
499 ms |
14328 KB |
Output is correct |
| 16 |
Correct |
99 ms |
14328 KB |
Output is correct |
| 17 |
Correct |
107 ms |
14428 KB |
Output is correct |
| 18 |
Correct |
102 ms |
14460 KB |
Output is correct |
| 19 |
Correct |
105 ms |
14332 KB |
Output is correct |
| 20 |
Correct |
103 ms |
14328 KB |
Output is correct |
| 21 |
Correct |
603 ms |
14356 KB |
Output is correct |
| 22 |
Correct |
606 ms |
14456 KB |
Output is correct |
| 23 |
Correct |
583 ms |
14456 KB |
Output is correct |
| 24 |
Correct |
589 ms |
14348 KB |
Output is correct |
| 25 |
Correct |
590 ms |
14456 KB |
Output is correct |
| 26 |
Correct |
663 ms |
14476 KB |
Output is correct |
| 27 |
Correct |
683 ms |
14352 KB |
Output is correct |
| 28 |
Correct |
663 ms |
14356 KB |
Output is correct |
| 29 |
Correct |
664 ms |
14388 KB |
Output is correct |
| 30 |
Correct |
492 ms |
14456 KB |
Output is correct |
| 31 |
Correct |
493 ms |
14480 KB |
Output is correct |
| 32 |
Correct |
499 ms |
14328 KB |
Output is correct |
| 33 |
Correct |
495 ms |
14456 KB |
Output is correct |
| 34 |
Correct |
493 ms |
14328 KB |
Output is correct |
| 35 |
Correct |
497 ms |
14384 KB |
Output is correct |
| 36 |
Correct |
492 ms |
14456 KB |
Output is correct |
| 37 |
Correct |
493 ms |
14356 KB |
Output is correct |
| 38 |
Correct |
492 ms |
14400 KB |
Output is correct |
| 39 |
Correct |
20 ms |
14328 KB |
Output is correct |
| 40 |
Correct |
19 ms |
14332 KB |
Output is correct |
| 41 |
Correct |
20 ms |
14328 KB |
Output is correct |
| 42 |
Correct |
20 ms |
14328 KB |
Output is correct |
| 43 |
Correct |
19 ms |
14328 KB |
Output is correct |
| 44 |
Correct |
21 ms |
14300 KB |
Output is correct |
| 45 |
Correct |
20 ms |
14328 KB |
Output is correct |
| 46 |
Correct |
21 ms |
14328 KB |
Output is correct |
| 47 |
Correct |
20 ms |
14328 KB |
Output is correct |
| 48 |
Correct |
21 ms |
14456 KB |
Output is correct |
| 49 |
Correct |
19 ms |
14328 KB |
Output is correct |
| 50 |
Correct |
19 ms |
14328 KB |
Output is correct |
| 51 |
Correct |
20 ms |
14328 KB |
Output is correct |
| 52 |
Correct |
20 ms |
14328 KB |
Output is correct |
| 53 |
Correct |
19 ms |
14328 KB |
Output is correct |
| 54 |
Correct |
17 ms |
14328 KB |
Output is correct |
| 55 |
Correct |
17 ms |
14328 KB |
Output is correct |
| 56 |
Correct |
17 ms |
14328 KB |
Output is correct |
| 57 |
Correct |
16 ms |
14328 KB |
Output is correct |
| 58 |
Correct |
17 ms |
14532 KB |
Output is correct |
| 59 |
Correct |
720 ms |
14328 KB |
Output is correct |
| 60 |
Correct |
710 ms |
14328 KB |
Output is correct |
| 61 |
Correct |
697 ms |
14456 KB |
Output is correct |
| 62 |
Correct |
717 ms |
14456 KB |
Output is correct |
| 63 |
Correct |
717 ms |
14400 KB |
Output is correct |
| 64 |
Correct |
833 ms |
14328 KB |
Output is correct |
| 65 |
Correct |
834 ms |
14328 KB |
Output is correct |
| 66 |
Correct |
834 ms |
14328 KB |
Output is correct |
| 67 |
Correct |
834 ms |
14456 KB |
Output is correct |
| 68 |
Correct |
832 ms |
14332 KB |
Output is correct |
| 69 |
Correct |
687 ms |
14332 KB |
Output is correct |
| 70 |
Correct |
682 ms |
14456 KB |
Output is correct |
| 71 |
Correct |
682 ms |
14328 KB |
Output is correct |
| 72 |
Correct |
691 ms |
14364 KB |
Output is correct |
| 73 |
Correct |
691 ms |
14360 KB |
Output is correct |
| 74 |
Correct |
143 ms |
14328 KB |
Output is correct |
| 75 |
Correct |
139 ms |
14364 KB |
Output is correct |
| 76 |
Correct |
139 ms |
14368 KB |
Output is correct |
| 77 |
Correct |
138 ms |
14364 KB |
Output is correct |
| 78 |
Correct |
137 ms |
14304 KB |
Output is correct |
