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Submission #461292

# Submission time Handle Problem Language Result Execution time Memory
461292 2021-08-09T16:53:53 Z wind_reaper Boat (APIO16_boat) C++17
100 / 100
 1905 ms 4504 KB 
#include <bits/stdc++.h>
/*
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
*/

using namespace std;
// using namespace __gnu_pbds;
using namespace chrono;

// mt19937 rng((int) std::chrono::steady_clock::now().time_since_epoch().count());
/*
template <class T> using ordered_set = tree <T, null_type, less <T>, rb_tree_tag, tree_order_statistics_node_update>;
*/

//***************** CONSTANTS *****************

const int MOD = 1000000007;
const int MXN = 505;

//***************** GLOBAL VARIABLES *****************

int A[MXN], B[MXN];
int64_t dp[MXN][MXN << 1], F[MXN], iF[MXN], C[MXN];

//***************** AUXILIARY STRUCTS *****************

int64_t power(int64_t n, int64_t x = MOD - 2){
	int64_t res = 1;
	while(x){
		if(x & 1)
			res = (res * n) % MOD;

		x >>= 1;
		n = (n * n) % MOD;
	}
	return res;
}

inline int64_t nCk(int n, int k){
	return F[n] * ((iF[n - k] * iF[k]) % MOD) % MOD;
}


//***************** MAIN BODY *****************

/*
	processing a range of values [D[i], D[i+1])

	we consider every [l, r] such that [1, l-1] lie in [..., D[i])
	and [l, r] lie in [D[i], D[i+1])

	> find the number of schools in [l, r] which can send boats in range [D[i], D[i+1])

	other schools are ignored

	>> add (D[i+1] - D[i]) C x where x is value calculated in >

	dp[i][j] -> insert i into j th interval

	dp[r][j] = sum(dp[l-1][j-1] + ways(l, r, j))

	ways(l, r, j) = >>

	C[i] -> no. of ways of picking up <= i items in increasing order from len items

	dp[i][j] = 
*/

void solve(){
	int N;
	cin >> N;

	vector<int> D;

	for(int i = 0; i < N; i++){
		cin >> A[i] >> B[i];
		D.push_back(A[i]);
		D.push_back(B[i] + 1);
	}

	F[0] = F[1] = 1;
	for(int i = 2; i < MXN; i++){
		F[i] = (F[i-1] * 1LL * i) % MOD;
	}

	iF[MXN - 1] = power(F[MXN - 1]);

	for(int i = MXN - 2; i >= 0; --i){
		iF[i] = (iF[i+1] * 1LL * (i + 1)) % MOD;
	}

	sort(D.begin(), D.end());
	D.erase(unique(D.begin(), D.end()), D.end());

	int n = D.size() - 1;

	int64_t ans = 0;

	for(int _ = 0; _ < n; _++){
		int len = D[_+1] - D[_];
		for(int i = 1; i <= N; i++){
			int64_t p = 1; C[i] = 0;
			for(int j = 1; j <= i; j++){
				p = (p * 1LL * (len - j + 1)) % MOD;
				C[i] = (C[i] + (((p * iF[j]) % MOD) * nCk(i - 1, j - 1)) % MOD) % MOD;
			}
		}

		for(int i = 0; i < N; i++) if(A[i] <= D[_] && B[i] >= D[_+1] - 1) {
			int cnt = 0;
			for(int j = i; j >= 0; j--){
				if(_) (dp[i][_] += dp[j][_-1] * C[cnt]) %= MOD;
				cnt += (A[j] <= D[_] && B[j] >= D[_+1] - 1);
			}
			(dp[i][_] += C[cnt]) %= MOD;
			ans = (ans + dp[i][_]) % MOD;
		}

		for(int i = 0; i < N; i++)
			(dp[i][_] += dp[i][_-1]) %= MOD;
	}

	cout << ans << '\n';
}

//***************** *****************

int32_t main(){
	ios_base::sync_with_stdio(NULL);
	cin.tie(NULL);

	#ifdef LOCAL
		auto begin = high_resolution_clock::now();
	#endif

	int tc = 1;
	// cin >> tc; 
	for (int t = 0; t < tc; t++)
		solve();

	#ifdef LOCAL 
		auto end = high_resolution_clock::now();
		cout << fixed << setprecision(4);
		cout << "Execution Time: " << duration_cast<duration<double>>(end - begin).count() << "seconds" << endl;
	#endif

	return 0;
}

/*
If code gives a WA, check for the following : 
1. I/O format

2. Are you clearing all global variables in between tests if multitests are a thing

3. Can you definitively prove the logic

4. If the code gives an inexplicable TLE, and you are sure you have the best possible complexity,
use faster io
*/

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 1589 ms 4300 KB Output is correct
2 Correct 1640 ms 4364 KB Output is correct
3 Correct 1589 ms 4276 KB Output is correct
4 Correct 1618 ms 4224 KB Output is correct
5 Correct 1617 ms 4272 KB Output is correct
6 Correct 1639 ms 4388 KB Output is correct
7 Correct 1606 ms 4364 KB Output is correct
8 Correct 1617 ms 4272 KB Output is correct
9 Correct 1601 ms 4396 KB Output is correct
10 Correct 1627 ms 4156 KB Output is correct
11 Correct 1624 ms 4212 KB Output is correct
12 Correct 1605 ms 4276 KB Output is correct
13 Correct 1606 ms 4392 KB Output is correct
14 Correct 1594 ms 4272 KB Output is correct
15 Correct 1635 ms 4340 KB Output is correct
16 Correct 282 ms 3016 KB Output is correct
17 Correct 302 ms 3016 KB Output is correct
18 Correct 289 ms 3016 KB Output is correct
19 Correct 310 ms 2976 KB Output is correct
20 Correct 296 ms 3120 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 1589 ms 4300 KB Output is correct
2 Correct 1640 ms 4364 KB Output is correct
3 Correct 1589 ms 4276 KB Output is correct
4 Correct 1618 ms 4224 KB Output is correct
5 Correct 1617 ms 4272 KB Output is correct
6 Correct 1639 ms 4388 KB Output is correct
7 Correct 1606 ms 4364 KB Output is correct
8 Correct 1617 ms 4272 KB Output is correct
9 Correct 1601 ms 4396 KB Output is correct
10 Correct 1627 ms 4156 KB Output is correct
11 Correct 1624 ms 4212 KB Output is correct
12 Correct 1605 ms 4276 KB Output is correct
13 Correct 1606 ms 4392 KB Output is correct
14 Correct 1594 ms 4272 KB Output is correct
15 Correct 1635 ms 4340 KB Output is correct
16 Correct 282 ms 3016 KB Output is correct
17 Correct 302 ms 3016 KB Output is correct
18 Correct 289 ms 3016 KB Output is correct
19 Correct 310 ms 2976 KB Output is correct
20 Correct 296 ms 3120 KB Output is correct
21 Correct 1662 ms 4416 KB Output is correct
22 Correct 1662 ms 4496 KB Output is correct
23 Correct 1612 ms 4256 KB Output is correct
24 Correct 1630 ms 4264 KB Output is correct
25 Correct 1632 ms 4324 KB Output is correct
26 Correct 1680 ms 4260 KB Output is correct
27 Correct 1733 ms 4504 KB Output is correct
28 Correct 1684 ms 4392 KB Output is correct
29 Correct 1657 ms 4312 KB Output is correct
30 Correct 1594 ms 4276 KB Output is correct
31 Correct 1611 ms 4268 KB Output is correct
32 Correct 1594 ms 4292 KB Output is correct
33 Correct 1634 ms 4396 KB Output is correct
34 Correct 1603 ms 4292 KB Output is correct
35 Correct 1593 ms 4444 KB Output is correct
36 Correct 1586 ms 4456 KB Output is correct
37 Correct 1655 ms 4328 KB Output is correct
38 Correct 1604 ms 4372 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 844 KB Output is correct
2 Correct 15 ms 780 KB Output is correct
3 Correct 15 ms 872 KB Output is correct
4 Correct 15 ms 876 KB Output is correct
5 Correct 16 ms 892 KB Output is correct
6 Correct 16 ms 844 KB Output is correct
7 Correct 16 ms 896 KB Output is correct
8 Correct 16 ms 844 KB Output is correct
9 Correct 16 ms 828 KB Output is correct
10 Correct 17 ms 804 KB Output is correct
11 Correct 17 ms 796 KB Output is correct
12 Correct 18 ms 836 KB Output is correct
13 Correct 15 ms 900 KB Output is correct
14 Correct 15 ms 820 KB Output is correct
15 Correct 18 ms 848 KB Output is correct
16 Correct 9 ms 716 KB Output is correct
17 Correct 9 ms 828 KB Output is correct
18 Correct 10 ms 784 KB Output is correct
19 Correct 9 ms 764 KB Output is correct
20 Correct 9 ms 820 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 1589 ms 4300 KB Output is correct
2 Correct 1640 ms 4364 KB Output is correct
3 Correct 1589 ms 4276 KB Output is correct
4 Correct 1618 ms 4224 KB Output is correct
5 Correct 1617 ms 4272 KB Output is correct
6 Correct 1639 ms 4388 KB Output is correct
7 Correct 1606 ms 4364 KB Output is correct
8 Correct 1617 ms 4272 KB Output is correct
9 Correct 1601 ms 4396 KB Output is correct
10 Correct 1627 ms 4156 KB Output is correct
11 Correct 1624 ms 4212 KB Output is correct
12 Correct 1605 ms 4276 KB Output is correct
13 Correct 1606 ms 4392 KB Output is correct
14 Correct 1594 ms 4272 KB Output is correct
15 Correct 1635 ms 4340 KB Output is correct
16 Correct 282 ms 3016 KB Output is correct
17 Correct 302 ms 3016 KB Output is correct
18 Correct 289 ms 3016 KB Output is correct
19 Correct 310 ms 2976 KB Output is correct
20 Correct 296 ms 3120 KB Output is correct
21 Correct 1662 ms 4416 KB Output is correct
22 Correct 1662 ms 4496 KB Output is correct
23 Correct 1612 ms 4256 KB Output is correct
24 Correct 1630 ms 4264 KB Output is correct
25 Correct 1632 ms 4324 KB Output is correct
26 Correct 1680 ms 4260 KB Output is correct
27 Correct 1733 ms 4504 KB Output is correct
28 Correct 1684 ms 4392 KB Output is correct
29 Correct 1657 ms 4312 KB Output is correct
30 Correct 1594 ms 4276 KB Output is correct
31 Correct 1611 ms 4268 KB Output is correct
32 Correct 1594 ms 4292 KB Output is correct
33 Correct 1634 ms 4396 KB Output is correct
34 Correct 1603 ms 4292 KB Output is correct
35 Correct 1593 ms 4444 KB Output is correct
36 Correct 1586 ms 4456 KB Output is correct
37 Correct 1655 ms 4328 KB Output is correct
38 Correct 1604 ms 4372 KB Output is correct
39 Correct 16 ms 844 KB Output is correct
40 Correct 15 ms 780 KB Output is correct
41 Correct 15 ms 872 KB Output is correct
42 Correct 15 ms 876 KB Output is correct
43 Correct 16 ms 892 KB Output is correct
44 Correct 16 ms 844 KB Output is correct
45 Correct 16 ms 896 KB Output is correct
46 Correct 16 ms 844 KB Output is correct
47 Correct 16 ms 828 KB Output is correct
48 Correct 17 ms 804 KB Output is correct
49 Correct 17 ms 796 KB Output is correct
50 Correct 18 ms 836 KB Output is correct
51 Correct 15 ms 900 KB Output is correct
52 Correct 15 ms 820 KB Output is correct
53 Correct 18 ms 848 KB Output is correct
54 Correct 9 ms 716 KB Output is correct
55 Correct 9 ms 828 KB Output is correct
56 Correct 10 ms 784 KB Output is correct
57 Correct 9 ms 764 KB Output is correct
58 Correct 9 ms 820 KB Output is correct
59 Correct 1823 ms 4360 KB Output is correct
60 Correct 1793 ms 4160 KB Output is correct
61 Correct 1790 ms 4340 KB Output is correct
62 Correct 1810 ms 4272 KB Output is correct
63 Correct 1803 ms 4356 KB Output is correct
64 Correct 1896 ms 4248 KB Output is correct
65 Correct 1905 ms 4328 KB Output is correct
66 Correct 1904 ms 4304 KB Output is correct
67 Correct 1903 ms 4276 KB Output is correct
68 Correct 1905 ms 4368 KB Output is correct
69 Correct 1755 ms 4292 KB Output is correct
70 Correct 1747 ms 4288 KB Output is correct
71 Correct 1746 ms 4312 KB Output is correct
72 Correct 1770 ms 4352 KB Output is correct
73 Correct 1756 ms 4336 KB Output is correct
74 Correct 332 ms 3232 KB Output is correct
75 Correct 334 ms 3056 KB Output is correct
76 Correct 330 ms 2932 KB Output is correct
77 Correct 353 ms 3012 KB Output is correct
78 Correct 332 ms 3004 KB Output is correct