답안 #45550 :: oj.uz

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
45550	2018-04-15T10:24:18 Z	fallingstar	Boat (APIO16_boat)	C++17	100 / 100	1148 ms	6464 KB

boat

/**
	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;
}

Subtask #1
9.0 / 9.0

#	결과	실행 시간	메모리	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

Subtask #2
22.0 / 22.0

#	결과	실행 시간	메모리	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

Subtask #3
27.0 / 27.0

#	결과	실행 시간	메모리	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

Subtask #4
42.0 / 42.0

#	결과	실행 시간	메모리	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

답안 #45550

Compilation message

Subtask #1 9.0 / 9.0

Subtask #2 22.0 / 22.0

Subtask #3 27.0 / 27.0

Subtask #4 42.0 / 42.0

Subtask #1
9.0 / 9.0

Subtask #2
22.0 / 22.0

Subtask #3
27.0 / 27.0

Subtask #4
42.0 / 42.0