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답안 #705066

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
705066 2023-03-03T10:28:12 Z 600Mihnea Boat (APIO16_boat) C++17
58 / 100
 2000 ms 9132 KB 
#include <cmath>
#include <functional>
#include <fstream>
#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <set>
#include <map>
#include <list>
#include <time.h>
#include <math.h>
#include <random>
#include <deque>
#include <queue>
#include <unordered_map>
#include <unordered_set>
#include <iomanip>
#include <cassert>
#include <bitset>
#include <sstream>
#include <chrono>
#include <cstring>
#include <numeric>

using namespace std;

typedef long long ll;
const int M = (int)1e9 + 7;
const int FACTN = 300000 + 7;

int add(int a, int b) {
	a += b;
	if (a >= M) return a - M;
	if (a < 0) return a + M;
	return a;
}

int mul(int a, int b) {
	return a * (ll)b % M;
}

int add(int a, int b, int c) {
	return add(add(a, b), c);
}

int mul(int a, int b, int c) {
	return mul(mul(a, b), c);
}

int add(int a, int b, int c, int d) {
	return add(add(a, b, c), d);
}

int mul(int a, int b, int c, int d) {
	return mul(mul(a, b, c), d);
}

int add(int a, int b, int c, int d, int e) {
	return add(add(a, b, c, d), e);
}

int mul(int a, int b, int c, int d, int e) {
	return mul(mul(a, b, c, d), e);
}

int add(int a, int b, int c, int d, int e, int f) {
	return add(add(a, b, c, d, e), f);
}

int mul(int a, int b, int c, int d, int e, int f) {
	return mul(mul(a, b, c, d, e), f);
}

int add(int a, int b, int c, int d, int e, int f, int g) {
	return add(add(a, b, c, d, e, f), g);
}

int mul(int a, int b, int c, int d, int e, int f, int g) {
	return mul(mul(a, b, c, d, e, f), g);
}

int add(int a, int b, int c, int d, int e, int f, int g, int h) {
	return add(add(a, b, c, d, e, f, g), h);
}

int mul(int a, int b, int c, int d, int e, int f, int g, int h) {
	return mul(mul(a, b, c, d, e, f, g), h);
}

int pw(int a, int b) {
	int r = 1;
	while (b) {
		if (b & 1) r = mul(r, a);
		a = mul(a, a);
		b /= 2;
	}
	return r;
}

int dv(int a, int b) {
	return mul(a, pw(b, M - 2));
}

void addup(int& a, int b) {
	a = add(a, b);
}

void mulup(int& a, int b) {
	a = mul(a, b);
}

void dvup(int& a, int b) {
	a = dv(a, b);
}

int fact[FACTN], ifact[FACTN];

void computeFACT() {
	fact[0] = 1;
	for (int i = 1; i < FACTN; i++) fact[i] = mul(fact[i - 1], i);
	ifact[FACTN - 1] = dv(1, fact[FACTN - 1]);
	for (int i = FACTN - 2; i >= 0; i--) ifact[i] = mul(ifact[i + 1], i + 1);
}

int getCOMB(int n, int k) {
	return mul(fact[n], mul(ifact[k], ifact[n - k]));
}

int fastComb(int n, int k)
{
	if (k > n)
	{
		return 0;
	}
	// n is very big
	// k is small
	assert(0 <= k && k <= n);
	int up = 1;
	for (int i = 1; i <= k; i++)
	{
		mulup(up, n + 1 - i);
	}
	return mul(up, ifact[k]);
}


int dumb(vector<pair<int, int>> segs)
{
	int n = (int)segs.size();
	vector<vector<int>> dp(n);
	for (int i = 0; i < n; i++)
	{
		assert(segs[i].first <= segs[i].second);
		dp[i].resize(segs[i].second - segs[i].first + 1, 1);
	}
	for (int i = 0; i < n; i++)
	{
		for (int j = 0; j < i; j++)
		{
			for (int y = segs[i].first; y <= segs[i].second; y++)
			{
				if (segs[j].second <= y - 1)
				{
					addup(dp[i][y - segs[i].first], dp[j].back());
				}
				else
				{
					if (segs[j].first <= y - 1)
					{
						addup(dp[i][y - segs[i].first], dp[j][y - 1 - segs[j].first]);
					}
				}
			}
		}
		int cur = 0;
		for (auto& it : dp[i])
		{
			addup(cur, it);
			it = cur;
		}
	}
	int sol = 0;
	for (int i = 0; i < n; i++)
	{
		addup(sol, dp[i].back());
	}
	return sol;
}


mt19937 rng(228);

int getrng(int l, int r)
{
	assert(l <= r);
	int x = rng() % (r - l + 1) + l;
	assert(l <= x && x <= r);
	return x;
}

vector<pair<int, int>> getrng()
{
	const int N = 10;
	const int L = 10;
	int n = getrng(1, N);
	vector<pair<int, int>> v(n);
	for (auto& it : v)
	{
		it.first = getrng(1, L);
		it.second = getrng(1, L);
		if (it.first > it.second)
		{
			swap(it.first, it.second);
		}
		assert(it.first <= it.second);
	}
	return v;
}

int smart(vector<pair<int, int>> v)
{
	int n = (int)v.size();
	map<int, int> mp;
	for (auto& it : v)
	{
		mp[it.first] = 0;
		mp[it.second + 1] = 0;
	}
	vector<int> xs;
	int y = 0;
	for (auto& it : mp)
	{
		xs.push_back(it.first);
		it.second = y++;
	}
	vector<int> dim;
	for (int i = 0; i + 1 < (int)xs.size(); i++)
	{
		dim.push_back(xs[i + 1] - xs[i]);
	}
	assert((int)dim.size() == y - 1);
	y = (int)dim.size();
	for (auto& it : v)
	{
		assert(mp.count(it.first));
		assert(mp.count(it.second + 1));
		it.first = mp[it.first];
		it.second = mp[it.second + 1] - 1;
	}
	vector<vector<int>> dp(y, vector<int>(n + 1, 0));
	vector<vector<int>> prod(y, vector<int>(n + 1, 0));
	for (int i = 0; i < y; i++)
	{
		prod[i][0] = 1;
		for (int j = 1; j <= n; j++)
		{
			prod[i][j] = mul(prod[i][j - 1], dim[i] + 1 - j);
		}
	}
	for (auto& seg : v)
	{
		vector<int> sigma(y + 1, 0);
		int l = seg.first, r = seg.second;
		auto ndp = dp; // nu fac nimic aici
		// incep ceva nou aici
		for (int i = l; i <= r; i++)
		{
			addup(ndp[i][1], +1);
		}
		for (int i = 0; i < y; i++)
		{
			int orice = 0;
			for (int t = 1; t <= n; t++)
			{
				addup(orice, mul(dp[i][t], mul(prod[i][t], ifact[t])));
			}
			if (max(l, i + 1) <= min(r, y - 1))
			{
				addup(sigma[max(l, i + 1)], orice);
				addup(sigma[min(r, y - 1)+1], -orice);
			}
		}
		int cur = 0;
		for (int i = 0; i < y; i++)
		{
			addup(cur, sigma[i]);
			addup(ndp[i][1], cur);
		}
		for (int i = l; i <= r; i++) 
		{
			for (int t = 1; t <= n; t++)
			{
				addup(ndp[i][t], dp[i][t - 1]);
			}
		}
		dp = ndp;
		//cout << " :--------------> " << dp[1][1] << "\n";
	}
	if (0)
	{
		for (auto& it : v)
		{
			cout << " ---> " << it.first << " " << it.second << "\n";
		}
		cout << "\n";
		cout << "dims = ";
		for (auto& d : dim)
		{
			cout << d << " ";
		}
		cout << "\n";
	}
	//for (int i = 0; i < y; i++)
	//{
	//	for (int j = 0; j <= n; j++)
	//	{
	//		cout << dp[i][j] << " ";
	//	}
	//	cout << "\n";
	//}
	int sol = 0;
	for (int i = 0; i < y; i++)
	{
		for (int t = 0; t <= n; t++)
		{
			addup(sol, mul(dp[i][t], fastComb(dim[i], t)));
			if (mul(dp[i][t], fastComb(dim[i], t)) > 0)
			{
				//cout << " : " << i << ", " << t << " ---> " << dp[i][t] << " and " << fastComb(dim[i], t) << "\n";
			}
		}
	}
	return sol;
}

signed main()
{
	computeFACT();
#ifdef ONPC	
	FILE* stream;
	freopen_s(&stream, "input.txt", "r", stdin);
#else
	ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#endif

	if (0)
	{
		vector<pair<int, int>> v;
		v = { {1, 2}, {1, 1} };
		int d = dumb(v);
		int s = smart(v);
		if (d != s)
		{
			cout << "WA!\n";
			cout << (int)v.size() << "\n";
			for (auto& it : v)
			{
				cout << it.first << " " << it.second << "\n";
			}
			cout << "good = " << d << "\n";
			cout << "me   = " << s << "\n";
			exit(0);
		}
		cout << "AC!\n";
		exit(0);
	}
	
	if (0)
	{
		cout << "debug time!\n";
		long long printtime = (long long)1e4;
		for (long long tc = 1; 1; tc++)
		{
			vector<pair<int, int>> v = getrng();
			int d = dumb(v);
			int s = smart(v);
			if (tc % printtime == 0)
			{
				cout << "done " << tc << ", n = " << (int)v.size() << ", sol = " << s << "\n";
			}
			if (d != s)
			{
				cout << "WA!\n";
				cout << (int)v.size() << "\n";
				for (auto& it : v)
				{
					cout << it.first << " " << it.second << "\n";
				}
				cout << "good = " << d << "\n";
				cout << "me   = " << s << "\n";
				exit(0);
			}
		}
		exit(0);
	}

	int n;
	cin >> n;
	vector<pair<int, int>> v(n);
	for (auto& it : v)
	{
		cin >> it.first >> it.second;
	}
	
	//cout << dumb(v) << "\n";
	cout << smart(v) << "\n";
	return 0;
}

Subtask #1
9.0 / 9.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1908 ms 9032 KB Output is correct
2 Correct 1837 ms 8828 KB Output is correct
3 Correct 1838 ms 8776 KB Output is correct
4 Correct 1827 ms 8956 KB Output is correct
5 Correct 1863 ms 9020 KB Output is correct
6 Correct 1906 ms 8952 KB Output is correct
7 Correct 1805 ms 8880 KB Output is correct
8 Correct 1823 ms 8956 KB Output is correct
9 Correct 1905 ms 8992 KB Output is correct
10 Correct 1861 ms 8912 KB Output is correct
11 Correct 1873 ms 9024 KB Output is correct
12 Correct 1822 ms 8812 KB Output is correct
13 Correct 1826 ms 8908 KB Output is correct
14 Correct 1825 ms 8844 KB Output is correct
15 Correct 1824 ms 8956 KB Output is correct
16 Correct 307 ms 3748 KB Output is correct
17 Correct 323 ms 3832 KB Output is correct
18 Correct 312 ms 3788 KB Output is correct
19 Correct 322 ms 3836 KB Output is correct
20 Correct 324 ms 3844 KB Output is correct

Subtask #2
22.0 / 22.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1908 ms 9032 KB Output is correct
2 Correct 1837 ms 8828 KB Output is correct
3 Correct 1838 ms 8776 KB Output is correct
4 Correct 1827 ms 8956 KB Output is correct
5 Correct 1863 ms 9020 KB Output is correct
6 Correct 1906 ms 8952 KB Output is correct
7 Correct 1805 ms 8880 KB Output is correct
8 Correct 1823 ms 8956 KB Output is correct
9 Correct 1905 ms 8992 KB Output is correct
10 Correct 1861 ms 8912 KB Output is correct
11 Correct 1873 ms 9024 KB Output is correct
12 Correct 1822 ms 8812 KB Output is correct
13 Correct 1826 ms 8908 KB Output is correct
14 Correct 1825 ms 8844 KB Output is correct
15 Correct 1824 ms 8956 KB Output is correct
16 Correct 307 ms 3748 KB Output is correct
17 Correct 323 ms 3832 KB Output is correct
18 Correct 312 ms 3788 KB Output is correct
19 Correct 322 ms 3836 KB Output is correct
20 Correct 324 ms 3844 KB Output is correct
21 Correct 1552 ms 8316 KB Output is correct
22 Correct 1533 ms 8392 KB Output is correct
23 Correct 1513 ms 8284 KB Output is correct
24 Correct 1617 ms 8552 KB Output is correct
25 Correct 1588 ms 8312 KB Output is correct
26 Correct 1558 ms 8080 KB Output is correct
27 Correct 1644 ms 8328 KB Output is correct
28 Correct 1609 ms 8264 KB Output is correct
29 Correct 1579 ms 8284 KB Output is correct
30 Correct 1868 ms 8956 KB Output is correct
31 Correct 1830 ms 8956 KB Output is correct
32 Correct 1832 ms 8936 KB Output is correct
33 Correct 1881 ms 8892 KB Output is correct
34 Correct 1858 ms 8920 KB Output is correct
35 Correct 1789 ms 9056 KB Output is correct
36 Correct 1893 ms 9132 KB Output is correct
37 Correct 1799 ms 8920 KB Output is correct
38 Correct 1836 ms 8988 KB Output is correct

Subtask #3
27.0 / 27.0

# 결과 실행 시간 메모리 Grader output
1 Correct 25 ms 2900 KB Output is correct
2 Correct 23 ms 2900 KB Output is correct
3 Correct 24 ms 2900 KB Output is correct
4 Correct 25 ms 2900 KB Output is correct
5 Correct 24 ms 2932 KB Output is correct
6 Correct 27 ms 2948 KB Output is correct
7 Correct 25 ms 2900 KB Output is correct
8 Correct 25 ms 2948 KB Output is correct
9 Correct 26 ms 2924 KB Output is correct
10 Correct 29 ms 2928 KB Output is correct
11 Correct 24 ms 2900 KB Output is correct
12 Correct 23 ms 2928 KB Output is correct
13 Correct 24 ms 2900 KB Output is correct
14 Correct 23 ms 2900 KB Output is correct
15 Correct 24 ms 2932 KB Output is correct
16 Correct 15 ms 2824 KB Output is correct
17 Correct 14 ms 2772 KB Output is correct
18 Correct 14 ms 2828 KB Output is correct
19 Correct 15 ms 2772 KB Output is correct
20 Correct 15 ms 2772 KB Output is correct

Subtask #4
0 / 42.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1908 ms 9032 KB Output is correct
2 Correct 1837 ms 8828 KB Output is correct
3 Correct 1838 ms 8776 KB Output is correct
4 Correct 1827 ms 8956 KB Output is correct
5 Correct 1863 ms 9020 KB Output is correct
6 Correct 1906 ms 8952 KB Output is correct
7 Correct 1805 ms 8880 KB Output is correct
8 Correct 1823 ms 8956 KB Output is correct
9 Correct 1905 ms 8992 KB Output is correct
10 Correct 1861 ms 8912 KB Output is correct
11 Correct 1873 ms 9024 KB Output is correct
12 Correct 1822 ms 8812 KB Output is correct
13 Correct 1826 ms 8908 KB Output is correct
14 Correct 1825 ms 8844 KB Output is correct
15 Correct 1824 ms 8956 KB Output is correct
16 Correct 307 ms 3748 KB Output is correct
17 Correct 323 ms 3832 KB Output is correct
18 Correct 312 ms 3788 KB Output is correct
19 Correct 322 ms 3836 KB Output is correct
20 Correct 324 ms 3844 KB Output is correct
21 Correct 1552 ms 8316 KB Output is correct
22 Correct 1533 ms 8392 KB Output is correct
23 Correct 1513 ms 8284 KB Output is correct
24 Correct 1617 ms 8552 KB Output is correct
25 Correct 1588 ms 8312 KB Output is correct
26 Correct 1558 ms 8080 KB Output is correct
27 Correct 1644 ms 8328 KB Output is correct
28 Correct 1609 ms 8264 KB Output is correct
29 Correct 1579 ms 8284 KB Output is correct
30 Correct 1868 ms 8956 KB Output is correct
31 Correct 1830 ms 8956 KB Output is correct
32 Correct 1832 ms 8936 KB Output is correct
33 Correct 1881 ms 8892 KB Output is correct
34 Correct 1858 ms 8920 KB Output is correct
35 Correct 1789 ms 9056 KB Output is correct
36 Correct 1893 ms 9132 KB Output is correct
37 Correct 1799 ms 8920 KB Output is correct
38 Correct 1836 ms 8988 KB Output is correct
39 Correct 25 ms 2900 KB Output is correct
40 Correct 23 ms 2900 KB Output is correct
41 Correct 24 ms 2900 KB Output is correct
42 Correct 25 ms 2900 KB Output is correct
43 Correct 24 ms 2932 KB Output is correct
44 Correct 27 ms 2948 KB Output is correct
45 Correct 25 ms 2900 KB Output is correct
46 Correct 25 ms 2948 KB Output is correct
47 Correct 26 ms 2924 KB Output is correct
48 Correct 29 ms 2928 KB Output is correct
49 Correct 24 ms 2900 KB Output is correct
50 Correct 23 ms 2928 KB Output is correct
51 Correct 24 ms 2900 KB Output is correct
52 Correct 23 ms 2900 KB Output is correct
53 Correct 24 ms 2932 KB Output is correct
54 Correct 15 ms 2824 KB Output is correct
55 Correct 14 ms 2772 KB Output is correct
56 Correct 14 ms 2828 KB Output is correct
57 Correct 15 ms 2772 KB Output is correct
58 Correct 15 ms 2772 KB Output is correct
59 Execution timed out 2057 ms 9064 KB Time limit exceeded
60 Halted 0 ms 0 KB -