Submission #376374

#	Time	Username	Problem	Language	Result	Execution time	Memory
376374		shivensinha4	Boat (APIO16_boat)	C++17	100 / 100	1811 ms	620 KiB

boat

#pragma GCC optimize("Ofast")
#include "bits/stdc++.h"
using namespace std;
#define for_(i, s, e) for (int i = s; i < (int) e; i++)
#define for__(i, s, e) for (ll i = s; i < e; i++)
typedef long long ll;
typedef vector<int> vi;
typedef array<int, 2> ii;
#define endl '\n'
 
const ll mod = 1e9+7;
const ll MAXN = 500;
ll numInv[MAXN+10], facInv[MAXN+10], fac[MAXN+10];

void pre() {
	numInv[0] = numInv[1] = 1;
	for (int i = 2; i <= MAXN; i++) numInv[i] = numInv[mod % i] * (mod - mod / i) % mod;

	facInv[0] = facInv[1] = 1;
	for (int i = 2; i <= MAXN; i++) facInv[i] = (numInv[i] * facInv[i - 1]) % mod;

	fac[0] = 1;
	for (int i = 1; i <= MAXN; i++) fac[i] = (fac[i - 1] * i) % mod;
}

ll nCr(ll n, ll r) {
	return ((fac[n] * facInv[r]) % mod * facInv[n - r]) % mod; 
}

ll choose[MAXN+1], dp[2][MAXN+1];
 
int main() {
#ifdef mlocal
	freopen("test.in", "r", stdin);
#endif
	
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	
	memset(choose, 0, sizeof(choose)); memset(dp, 0, sizeof(dp));
	pre();
	
	int n; cin >> n;
	vector<ii> lt(n);
	vi raw(2*n);
	
	for_(i, 0, n) {
		cin >> lt[i][0] >> lt[i][1];
		lt[i][1]++;
		raw[2*i] = lt[i][0], raw[2*i+1] = lt[i][1];
	}
	
	sort(raw.begin(), raw.end());
	raw.resize(unique(raw.begin(), raw.end()) - raw.begin());
	
	int ns = raw.size()-1;
	
	int cs = 0; ll len, val;
	dp[1][n] = 1;
	for (int s = ns-1; s >= 0; s--) {
		choose[0] = 1;
		
		len = raw[s+1]-raw[s];
		for_(r, 1, n+1) {
			choose[r] = 0;
			val = 1;
			for_(t, 1, r+1) {
				if (t > len) val = 0;
				else val = ((val * (len-t+1)) % mod) % mod;
				choose[r] += (((nCr(r-1, t-1) * val) % mod) * facInv[t]) % mod;
				if (choose[r] >= mod) choose[r] -= mod;
			}
		}
		
		
		dp[cs][n] = 1;
		for_(i, 0, n) {
			dp[cs][i] = dp[1-cs][i];
			int ct = raw[s] >= lt[i][0] and raw[s+1] <= lt[i][1];
			if (ct) {
				for_(j, i+1, n+1) {
					dp[cs][i] += (choose[ct] * dp[1-cs][j]) % mod;
					if (dp[cs][i] >= mod) dp[cs][i] -= mod;
					if (j < n and raw[s] >= lt[j][0] and raw[s+1] <= lt[j][1]) ct++;
				}
			}
		}
		
		cs = 1-cs;
	}
	
	ll ans = 0;
	for_(i, 0, n) {
		ans += dp[1-cs][i];
		if (ans >= mod) ans -= mod;
	}
	
	cout << ans << endl;
}

• Subtask 1: 9 / 9
• Subtask 2: 22 / 22
• Subtask 3: 27 / 27
• Subtask 4: 42 / 42