Submission #246277

#	Time	Username	Problem	Language	Result	Execution time	Memory
246277		kostia244	Ruins 3 (JOI20_ruins3)	C++17	100 / 100	767 ms	6752 KiB

ruins3

#include<bits/stdc++.h>
using namespace std;
using ll = long long;
const int maxn = 666, mod = 1e9 + 7;
int n, h[maxn][maxn][2], dp[maxn][maxn], pre[maxn][maxn], a[maxn], pa[maxn], fact[maxn], inv[maxn];
inline void add(int &a, int b) {
	a = a+b > mod ? a+b-mod : a+b;
}
inline int mul(int a, int b) {
	return a*1ll*b%mod;
}
int bp(int a, int p) {
	int r = 1;
	while(p) {
		if(p&1) r = mul(a, r);
		a = mul(a, a), p>>=1;
	}
	return r;
}
void setup() {
	for(int i = 0; i < maxn; i++)
		if(i < 2) fact[i] = inv[i] = 1;
		else fact[i] = i, inv[i] = mod - mul(mod/i, inv[mod%i]);
	for(int* a : {fact, inv})
	for(int i = 2; i < maxn; i++)
		a[i] = mul(a[i-1], a[i]);
}
inline int nck(int n, int k) {
	return n < 0 || k > n ? 0 : mul(fact[n], mul(inv[n-k], inv[k]));
}
inline int A(int n, int k) {
	return n < 0 || k > n ? 0 : mul(fact[n], inv[n-k]);
}
void calch() {
	h[0][0][0] = 1;
	for(int i = 0; i < n; i++)
		for(int j = i; j <= n; j++) {
			for(int f = 0; f < 2; f++) {
				add(h[i+1][j][f], mul(h[i][j][f], inv[2]));
				add(h[i+1][j+1][f], h[i][j][f]);
				add(h[i+1][j+2][f], mul(h[i][j][f], inv[2]));
			}
			add(h[i+1][j][1], mul(h[i][j][0], inv[2]));
			add(h[i+1][j+1][1], mul(h[i][j][0], inv[2]));
		}
}
inline int prod(int l, int r) {
	if(r < l) return 1;
	if(l <= 0) return 0;
	return mul(fact[r], inv[l-1]);
}
inline int contrib(int lst, int i) {
	int N = lst - (i>1?pa[i-2]:0);
	return prod(N-a[i-1]+1, N);
}
void calcdp() {
	dp[0][0] = 1;
	for(int i = 0; i <= n; i++)
		for(int lst = 0; lst <= i; lst++) {
			int q;
			for(int olst = 0; olst < lst; olst++) {
				int dif = lst-olst-1;
				q = pre[i][olst];
				q = mul(q, mul(h[dif][dif][0] + h[dif][dif][1], A(i-olst-1, dif)));
				q = mul(q, contrib(lst, i));
				add(dp[i][lst], q);
			}
			if(i == n || !dp[i][lst]) continue;
			q = 1;
			for(int ni = i+1; ni <= n; ni++) {
				add(pre[ni][lst], mul(q, dp[i][lst]));
				q = mul(q, contrib(lst, ni));
			}
		}
}

int main() {
	cin.tie(0)->sync_with_stdio(0);
	setup();
	cin >> n;
	for(int i = 0; i < n; i++) cin >> a[i];
	reverse(a, a+n);
	if(a[0] != 2*n)  return cout << 0, 0;
	for(int i = 0; i < n; i++) a[i] = a[i] - a[i+1] - 1;
	pa[0] = a[0];
	for(int i = 1; i < n; i++) pa[i] = pa[i-1] + a[i];
	calch();
	calcdp();
	cout << dp[n][n] << '\n';
}

• Subtask 1: 6 / 6
• Subtask 2: 52 / 52
• Subtask 3: 42 / 42