Submission #579360

#	Time	Username	Problem	Language	Result	Execution time	Memory
579360		jiahng	Boat (APIO16_boat)	C++14	9 / 100	845 ms	29512 KiB

boat

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
#define int ll
typedef pair<int32_t, int32_t> pi;
typedef vector <int> vi;
typedef vector <pi> vpi;
typedef pair<pi, ll> pii;
typedef set <ll> si;
typedef long double ld;
#define f first
#define s second
#define mp make_pair
#define FOR(i,s,e) for(int i=s;i<=int(e);++i)
#define DEC(i,s,e) for(int i=s;i>=int(e);--i)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define lbd(x, y) lower_bound(all(x), y)
#define ubd(x, y) upper_bound(all(x), y)
#define aFOR(i,x) for (auto i: x)
#define mem(x,i) memset(x,i,sizeof x)
#define fast ios_base::sync_with_stdio(false),cin.tie(0),cout.tie(0)
#define maxn 1010
#define INF (ll)1e9+10
#define MOD 1000000007
typedef pair <vi, int> pvi;
typedef pair <int,pi> ipi;
typedef vector <pii> vpii;
int N,A[maxn],B[maxn];
int fac[maxn], invfac[maxn];
int qexp(int a,int b){
    int ans = 1;
    while (b){
        if (b&1) (ans *= a) %= MOD;
        (a *= a) %= MOD;
        b >>= 1;
    }
    return ans;
}
int nck(int n,int k){
    if (k > n) return 0;
    return (((fac[n] * invfac[k]) % MOD) * invfac[n-k]) % MOD;
}
int suffmult[2*maxn][maxn];
int dp[maxn][2*maxn];
int S[2*maxn],E[2*maxn];
int specnck(int x,int k){
	//~ cout << E[x]-S[x]+1 << ' ' << k << ' ' << (invfac[k] * suffmult[x][k]) % MOD << '\n';
	return (invfac[k] * suffmult[x][k]) % MOD;
}

int memo[maxn][maxn];
int f(int x,int y){
	if (memo[x][y] != -1) return memo[x][y];
	int ans = 0;
	FOR(z,1,x){
		ans += nck(x-1,z-1) * specnck(y,z);
	}
	return memo[x][y] = ans;
}
int32_t main(){
    cin >> N;
    FOR(i,1,N) cin >> A[i] >> B[i];
    fac[0] = 1;
    FOR(i,1,N) fac[i] = (fac[i-1] * i) % MOD;
    invfac[N] = qexp(fac[N], MOD-2);
    DEC(i,N-1,0) invfac[i] = (invfac[i+1] * (i+1)) % MOD;
    vi v;
    FOR(i,1,N){
		v.pb(A[i]); v.pb(B[i]);
	}
	v.pb(0); v.pb(INF);
    sort(all(v)); v.erase(unique(all(v)),v.end());
	
	int M = 1;
	FOR(i,0,(int)v.size()-1){
		S[M] = v[i]; E[M] = v[i];
		M++;
        if (i + 1 < (int)v.size() && v[i] + 1 < v[i+1]){
			S[M] = v[i]+1; E[M] = v[i+1]-1; M++;
		}
    }
	M--;
    
    FOR(i,1,M){
		suffmult[i][0] = 1;
		int x = E[i] - S[i] + 1;
		FOR(j,1,N){
			suffmult[i][j] = (suffmult[i][j-1] * x) % MOD;
			x--;
		}
	}
    FOR(i,1,M) dp[N+1][i] = 1;
    mem(memo, -1);
    DEC(i,N,1){
		DEC(j,M,1){
			if (B[i] < S[j]){
				dp[i][j] = 0; continue;
			}
			dp[i][j] = dp[i][j+1];
			
			if (A[i] <= S[j] && E[j] <= B[i]){
				int num = 1;
				FOR(k,i+1,N+1){
					(dp[i][j] += (dp[k][j+1] * f(num, j)) % MOD) %= MOD;
					if (A[k] <= S[j] && E[j] <= B[k]) num++;
					
				}
			}
				
		}
    }
	int ans = 0;
	FOR(i,1,N){
		(ans += dp[i][1]) %= MOD;
	}
    cout << ans;
}

• Subtask 1: 9 / 9
• Subtask 2: 0 / 22
• Subtask 3: 0 / 27
• Subtask 4: 0 / 42