Submission #1027545

#	Time	Username	Problem	Language	Result	Execution time	Memory
1027545		_8_8_	Boat (APIO16_boat)	C++17	100 / 100	1567 ms	19092 KiB

boat

#include <bits/stdc++.h>
 
using namespace std;
 
typedef long long ll;
const int  N = 1e3 + 20, MOD = (int)1e9+7;

ll binpow(ll a,ll b) {
    ll ans = 1,k = a;
    while(b) {
        if(b % 2)ans *= k;
        ans %= MOD;
        k *= k;
        k %= MOD;
        b /= 2ll;
    }
    return ans;
}
ll bp[N];
ll ceis(ll n,ll k){
    if(k > n) return 0;     
    ll d = 1;
    for(ll i = n - k + 1;i <= n;i++){
        d = i % MOD * d % MOD;
    }
    for(ll i = 2;i <= k;i++){   
        d = d * bp[i]%MOD;
    }
    return d;
}
int n;
array<int,2> a[N];
vector<int> b;
vector<array<int,2>> o;
ll dp[N][N],pref[N][N],c[N][N],prec[N/2][N/2];
int m;
void test(){
    cin >> n;
    for(int i = 1;i <= n;i++){
        cin >> a[i][0] >> a[i][1];
        b.push_back(a[i][0]);
        b.push_back(a[i][1] + 1);
        bp[i] = binpow(i,MOD-2);
    }
    sort(b.begin(),b.end());
    b.resize(unique(b.begin(),b.end()) - b.begin()); 
    for(int i = 1;i < (int)b.size();i++){
        o.push_back({b[i-1],b[i]-1});
    }
    int m = (int)o.size();
    for(int i = 0;i <= m;i++){
        pref[0][i] = 1;
    }
    for(int i = 0;i <= n;i++){
        for(int j = 0;j <= i;j++){
            prec[i][j] = ceis(i,j);
        }
    }
    for(int i = 1;i <= m;i++){
        int s = (o[i - 1][1] - o[i - 1][0]+1);
        c[i][1] = s;
        vector<int> C(n+1,0);
        for(int j = 0;j <= n;++j){
            C[j] = ceis(s,j);
        }
        for(int j = 2;j <= n;j++){
            for(int k = 0;k <= j-2;k++){
                c[i][j] = (c[i][j] + prec[j-2][k]*1ll*C[j-k]%MOD);
                if(c[i][j] >= MOD) c[i][j] -= MOD;
            }
        }
    }
    for(int i = 1;i <= n;i++){
        pref[i][0] = 1;
        for(int j = 1;j <= m;j++){
            dp[i][j] = dp[i - 1][j];
            if(a[i][0] <= o[j - 1][0] && a[i][1] >= o[j-1][1]){
                for(int k = i,col = 0;k >= 1;k--){
                    if(a[k][0] <= o[j-1][0] && a[k][1] >= o[j-1][1]){
                        ++col;
                        dp[i][j] += pref[k-1][j-1]*1ll*c[j][col]%MOD;
                        if(dp[j][j] >= MOD) dp[i][j] -= MOD;
                    }
                }
            }
        }
        for(int j = 1;j <= m;j++){
            pref[i][j] = (pref[i][j - 1] + dp[i][j])%MOD;
        }
    }
    cout << (pref[n][m]-1+MOD)%MOD << '\n';
}
signed main() {
    ios_base::sync_with_stdio(false);cin.tie(0);
    int t = 1; 
    // cin >> t;
    while(t--){
        test();
    }
}

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