Submission #1027047

#	Time	Username	Problem	Language	Result	Execution time	Memory
1027047		_8_8_	Boat (APIO16_boat)	C++17	0 / 100	2060 ms	4948 KiB

boat

#include <bits/stdc++.h>
 
using namespace std;
 
typedef long long ll;
const int  N = 5e2 + 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<pair<int,int>> o;
ll dp[N][N],pref[N][N],c[N][N];
bool cc[N][N];
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.emplace_back(b[i - 1],b[i] - 1);
    }
    // for(auto [l,r]:o){
    //     cout << l << ' ' << r << '\n';
    // }
    for(int i = 0;i <= (int)o.size();i++){
        pref[0][i] = 1;
    }
    for(int i = 1;i <= (int)o.size();i++){
        int s = (o[i - 1].second - o[i - 1].first) + 1;
        for(int j = 1;j <= n;j++){
            c[i][j] = ceis(s,j);
            for(int k = 1;k < j-1;k++){
                c[i][j] += (ceis(j-1,k)-k) * ceis(s,j-k)%MOD;
                c[i][j]%=MOD;
                // cout << i << ' ' << j << ' ' << k << ' ' << (ceis(j-1,k)-k) << ' ' << ceis(s,j-k) << '\n';
            }
        }
    }
    for(int i = 1;i <= n;i++){
        vector<int> can;
        for(int j = 0;j < (int)o.size();j++){
            if(o[j].first >= a[i][0] && o[j].second <= a[i][1])
            {
                cc[i][j + 1] =1;
                can.push_back(j + 1);
            }
            dp[i][j + 1] = dp[i - 1][j + 1];
        }
        for(int j:can){
            ll F = 0;
            int _ = 0;
            for(int f = 1;f <= i;f++){
                int lst = i - (f);
                if(lst!=i && !cc[lst+1][j]){
                    _++;
                    continue;
                }
                dp[i][j] += pref[lst][j - 1] * c[j][f-_] % MOD; 
                F +=pref[lst][j - 1] * c[j][f] % MOD;
                if(dp[i][j] >= MOD) dp[i][j] -= MOD;
            }
            // cout << F << "x\n";
        }
        pref[i][0] = 1;
        // for(int j = 0;j <= (int)o.size();j++){
        //     cout << dp[i][j] << ' ';
        // }
        // cout << '\n';
        for(int j = 1;j <= (int)o.size();j++){
            pref[i][j] = pref[i][j - 1] + dp[i][j];
            if(pref[i][j] >= MOD) pref[i][j] -= MOD;
        }
        // cout << '\n';
    }
    cout << (pref[n][(int)o.size()] - 1 + MOD)%MOD << '\n';
}
int main() {
    ios_base::sync_with_stdio(false);cin.tie(0);
    int t = 1; 
    // cin >> t;
    while(t--){
        test();
    }
}

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