Submission #1335543

#TimeUsernameProblemLanguageResultExecution timeMemory
1335543Zbyszek99Boat (APIO16_boat)C++20
100 / 100
1490 ms12304 KiB
#include <bits/stdc++.h>
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
//mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
//ll rand(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;

ll P(ll x)
{
    ll ans = 1;
    rep(bit,30)
    {
        if((MOD-2)&(1<<bit)) ans = (ans*x)%MOD;
        x = (x*x)%MOD;
    }
    return ans;
}

ll dist[1003];
ll dp[2][1003][501];
ll dp_pref[2][1003];
ll newton[1003][501];
ll odw[1003];

int main()
{
    ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    //random_start();
    int n;
    cin >> n;   
    vector<pii> segs = {{-1,-1}};
    map<int,int> mp;
    rep(i,n)
    {
        int a,b;
        cin >> a >> b;
        segs.pb({a-1,b});
        mp[a-1] = 1;
        mp[b] = 1;
    }
    int cur = 1;
    int pop = 0;
    forall(it,mp)
    {
        dist[cur] = it.ff-pop;
        mp[it.ff] = cur++;
        pop = it.ff;
    }
    cur--;
    dp[0][0][0] = 1;
    rep2(i,0,cur) dp_pref[0][i] = 1;
    rep2(i,1,n) odw[i] = P(i); 
    rep2(seg,0,cur)
    {
        ll ans = 1;
        newton[seg][0] = 1;
        rep2(k,1,n)
        {
            ans = (((ans*(dist[seg]-k+1))%MOD)*odw[k])%MOD;
            newton[seg][k] = ans;
        }
    }
    rep2(i,1,n)
    {
        int l = mp[segs[i].ff]+1;
        int r = mp[segs[i].ss];
        rep2(seg,l,r)
        {
            dp[1][seg][1] = dp_pref[0][seg-1];
            rep2(k,2,n) dp[1][seg][k] = dp[0][seg][k-1];
        }
        rep2(seg,0,cur) rep2(k,0,n) dp[1][seg][k] = (dp[1][seg][k]+dp[0][seg][k])%MOD;
        dp_pref[1][0] = dp[1][0][0];
        rep2(seg,1,cur)
        {
            dp_pref[1][seg] = dp_pref[1][seg-1];
            rep2(k,1,n) dp_pref[1][seg] = (dp_pref[1][seg]+dp[1][seg][k]*newton[seg][k])%MOD;
        }
        rep2(seg,0,cur)
        {
            rep2(k,0,n)
            {
                swap(dp[0][seg][k],dp[1][seg][k]);
                dp[1][seg][k] = 0;
            }
            swap(dp_pref[0][seg],dp_pref[1][seg]);
            dp_pref[1][seg] = 0;
        }
    }
    cout << (dp_pref[0][cur]-1+MOD)%MOD;
}
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