Submission #589540

#	Time	Username	Problem	Language	Result	Execution time	Memory
589540		chonka	Boat (APIO16_boat)	C++17	100 / 100	824 ms	3448 KiB

boat

#include<bits/stdc++.h>
using namespace std ;
typedef long long ll ;
const int MAXN = 503 ;
const int MOD = 1e9 + 7 ;
// mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());

int n ;
pair < int , int > a[ MAXN ] ;
int v[ 2 * MAXN ] ;

ll dp[ MAXN ][ 2 * MAXN ] ;
ll en[ MAXN ] , nw[ MAXN ] ;
ll inv[ MAXN ] ;

ll fastpow ( ll x , ll pw ) {
    ll ret = 1 ;
    while ( pw > 0 ) {
        if ( ( pw % 2 ) == 0 ) {
            x = ( x * x ) % MOD ;
            pw /= 2 ;
        }
        else {
            ret = ( ret * x ) % MOD ;
            -- pw ;
        }
    }
    return ret ;
}
set < int > s ;

void solve ( ) {
    cin >> n ;
    for ( int i = 1 ; i <= n ; ++ i ) {
        cin >> a[ i ].first >> a[ i ].second ;
        s.insert ( a[ i ].first ) ;
        s.insert ( a[ i ].second + 1 ) ;
    }
    int k = 0 ;
    for ( auto x : s ) {
        v[ ++ k ] = x ;
    }
    for ( int i = 1 ; i < MAXN ; ++ i ) {
        inv[ i ] = fastpow ( i , MOD - 2 ) ;
    }
    dp[ 0 ][ 0 ] = 1 ;
    for ( int i = 0 ; i <= n ; ++ i ) {
        en[ i ] = nw[ i ] = 1 ;
    }
    for ( int j = 1 ; j <= k ; ++ j ) {
        for ( int i = 1 ; i <= n ; ++ i ) {
            for ( int t = i ; t >= 1 ; -- t ) { 
                dp[ i ][ t ] = dp[ i - 1 ][ t ] ;
                if ( a[ i ].first <= v[ j ] && v[ j + 1 ] <= a[ i ].second + 1 ) {
                    if ( v[ j + 1 ] - v[ j ] - t + 1 > 0 ) {
                        ll coef = 1 ;
                        coef = ( coef * ( v[ j + 1 ] - v[ j ] - t + 1 ) ) % MOD ;
                        coef = ( coef * inv[ t ] ) % MOD ;
                        if ( t > 1 ) {
                            dp[ i ][ t ] = ( dp[ i ][ t ] + dp[ i - 1 ][ t - 1 ] * coef ) % MOD ;
                        }
                        else {
                            dp[ i ][ t ] = ( dp[ i ][ t ] + en[ i - 1 ] * coef ) % MOD ;
                        }
                    }
                }
                nw[ i ] = ( nw[ i ] + dp[ i ][ t ] ) % MOD ;
            }
        }
        for ( int i = 1 ; i <= n ; ++ i ) {
            en[ i ] = nw[ i ] ;
        }
    }
    cout << ( en[ n ] - 1 + MOD ) % MOD << "\n" ;
}

int main ( ) {
    ios_base :: sync_with_stdio ( false ) ;
    cin.tie ( NULL ) ;
    int t = 1 ; // cin >> t ; 
    while ( t -- ) { solve ( ) ; }
    return 0 ;
}

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