oj.uz

Submission #703792

# Submission time Handle Problem Language Result Execution time Memory
703792 2023-02-28T12:10:42 Z Doncho_Bonboncho Building Bridges (CEOI17_building) C++14
100 / 100
 109 ms 11320 KB 
#include <bits/stdc++.h>
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;

const int MAX_N = 1e6;
const int INF = 1e9;
const int mod = 1e9 + 7;

struct Line{

	bool type;
	double x;
	ll m, c;
};

bool operator<( const Line& a, const Line& b ){
	if( a.type || b.type ) return a.x < b.x;
	else return a.m > b.m;
}

std::set<Line> cht;

bool hasPrev( const std::set<Line>::iterator& it ){
	return it != cht.begin();
}

bool hasNext( const std::set<Line>::iterator& it ){
	return it != cht.end() and next(it) != cht.end();
}

double intersection( const std::set<Line>::iterator& a, const std::set<Line>::iterator& b ){
	return (double)( a -> c - b -> c )/( b -> m - a -> m );
}

void calcX( const std::set<Line>::iterator& it ){
	if( hasPrev(it) ){
		Line l = *it;
		l.x = intersection( prev(it), it );
		cht.insert( cht.erase(it), l );
	}
}

bool bad( const std::set<Line>::iterator& it ){
	if(  hasNext(it) and next(it) -> c <= it -> c ) return true;
	return hasNext(it) and hasPrev(it) and intersection( prev(it), next(it) ) <= intersection( prev(it), it );
}

void addLine( ll m, ll c ){
	std::set<Line>::iterator it;
	it = cht.lower_bound({ 0, 0, m, c});

	if( it != cht.end() and it -> m == m ){
		if( it -> c <= c  ) return ;
		cht.erase( it );
	}

	it = cht.insert({0, 0, m, c}).first;
	if( bad( it ) ) cht.erase(it);
	else{
		while( hasPrev(it) and bad(prev(it)) ) cht.erase(prev(it));
		while( hasNext(it) and bad(next(it)) ) cht.erase(next(it));

		if( hasNext(it) ) calcX(next(it));
		calcX(it);
	}
}

ll query( ll h ){
	Line l = *prev(cht.upper_bound({1, double(h), 0, 0}));
	return l.m * h + l.c;
}

ll dp[MAX_N];

ll h[MAX_N];
ll w[MAX_N];

int main () {

	std::ios_base::sync_with_stdio(false); std::cin.tie(NULL);
	
	int n;
	std::cin>>n;
	ll tot = 0;
	for( int i=1 ; i<=n ; i++ ) std::cin>>h[i];
	for( int i=1 ; i<=n ; i++ ) std::cin>>w[i], tot += w[i];

	dp[1] = -w[1];
	for( int i=2 ; i<=n ; i++ ){
		addLine( -2*h[i-1], dp[i-1] + h[i-1] * h[i-1] );
		dp[i] = query( h[i] ) + h[i] * h[i] - w[i];
	}

	std::cout<<dp[n] + tot<<"\n";

	return 0;
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 69 ms 3696 KB Output is correct
2 Correct 70 ms 3688 KB Output is correct
3 Correct 66 ms 3716 KB Output is correct
4 Correct 65 ms 3588 KB Output is correct
5 Correct 62 ms 5068 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 69 ms 3696 KB Output is correct
7 Correct 70 ms 3688 KB Output is correct
8 Correct 66 ms 3716 KB Output is correct
9 Correct 65 ms 3588 KB Output is correct
10 Correct 62 ms 5068 KB Output is correct
11 Correct 60 ms 3788 KB Output is correct
12 Correct 72 ms 3784 KB Output is correct
13 Correct 44 ms 3744 KB Output is correct
14 Correct 67 ms 3912 KB Output is correct
15 Correct 109 ms 11320 KB Output is correct
16 Correct 61 ms 5088 KB Output is correct
17 Correct 19 ms 3672 KB Output is correct
18 Correct 17 ms 3668 KB Output is correct