oj.uz

Submission #731073

# Submission time Handle Problem Language Result Execution time Memory
731073 2023-04-26T22:34:42 Z Doncho_Bonboncho Building Bridges (CEOI17_building) C++14
100 / 100
 108 ms 12924 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;
	ld x;
	ll m, c;
};

typedef const Line& cLine;
typedef const std::set<Line>::iterator& cIter;

std::set<Line> cht;

bool operator <( cLine a, cLine b ){
	if( a.type || b.type ) return a.x < b.x;
	return a.m > b.m;
}

bool hasPrev( cIter it ){
	return it != cht.begin();
}

bool hasNext( cIter it ){
	return it != cht.end() and next(it) != cht.end();
}

ld intersection( cIter a, cIter b ){
	return (ld)( a -> c - b->c ) / ( b->m - a->m );
}

void calcX( cIter it ){
	if( !hasPrev(it) ) return;
	Line l = *it;
	l.x = intersection( prev(it), it );
	cht.insert(cht.erase(it), l);	
}

bool bad( cIter it ){
	if(  hasNext(it) and next(it) -> c <= it -> c ) return true;
	return hasPrev(it) and hasNext(it) and intersection( prev(it), next(it) ) <= intersection( prev(it), it );
}

void addLine( ll m, ll c ){
	std::set<Line>::iterator it = cht.lower_bound({0, 0, m, c});
	if( it != cht.end() and m == it -> 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 x ){
	Line l = *prev(cht.upper_bound({1, (ld)x, 0, 0}));
	return l.m * x + l.c;
}


ll dp[MAX_N];
ll h[MAX_N];
ll w[MAX_N];
ll sumW = 0;

int main () {

	std::ios_base::sync_with_stdio(false); std::cin.tie(NULL);

	int n;
	std::cin>>n;
	for( int i=1 ; i<=n ; i++ ) std::cin>>h[i];
	for( int i=1 ; i<=n ; i++ ){ std::cin>>w[i]; sumW += 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] + sumW<<"\n";

	return 0;
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 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 68 ms 2768 KB Output is correct
2 Correct 71 ms 2776 KB Output is correct
3 Correct 77 ms 2716 KB Output is correct
4 Correct 69 ms 2632 KB Output is correct
5 Correct 61 ms 4432 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 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 68 ms 2768 KB Output is correct
7 Correct 71 ms 2776 KB Output is correct
8 Correct 77 ms 2716 KB Output is correct
9 Correct 69 ms 2632 KB Output is correct
10 Correct 61 ms 4432 KB Output is correct
11 Correct 62 ms 2752 KB Output is correct
12 Correct 76 ms 3720 KB Output is correct
13 Correct 50 ms 3796 KB Output is correct
14 Correct 82 ms 3892 KB Output is correct
15 Correct 108 ms 12924 KB Output is correct
16 Correct 75 ms 5416 KB Output is correct
17 Correct 28 ms 3680 KB Output is correct
18 Correct 28 ms 3724 KB Output is correct