Submission #900243

#	Time	Username	Problem	Language	Result	Execution time	Memory
900243		LeticiaFCS	Building Bridges (CEOI17_building)	C++17	100 / 100	42 ms	9824 KiB

building

#include"bits/stdc++.h"

using lint = int64_t;

using namespace std;


using ll = int64_t;
struct Line {
	mutable ll k, m, p;
	bool operator<(const Line& o) const { return k < o.k; }
	bool operator<(ll x) const { return p < x; }
};
struct LineContainer : multiset<Line, less<>> {
	static const ll inf = LLONG_MAX; //for doubles 1/.0
	ll div(ll a, ll b) { //for doubles a/b
		return a / b - ((a ^ b) < 0 && a % b); }
	bool isect(iterator x, iterator y) {
		if (y == end()) { x->p = inf; return false; }
		if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
		else x->p = div(y->m - x->m, x->k - y->k);
		return x->p >= y->p;
	}
	void add(ll k, ll m) {
		auto z = insert({k, m, 0}), y = z++, x = y;
		while (isect(y, z)) z = erase(z);
		if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
		while ((y = x) != begin() && (--x)->p >= y->p) 
			isect(x, erase(y));
	}
	ll query(ll x) {
		assert(!empty()); auto l = *lower_bound(x);
		return l.k * x + l.m;
	}
};

int main(){
    cin.tie(nullptr)->sync_with_stdio(false);
    int n; cin>>n;
    lint W = 0;
    vector<lint> h(n+1), w(n+1);
    for(int i=1; i<=n; i++) cin>>h[i];
    for(int i=1; i<=n; i++) cin>>w[i], W += w[i];
    vector<lint> dp(n+1);
    /*
    dp[i] = min(dp[j] + (hj - hi)^2 - wi)
    dp[i] = min dp[j] + hj^2 -hi*hj + hi^2 - wi
    dp[i] = (hi^2 - wi) -2hj * hi + (dp[j] + hj^2)
    */

    dp[1] = -w[1];
    LineContainer cht;
    cht.add(2*h[1], -(dp[1] + h[1]*h[1]));
    for(int i = 2; i <= n; i++){
        dp[i] = h[i]*h[i] - w[i] - cht.query(h[i]);
        cht.add(2*h[i], -(dp[i] + h[i]*h[i]));
    }
    cout<<W + dp[n]<<"\n";

    

    return 0;
}

• Subtask 1: 30 / 30
• Subtask 2: 30 / 30
• Subtask 3: 40 / 40