Submission #45956

#	Time	Username	Problem	Language	Result	Execution time	Memory
45956		sorry_Benq	Building Bridges (CEOI17_building)	C++17	100 / 100	123 ms	18292 KiB

building

#pragma GCC optimize("O3")
#pragma GCC target("sse4")

#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>

using namespace std;
using namespace __gnu_pbds;
 
typedef long long ll;
typedef vector<int> vi;
typedef pair<int, int> pii;
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

#define FOR(i, a, b) for (int i=a; i<(b); i++)
#define F0R(i, a) for (int i=0; i<(a); i++)
#define FORd(i,a,b) for (int i = (b)-1; i >= a; i--)
#define F0Rd(i,a) for (int i = (a)-1; i >= 0; i--)

#define sz(x) (int)(x).size()
#define mp make_pair
#define pb push_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
#define all(x) x.begin(), x.end()

int w[100005];
ll h[100005];
ll dp[100005];
ll res = 0;

bool Q;
struct Line {
	mutable ll k, m, p; // slope, y-intercept, last optimal x
	bool operator<(const Line& o) const {
		return Q ? p < o.p : k < o.k;
	}
};

struct LineContainer : multiset<Line> { 
	const ll inf = LLONG_MAX;
	ll div(ll a, ll b) { // floored division
	    if (b < 0) a *= -1, b *= -1;
	    if (a >= 0) return a/b;
	    return -((-a+b-1)/b);
	}
	
	// updates x->p, determines if y is unneeded
	bool isect(iterator x, iterator y) { 
		if (y == end()) { x->p = inf; return 0; }
		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) { // gives max value
		assert(!empty());
		Q = 1; auto l = *lb({0,0,x}); Q = 0;
		return l.k * x + l.m;
	}
};

int main(){
	LineContainer L;
	int N; cin >> N;
	for (int i = 0; i < N; i++){
		cin >> h[i];
	}
	for (int i = 0; i < N; i++){
		cin >> w[i];
		res += w[i];
		w[i] = -w[i];
	}
	dp[0] = w[0];
	L.add(2*h[0], -h[0]*h[0] - dp[0]);
	for (int i = 1; i < N; i++){
		dp[i] = h[i]*h[i] + w[i] - L.query(h[i]);
		L.add(2*h[i], -h[i]*h[i] - dp[i]);
	}
	cout << res + dp[N - 1] << endl;
}

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