oj.uz

Submission #900243

# Submission time Handle Problem Language Result Execution time Memory
900243 2024-01-08T01:15:13 Z LeticiaFCS Building Bridges (CEOI17_building) C++17
100 / 100
 42 ms 9824 KB 
#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
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 31 ms 3820 KB Output is correct
2 Correct 30 ms 3676 KB Output is correct
3 Correct 30 ms 3676 KB Output is correct
4 Correct 29 ms 3676 KB Output is correct
5 Correct 26 ms 4772 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 31 ms 3820 KB Output is correct
7 Correct 30 ms 3676 KB Output is correct
8 Correct 30 ms 3676 KB Output is correct
9 Correct 29 ms 3676 KB Output is correct
10 Correct 26 ms 4772 KB Output is correct
11 Correct 29 ms 4184 KB Output is correct
12 Correct 31 ms 3676 KB Output is correct
13 Correct 24 ms 3932 KB Output is correct
14 Correct 31 ms 3932 KB Output is correct
15 Correct 42 ms 9824 KB Output is correct
16 Correct 26 ms 4688 KB Output is correct
17 Correct 16 ms 3676 KB Output is correct
18 Correct 17 ms 4188 KB Output is correct