oj.uz

Submission #1001060

# Submission time Handle Problem Language Result Execution time Memory
1001060 2024-06-18T13:54:23 Z vjudge1 Building Bridges (CEOI17_building) C++14
100 / 100
 77 ms 11944 KB 
#include<bits/stdc++.h>
using namespace std;

#define ll long long
#define ii pair<int, int>
#define fi first
#define se second
#define pll pair<ll, ll>
#define vi vector<int>
#define db long double

const int maxn = 1e5+5;
const ll mod = 1e9+7;
const ll inf = 1e18+7;
const double eps = 1e-9;
const double pi = acos(-1);
const int block_size = 320;

int n, h[maxn], w[maxn];
ll s[maxn];
ll dp[maxn];

struct Line{
    bool t;
    db x;
    ll a, b;

    bool operator < (const Line &l) const{
        if(t || l.t) return x < l.x;
        return a > l.a;
    }
};

struct linecontainer{
    set<Line> cht;

    bool has_prev(set<Line>::iterator it) {return it != cht.begin();}
    bool has_next(set<Line>::iterator it) {return it != cht.end() && next(it) != cht.end();}

    db intersect(set<Line>::iterator l1, set<Line>::iterator l2){
        return (double) (l2->b - l1->b) / (l1->a - l2->a);
    }

    void cal_x(set<Line>::iterator it){
        if(has_prev(it)){
            Line l = *it;
            l.x = intersect(prev(it), it);
            cht.insert(cht.erase(it), l);
        }
    }

    bool bad(set<Line>::iterator it){
        return has_prev(it) && has_next(it) && (intersect(prev(it), next(it)) <= intersect(prev(it), it));
    }

    void add(ll a, ll b){
        set<Line>::iterator it;
        it = cht.lower_bound({0, 0, a, b});
        if(it != cht.end() && it->a == a){
            if(it->b >= b) cht.erase(it);
            else return;
        }
        it = cht.insert({0, 0, a, b}).first;
        if(bad(it)) cht.erase(it);
        else{
            while(has_prev(it) && bad(prev(it))) cht.erase(prev(it));
            while(has_next(it) && bad(next(it))) cht.erase(next(it));
            if(has_next(it)) cal_x(next(it));
            cal_x(it);
        }
    }

    ll query(ll x){
        Line l = *prev(cht.upper_bound({1, (double)x, 0, 0}));
        return l.a * x + l.b;
    }
};

void solve(){
    cin >> n;
    for(int i=1; i<=n; i++){
        cin >> h[i];
    }
    for(int i=1; i<=n; i++){
        cin >> w[i];
        s[i] = s[i-1] + w[i];
    }
    linecontainer cht;
    ll a = -2*h[1];
    ll b = 1ll*h[1]*h[1] - s[1];
    cht.add(a, b);
    for(int i=2; i<=n; i++){
        dp[i] = cht.query(h[i]) + 1ll*h[i]*h[i] + s[i-1];
        a = -2*h[i];
        b = dp[i] + 1ll*h[i]*h[i] - s[i];
        cht.add(a, b);
    }
    cout << dp[n] << "\n";
}

int main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    int test = 1;
//    cin >> test;
    while(test--){
        solve();
    }
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 2396 KB Output is correct
2 Correct 1 ms 2396 KB Output is correct
3 Correct 1 ms 2396 KB Output is correct
4 Correct 1 ms 2396 KB Output is correct
5 Correct 1 ms 2396 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 52 ms 2880 KB Output is correct
2 Correct 69 ms 2900 KB Output is correct
3 Correct 50 ms 2900 KB Output is correct
4 Correct 46 ms 2652 KB Output is correct
5 Correct 51 ms 4436 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 2396 KB Output is correct
2 Correct 1 ms 2396 KB Output is correct
3 Correct 1 ms 2396 KB Output is correct
4 Correct 1 ms 2396 KB Output is correct
5 Correct 1 ms 2396 KB Output is correct
6 Correct 52 ms 2880 KB Output is correct
7 Correct 69 ms 2900 KB Output is correct
8 Correct 50 ms 2900 KB Output is correct
9 Correct 46 ms 2652 KB Output is correct
10 Correct 51 ms 4436 KB Output is correct
11 Correct 45 ms 2652 KB Output is correct
12 Correct 58 ms 2900 KB Output is correct
13 Correct 47 ms 2636 KB Output is correct
14 Correct 56 ms 2896 KB Output is correct
15 Correct 77 ms 11944 KB Output is correct
16 Correct 46 ms 4696 KB Output is correct
17 Correct 17 ms 2652 KB Output is correct
18 Correct 10 ms 2652 KB Output is correct