oj.uz

Submission #972130

# Submission time Handle Problem Language Result Execution time Memory
972130 2024-04-30T06:45:19 Z efedmrlr Building Bridges (CEOI17_building) C++17
100 / 100
 64 ms 22472 KB 
#include <bits/stdc++.h>

#define int long long int
#define lli int
#define ld long double
#define pb push_back
#define MP make_pair
#define REP(i, n) for(int i = 0; (i) < (n); (i)++)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()

using namespace std;

void fastio() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
}

const int N = 1e5 + 5;
const lli INF = 1e17;

struct Line {
    lli a, b;
    Line() {}
    Line(lli aa, lli bb) : a(aa), b(bb) {}
    ld intersect(Line &oth) {
        return (ld)(oth.b - b) / (a - oth.a);
    }
    lli eval(int x) {
        return a * x + b;
    }
    bool operator<(Line &oth) {
        return a < oth.a;
    }
    
    void print() {
        cout << a << " x + " << b << "\n";
    }
};

struct Node {
    Line x;
    int lc, rc;
    Node() : x(Line(0, INF)), lc(-1), rc(-1) {}
};

struct LiChao {
    const int MX = 1e6 + 5;
    vector<Node> st;
    int pt;
    int create_node() {
        st.pb(Node()); 
        return pt++;
    }
    void reset() {
        pt = 0;
        st.clear();
        create_node();
    }
    void extend(int v) {
        if(st[v].lc == -1) st[v].lc = create_node();
        if(st[v].rc == -1) st[v].rc = create_node();
    } 
    void update(int tl, int tr, int v, Line nw) {
        if(nw.a == st[v].x.a) {
            if(nw.b < st[v].x.b) {
                swap(nw, st[v].x);
            }
            return;
        }
        if(tl == tr) {
            if(nw.eval(tl) < st[v].x.eval(tl)) {
                st[v].x = nw;
            }
            return;
        } 
        extend(v);
        int tm = (tl + tr) >> 1;
        if(nw.a > st[v].x.a) {
            swap(nw, st[v].x);
        } 
        ld inter = nw.intersect(st[v].x);
        if(inter < (ld)tm) {
            swap(st[v].x, nw);
            update(tl, tm, st[v].lc, nw);
        }
        else {
            update(tm + 1, tr, st[v].rc, nw);
        }
    }
    void update(Line nw) {
        // nw.print();
        update(0, MX, 0, nw);
    }
    lli query(int tl, int tr, int v, int ind) {
        if(tl == tr) {
            return st[v].x.eval(ind);
        }
        int tm = (tl + tr) >> 1;
        extend(v);
        if(ind <= tm) {
            return min(query(tl, tm, st[v].lc, ind), st[v].x.eval(ind));
        } 
        else {
            return min(query(tm + 1, tr, st[v].rc, ind), st[v].x.eval(ind));
        }
    }
    lli query(int ind) {
        return query(0, MX, 0, ind);
    }

};
LiChao st;
vector<int> h(N), w(N);
vector<lli> dp(N, INF), pr(N, 0);
void solve() {
    int n;
    cin >> n;
    for(int i = 1; i <= n; i++) {
        cin >> h[i];
    }
    for(int i = 1; i <= n; i++) {
        cin >> w[i];
    }
    for(int i = 1; i <= n; i++) {
        pr[i] = pr[i - 1] + w[i];
    }
    dp[1] = 0;
    st.reset();
    st.update(Line(-2 * h[1], h[1] * h[1] - pr[1] + dp[1]));
    for(int i = 2; i <= n; i++) {
        dp[i] = st.query(h[i]) + pr[i - 1] + h[i] * h[i];
        st.update(Line(-2 * h[i], h[i] * h[i] - pr[i] + dp[i]));
    }
    cout << dp[n];
}

signed main() {
    fastio();
    solve();
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 3420 KB Output is correct
2 Correct 1 ms 3676 KB Output is correct
3 Correct 2 ms 3420 KB Output is correct
4 Correct 2 ms 3676 KB Output is correct
5 Correct 2 ms 3676 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 40 ms 4572 KB Output is correct
2 Correct 40 ms 5784 KB Output is correct
3 Correct 40 ms 5628 KB Output is correct
4 Correct 39 ms 4752 KB Output is correct
5 Correct 41 ms 21964 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 3420 KB Output is correct
2 Correct 1 ms 3676 KB Output is correct
3 Correct 2 ms 3420 KB Output is correct
4 Correct 2 ms 3676 KB Output is correct
5 Correct 2 ms 3676 KB Output is correct
6 Correct 40 ms 4572 KB Output is correct
7 Correct 40 ms 5784 KB Output is correct
8 Correct 40 ms 5628 KB Output is correct
9 Correct 39 ms 4752 KB Output is correct
10 Correct 41 ms 21964 KB Output is correct
11 Correct 64 ms 13000 KB Output is correct
12 Correct 54 ms 13512 KB Output is correct
13 Correct 40 ms 5844 KB Output is correct
14 Correct 56 ms 14020 KB Output is correct
15 Correct 42 ms 22464 KB Output is correct
16 Correct 41 ms 22472 KB Output is correct
17 Correct 21 ms 4444 KB Output is correct
18 Correct 20 ms 4444 KB Output is correct