oj.uz

Submission #972132

# Submission time Handle Problem Language Result Execution time Memory
972132 2024-04-30T06:48:26 Z efedmrlr Building Bridges (CEOI17_building) C++17
100 / 100
 57 ms 16824 KB 
#include <bits/stdc++.h>

#define lli long long 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(0ll, 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(-2ll * h[1], 1ll * h[1] * h[1] - pr[1] + dp[1]));
    for(int i = 2; i <= n; i++) {
        dp[i] = st.query(h[i]) + pr[i - 1] + 1ll * h[i] * h[i];
        st.update(Line(-2ll * h[i], 1ll * 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 2652 KB Output is correct
2 Correct 1 ms 2652 KB Output is correct
3 Correct 1 ms 2652 KB Output is correct
4 Correct 2 ms 2908 KB Output is correct
5 Correct 2 ms 2908 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 42 ms 3568 KB Output is correct
2 Correct 44 ms 3668 KB Output is correct
3 Correct 41 ms 3668 KB Output is correct
4 Correct 38 ms 2908 KB Output is correct
5 Correct 41 ms 16576 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2652 KB Output is correct
2 Correct 1 ms 2652 KB Output is correct
3 Correct 1 ms 2652 KB Output is correct
4 Correct 2 ms 2908 KB Output is correct
5 Correct 2 ms 2908 KB Output is correct
6 Correct 42 ms 3568 KB Output is correct
7 Correct 44 ms 3668 KB Output is correct
8 Correct 41 ms 3668 KB Output is correct
9 Correct 38 ms 2908 KB Output is correct
10 Correct 41 ms 16576 KB Output is correct
11 Correct 56 ms 10176 KB Output is correct
12 Correct 57 ms 10864 KB Output is correct
13 Correct 42 ms 3672 KB Output is correct
14 Correct 56 ms 10700 KB Output is correct
15 Correct 43 ms 15804 KB Output is correct
16 Correct 41 ms 16824 KB Output is correct
17 Correct 28 ms 2824 KB Output is correct
18 Correct 22 ms 2648 KB Output is correct