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Submission #598751

# Submission time Handle Problem Language Result Execution time Memory
598751 2022-07-18T22:14:53 Z devedude Building Bridges (CEOI17_building) C++17
100 / 100
 52 ms 9700 KB 
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef tuple<int, int> ii;
typedef tuple<int, int, int> iii;
typedef vector<int> vi;

#define FOR(i, a, b) for (int i = (a); i < (b); ++i)

const ll inf = LLONG_MAX;

void run();

signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    run();
}

inline ll sqr(ll x) {
    return x * x;
}

struct Line {
    ll a, b;
    mutable ll max_x;
    bool operator<(const Line &o) const {
        return a > o.a;
    }
    bool operator<(ll x) const {
        return max_x < x;
    }
};

struct LineContainer : multiset<Line, less<>> {
    ll div(ll n, ll d) { // floor division for negative and positive lls
        return n / d - ((n ^ d) < 0 && n % d);
    }
    bool isect(iterator l, iterator m) {
        // assumption: l and m are neighbouring lines, with m > l
        // do: adjust the max_x for l
        // return: l covers x after or equal to last x of m
        if (m == end()) { // handle case l is last line
            l->max_x = inf;
            return false;
        }
        if (l->a == m->a) { // prevent division by zero
            l->max_x = l->b < m->b ? inf : -inf;
        } else { // default case, intersection point of l and m floored
            l->max_x = div(m->b - l->b, l->a - m->a);
        }
        return l->max_x >= m->max_x;
    }
    void add(ll a, ll b) {
        auto cur = insert({a, b, 0}), pre = cur, nex = cur; // iterators
        //cerr << "Adding line " << cur->a << ' ' << cur->b << ' ';
        ++nex;
        while (isect(cur, nex)) nex = erase(nex); // keep erasing redundant lines after cur, note how this sets max_x of cur
        //cerr << cur->max_x << '\n';
        if (cur != begin() && isect(--pre, cur)) { // added line itself is redundant, erase and return
            cur = erase(cur);
            isect(pre, cur);
        }
        while ((cur = pre) != begin() && (--pre)->max_x >= cur->max_x) isect(pre, erase(cur)); // keep erasing redundant lines before cur, and adjust max_x of line left
    }
    ll min_y(ll x) {
        auto l = lower_bound(x);
        //cerr << "Minimal for x = " << x << " is line a = " << l->a << " b = " << l->b << " at y = " << l->y(x) << '\n';
        return l->a * x + l->b;
    }
};

int N;
ll h[100005];
ll W[100005];
ll dp[100005];

void run() {
    cin >> N;
    FOR(i, 0, N) cin >> h[i];
    FOR(i, 0, N) {
        ll w; cin >> w;
        W[i+1] = W[i] + w;
    }
    LineContainer lc;
    FOR(i, 1, N) {
        lc.add(-2*h[i-1], dp[i-1] + h[i-1]*h[i-1] - W[i]);
        dp[i] = h[i]*h[i] + W[i] + lc.min_y(h[i]);
    }
    // for (auto &l : lc) {
    //     cerr << l.a << ' ' << l.b << ' ' << l.max_x << '\n';
    // }
    cout << dp[N-1] << '\n';
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 40 ms 3680 KB Output is correct
2 Correct 36 ms 3660 KB Output is correct
3 Correct 41 ms 3640 KB Output is correct
4 Correct 37 ms 3556 KB Output is correct
5 Correct 36 ms 4704 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 40 ms 3680 KB Output is correct
7 Correct 36 ms 3660 KB Output is correct
8 Correct 41 ms 3640 KB Output is correct
9 Correct 37 ms 3556 KB Output is correct
10 Correct 36 ms 4704 KB Output is correct
11 Correct 37 ms 3864 KB Output is correct
12 Correct 36 ms 3660 KB Output is correct
13 Correct 32 ms 3772 KB Output is correct
14 Correct 42 ms 3988 KB Output is correct
15 Correct 52 ms 9700 KB Output is correct
16 Correct 35 ms 4776 KB Output is correct
17 Correct 20 ms 3748 KB Output is correct
18 Correct 21 ms 3740 KB Output is correct