oj.uz

Submission #154446

# Submission time Handle Problem Language Result Execution time Memory
154446 2019-09-21T21:52:44 Z dolphingarlic Building Bridges (CEOI17_building) C++14
100 / 100
 119 ms 11400 KB 
#include <bits/stdc++.h>
#define FOR(i, x, y) for (int i = x; i < y; i++)
typedef long long ll;
using namespace std;

struct Line {
    bool type;
    double x;
    ll m, c;
};

bool operator<(Line l1, Line l2) {
    if (l1.type || l2.type) return l1.x < l2.x;
    return l1.m > l2.m;
}

set<Line> cht;
ll h[100001], w[100001], tot = 0;
ll dp[100001];

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

double intersect(set<Line>::iterator l1, set<Line>::iterator l2) {
    return (double)(l1->c - l2->c) / (l2->m - l1->m);
}

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

bool bad(set<Line>::iterator it) {
    if (hasNext(it) && next(it)->c <= it->c) return true;
    return (hasPrev(it) && hasNext(it) &&
            intersect(prev(it), next(it)) <= intersect(prev(it), it));
}

void add_line(ll m, ll c) {
    set<Line>::iterator it;
    
    it = cht.lower_bound({0, 0, m, c});
    if (it != cht.end() && it->m == m) {
        if (it->c <= c) return;
        else cht.erase(it);
    }

    it = cht.insert({0, 0, m, c}).first;
    if (bad(it)) cht.erase(it);
    else {
        while (hasPrev(it) && bad(prev(it))) cht.erase(prev(it));
        while (hasNext(it) && bad(next(it))) cht.erase(next(it));

        if (hasNext(it)) calcX(next(it));
        calcX(it);
    }
}
ll query(ll h) {
    Line l = *prev(cht.upper_bound({1, (double)h, 0, 0}));
    return l.m * h + l.c;
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    int n;
    cin >> n;
    FOR(i, 1, n + 1) cin >> h[i];
    FOR(i, 1, n + 1) {
        cin >> w[i];
        tot += w[i];
    }

    dp[1] = -w[1];
    FOR(i, 2, n + 1) {
        add_line(-2 * h[i - 1], dp[i - 1] + h[i - 1] * h[i - 1]);
        dp[i] = query(h[i]) - w[i] + h[i] * h[i];
    }

    cout << tot + dp[n];
    return 0;
}

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB Output is correct
2 Correct 2 ms 376 KB Output is correct
3 Correct 2 ms 376 KB Output is correct
4 Correct 3 ms 504 KB Output is correct
5 Correct 3 ms 376 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 101 ms 3840 KB Output is correct
2 Correct 98 ms 3832 KB Output is correct
3 Correct 99 ms 3844 KB Output is correct
4 Correct 97 ms 3704 KB Output is correct
5 Correct 76 ms 5100 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB Output is correct
2 Correct 2 ms 376 KB Output is correct
3 Correct 2 ms 376 KB Output is correct
4 Correct 3 ms 504 KB Output is correct
5 Correct 3 ms 376 KB Output is correct
6 Correct 101 ms 3840 KB Output is correct
7 Correct 98 ms 3832 KB Output is correct
8 Correct 99 ms 3844 KB Output is correct
9 Correct 97 ms 3704 KB Output is correct
10 Correct 76 ms 5100 KB Output is correct
11 Correct 98 ms 3904 KB Output is correct
12 Correct 103 ms 3708 KB Output is correct
13 Correct 62 ms 3832 KB Output is correct
14 Correct 98 ms 3876 KB Output is correct
15 Correct 119 ms 11400 KB Output is correct
16 Correct 78 ms 5168 KB Output is correct
17 Correct 31 ms 3704 KB Output is correct
18 Correct 28 ms 3704 KB Output is correct