oj.uz

Submission #939398

# Submission time Handle Problem Language Result Execution time Memory
939398 2024-03-06T10:22:56 Z caterpillow Building Bridges (CEOI17_building) C++17
100 / 100
 44 ms 8984 KB 
#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using pl = pair<ll, ll>;
#define vt vector
#define f first
#define s second
#define all(x) x.begin(), x.end() 
#define pb push_back
#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define ROF(i, a, b) for (int i = (b) - 1;i >= (a); i--)
#define F0R(i, b) FOR (i, 0, b)
#define endl '\n'
#define debug(x) do{auto _x = x; cerr << #x << " = " << _x << endl;} while(0)
const ll INF = 1e18;

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

ll sign = -1; // -1 for min, 1 for max
struct LineContainer : multiset<Line, less<>> {
    // (for doubles, use inf = 1/.0, div(a,b) = a/b)
    ll div(ll a, ll b) { // floored division
        return a / b - ((a ^ b) < 0 && a % b); 
    }
    bool isect(auto x, auto y) {
        if (y == end()) { x->p = INF; return false; }
        if (x->a == y->a) x->p = x->b > y->b ? INF : -INF;
        else x->p = div(y->b - x->b, x->a - y->a);
        return x->p >= y->p;
    }
    void add(ll a, ll b) {
    a *= sign, b *= sign;
        auto z = insert({a, b, 0}), y = z++, x = y;
        while (isect(y, z)) z = erase(z);
        if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
        while ((y = x) != begin() && (--x)->p >= y->p) isect(x, erase(y));
    }
    ll query(ll x) {
        assert(size());
        auto l = *lower_bound(x);
        return -l.a * x - l.b;
    }
};

/*

assume all bridges are getting broken already and add back the ones that are not

dp[i] = min(h[i] - h[j]) ^ 2 + d[j]) - w[i]
dp[i] = h[i] ^ 2 - w[i] + min(-2 * h[i] * h[j] + h[j]^2 + dp[j])

*/

ll n;
vt<ll> h, w;

main() {    
    cin.tie(0)->sync_with_stdio(0);
    
    cin >> n;
    h = w = vt<ll>(n);
    F0R (i, n) cin >> h[i];
    F0R (i, n) cin >> w[i];

    vt<ll> dp(n);
    dp[0] = -w[0];

    LineContainer lc;
    lc.add(-2 * h[0], h[0] * h[0] + dp[0]);

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

    cout << dp[n - 1] + accumulate(all(w), 0ll) << endl;
}

Compilation message

building.cpp:31:16: warning: use of 'auto' in parameter declaration only available with '-fconcepts-ts'
   31 |     bool isect(auto x, auto y) {
      |                ^~~~
building.cpp:31:24: warning: use of 'auto' in parameter declaration only available with '-fconcepts-ts'
   31 |     bool isect(auto x, auto y) {
      |                        ^~~~
building.cpp:63:1: warning: ISO C++ forbids declaration of 'main' with no type [-Wreturn-type]
   63 | main() {
      | ^~~~

Subtask #1
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 344 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 30 ms 3060 KB Output is correct
2 Correct 30 ms 2652 KB Output is correct
3 Correct 30 ms 2652 KB Output is correct
4 Correct 29 ms 2648 KB Output is correct
5 Correct 26 ms 3932 KB Output is correct

Subtask #3
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 344 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 30 ms 3060 KB Output is correct
7 Correct 30 ms 2652 KB Output is correct
8 Correct 30 ms 2652 KB Output is correct
9 Correct 29 ms 2648 KB Output is correct
10 Correct 26 ms 3932 KB Output is correct
11 Correct 29 ms 2652 KB Output is correct
12 Correct 30 ms 2652 KB Output is correct
13 Correct 24 ms 2652 KB Output is correct
14 Correct 30 ms 2648 KB Output is correct
15 Correct 44 ms 8984 KB Output is correct
16 Correct 26 ms 3928 KB Output is correct
17 Correct 16 ms 2652 KB Output is correct
18 Correct 16 ms 3676 KB Output is correct