oj.uz

답안 #121005

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
121005 2019-06-26T01:14:46 Z silxikys Building Bridges (CEOI17_building) C++14
100 / 100
 177 ms 12892 KB 
#include <bits/stdc++.h>
using namespace std;
using ll = long long;

//so my brute force is correct, my hull is wrong

const int maxn = 1e5+5;
typedef long double ld;
const ll INF = 1LL<<62;

struct FN
{
    ll m, b; //in this case, function is a line
    bool is_query;
    FN(ll _m, ll _b, bool is = false) : m(_m), b(_b), is_query(is) {}
    mutable function<ld()> xRight; //right intersection point of line in hull, is infinity for rightmost line
    ll eval(ll x) const {
        return m*x + b;
    }
    ld intersect(const FN& r) const { //returns x coordinate of intersection
        //assert(m != r.m);
        return (ld)(r.b-b)/(ld)(m-r.m);
    }

    friend bool comp(const FN& l1, const FN& l2, const FN& l) {
    	//order in deque: l1, l2, l
    	//true --> l2 is unnecessary
    	ld x1 = l1.intersect(l);
        ld x2 = l1.intersect(l2);
        return x1 <= x2;
    }

    bool operator<(const FN& rhs) const {
        //make sure to check which </> should be used
        if (!rhs.is_query) return m > rhs.m;
        //greater since we want smaller slopes to the right
        ll x = rhs.m;
        return xRight() < (ld)x; //always stays the same
    }
};

//goal: dynamic variant of convex hull
//insert, delete, and query in O(log n)
struct Hull: public set<FN> //convex hull for maximum
{
    void addFN(FN fn) {
        Hull::iterator it = lower_bound(fn);
        if (it != end() && it->m == fn.m) {
            if (it->b <= fn.b) return; //no need to consider it
            //this line must be changed based on +/- slope!!!
            //min-neg --> <=
            erase(it);
        }
        it = insert(fn).first;
        //check if what we just inserted is necessary
        if (it != begin() && next(it) != end()) {
            if (comp(*prev(it),*it,*next(it))) {
                //not needed
                erase(it);
                return;
            }
        }
        it->xRight = [=] { return next(it) == end() ? INF : it->intersect(*next(it)); };
        //function pointer magic
        //Removes unnecessary lines above and below
        Hull::iterator b1, b2, f1, f2;
        while (true) {
            if (it == begin()) break;
            else {
                b1 = prev(it);
                if (b1 == begin()) break;
                else {
                    b2 = prev(b1);
                    if (comp(*b2,*b1,*it)) {
                        erase(b1);
                    }  
                    else break;     
                }
            }
        }
        while (true) {
            f1 = next(it);
            if (f1 == end()) break;
            else {
                f2 = next(f1);
                if (f2 == end()) break;
                else {
                    if (comp(*it,*f1,*f2)) {
                        erase(f1);
                    }
                    else break;
                }
            }
        }
    }

    ll query(ll x) {
        //if (this->empty()) return 0; //because querying for maximum
        assert(!this->empty());
        auto it = lower_bound(FN(x,0,true));
        return it->eval(x);
    }
};


//dp[i] = min_{1 <= j < i} (h[i]-h[j])^2 + sum(w[j+1]..w[i-1]) + dp[j]
// = (h[i]-h[j])^2 + pfx[i-1]-pfx[j]+dp[j]
// = h[i]^2 - 2h[i]*h[j] + h[j]^2 + pfx[i-1] - pfx[j] + dp[j]
// = (h[i]^2+pfx[i-1]) + (-2h[j])*h[i] + (dp[j]-pfx[j]) + h[j]^2
// =  (independent)    + (mx)          -      b 
// So each j has (m,b) = (-2h[j],dp[j]-pfx[j]+h[j]^2)
// Unfortunately, the h[i]'s and h[j]'s aren't monotonic, so we have implement a hull w/ dynamic 
// queries/insertions
//

int n;
ll h[maxn], w[maxn], pfx[maxn];

int main()
{
    ios_base::sync_with_stdio(false); cin.tie(0);
    cin >> n;
    for (int i = 1; i <= n; i++) {
        cin >> h[i];
    }
    for (int i = 1; i <= n; i++) {
        cin >> w[i];
        pfx[i] = w[i] + pfx[i-1];
    }
    Hull hull;
    hull.addFN(FN(-2*h[1],-pfx[1]+h[1]*h[1]));
    for (int i = 2; i <= n; i++) {
        ll q = hull.query(h[i]) + (h[i]*h[i])+pfx[i-1];
        /*
        cout << hull.query(h[i]) << '\n';
        cout << i << ": " << q << '\n';
        */
        hull.addFN(FN(-2*h[i],q-pfx[i]+h[i]*h[i]));
        if (i == n) {
            cout << q << '\n';
        }
    }
}

Subtask #1
30.0 / 30.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 384 KB Output is correct
2 Correct 2 ms 384 KB Output is correct
3 Correct 2 ms 384 KB Output is correct
4 Correct 2 ms 384 KB Output is correct
5 Correct 2 ms 384 KB Output is correct

Subtask #2
30.0 / 30.0

# 결과 실행 시간 메모리 Grader output
1 Correct 78 ms 3852 KB Output is correct
2 Correct 77 ms 3892 KB Output is correct
3 Correct 78 ms 3956 KB Output is correct
4 Correct 69 ms 3840 KB Output is correct
5 Correct 88 ms 5496 KB Output is correct

Subtask #3
40.0 / 40.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 384 KB Output is correct
2 Correct 2 ms 384 KB Output is correct
3 Correct 2 ms 384 KB Output is correct
4 Correct 2 ms 384 KB Output is correct
5 Correct 2 ms 384 KB Output is correct
6 Correct 78 ms 3852 KB Output is correct
7 Correct 77 ms 3892 KB Output is correct
8 Correct 78 ms 3956 KB Output is correct
9 Correct 69 ms 3840 KB Output is correct
10 Correct 88 ms 5496 KB Output is correct
11 Correct 69 ms 3976 KB Output is correct
12 Correct 78 ms 3788 KB Output is correct
13 Correct 45 ms 3864 KB Output is correct
14 Correct 78 ms 3984 KB Output is correct
15 Correct 177 ms 12892 KB Output is correct
16 Correct 86 ms 5496 KB Output is correct
17 Correct 21 ms 3712 KB Output is correct
18 Correct 21 ms 3712 KB Output is correct