제출 #66181

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
66181		polyfish	Building Bridges (CEOI17_building)	C++14	0 / 100	89 ms	28588 KiB

building

//I love armpit fetish

#include <bits/stdc++.h>
using namespace std;

#define debug(x) cerr << #x << " = " << x << '\n';
#define BP() cerr << "OK!\n";
#define PR(A, n) {cerr << #A << " = "; for (int _=1; _<=n; ++_) cerr << A[_] << ' '; cerr << '\n';}
#define PR0(A, n) {cerr << #A << " = "; for (int _=0; _<n; ++_) cerr << A[_] << ' '; cerr << '\n';}
#define FILE_NAME "building"

const int MAX_N = 100002;
const int64_t INF = 1e18;

struct line {
    int64_t a, b;

    line() {}
    line(int64_t a, int64_t b):
        a(a), b(b) {}

    int64_t get(int64_t x) {
        return a * x + b;
    }
};

class IT {
public:
    struct node {
        line d;
        node *left_child, *right_child;

        node() {
            d.a = 0;
            d.b = INF;
            left_child = NULL;
            right_child = NULL;
        }

        void make_children() {
            if (left_child==NULL) {
                left_child = new node();
                right_child = new node();
            }
        }
    };

    int n;
    node *root;

    IT(int _n) {
        n = _n;
        root = new node();
    }

    void upd(line val, int l, int r, node *cur) {
        if (l>r)
            return;
        int mid = (l + r) / 2;
        cur->make_children();
        if (val.get(l)<=cur->d.get(l) && val.get(r)<=cur->d.get(r))
            cur->d = val;
        else if (val.get(l)>=cur->d.get(l) && val.get(r)>=cur->d.get(r))
            return;
        else if (val.get(l)>=cur->d.get(l) && val.get(mid)>=cur->d.get(mid))
            upd(val, mid+1, r, cur->right_child);
        else if (val.get(l)<=cur->d.get(l) && val.get(mid)<=cur->d.get(mid)) {
            upd(cur->d, mid+1, r, cur->right_child);
            cur->d = val;
        }
        else if (val.get(r)>=cur->d.get(r) && val.get(mid)>=cur->d.get(mid))
            upd(val, l, mid, cur->left_child);
        else if (val.get(r)<=cur->d.get(r) && val.get(mid)<=cur->d.get(mid)) {
            upd(cur->d, l, mid, cur->left_child);
            cur->d = val;
        }
    }

    int64_t get(int pos, int l, int r, node *cur) {
        if (pos<l || pos>r)
            return INF;
        cur->make_children();
        int64_t res = cur->d.get(pos);
        if (l==r)
            return res;
        int mid = (l + r) / 2;
        return min(res, min(get(pos, l, mid, cur->left_child),
                            get(pos, mid+1, r, cur->right_child)));
    }

    void upd(line val) {
        upd(val, 1, n, root);
    }

    int64_t get(int pos) {
        return get(pos, 1, n, root);
    }
};

int n;
int64_t h[MAX_N], w[MAX_N], f[MAX_N];

int64_t sqr(int64_t x) {
    return x * x;
}

void enter() {
    cin >> n;
    for (int i=1; i<=n; ++i) {
        cin >> h[i];
    }
    for (int i=1; i<=n; ++i) {
        cin >> w[i];
        w[i] += w[i-1];
    }
}

void solve() {
    IT tr(*max_element(h+1, h+n+1));
    tr.upd(line(-2*h[1], f[1] - w[1] + sqr(h[1])));
    for (int i=2; i<=n; ++i) {
        f[i] = tr.get(h[i]) + w[i-1] + sqr(h[i]);
        tr.upd(line(-2*h[i], f[i] - w[i] + sqr(h[i])));
    }
    cout << f[n];
}

int main() {
	//#define OFFLINE_JUDGE doraemon
	#ifdef OFFLINE_JUDGE
		freopen(FILE_NAME".inp", "r", stdin);
		//freopen(FILE_NAME".out", "w", stdout);
	#endif
	ios::sync_with_stdio(0); cin.tie(0);
	enter();
    solve();
}

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