Apio10a.cpp

// Ivan Carvalho
// Solution to https://www.spoj.com/problems/APIO10A/
#include <algorithm>
#include <cstdio>
#include <set>
#define gc getchar_unlocked
using namespace std;
typedef long long ll;
void getll(ll &x) {
    register ll c = gc();
    x = 0;
    for (; (c < 48 || c > 57); c = gc())
        ;
    for (; c > 47 && c < 58; c = gc()) {
        x = (x << 1) + (x << 3) + c - 48;
    }
}
struct line {
    ll a, b;
    double xleft;
    bool type;
    line(long long _a, long long _b) {
        a = _a;
        b = _b;
        type = 0;
    }
    bool operator<(const line &other) const {
        if (other.type) return xleft < other.xleft;
        return a > other.a;
    }
};
double meet(line x, line y) { return 1.0 * (y.b - x.b) / (x.a - y.a); }
struct cht {
    set<line> hull;
    cht() { hull.clear(); }
    typedef set<line>::iterator ite;
    bool hasleft(ite node) { return node != hull.begin(); }
    bool hasright(ite node) { return node != prev(hull.end()); }
    void updateborder(ite node) {
        if (hasright(node)) {
            line temp = *next(node);
            hull.erase(temp);
            temp.xleft = meet(*node, temp);
            hull.insert(temp);
        }
        if (hasleft(node)) {
            line temp = *node;
            temp.xleft = meet(*prev(node), temp);
            hull.erase(node);
            hull.insert(temp);
        } else {
            line temp = *node;
            hull.erase(node);
            temp.xleft = -1e16;
            hull.insert(temp);
        }
    }
    bool useless(line left, line mid, line right) {
        double x = meet(left, right);
        double y = x * mid.a + mid.b;
        double ly = left.a * x + left.b;
        return y > ly;
    }
    bool useless(ite node) {
        if (hasleft(node) && hasright(node)) {
            return useless(*prev(node), *node, *next(node));
        }
        return 0;
    }
    void addline(ll a, ll b) {
        line temp = line(a, b);
        ite it = hull.lower_bound(temp);
        if (it != hull.end() && it->a == a) {
            if (it->b > b) {
                hull.erase(it);
            } else {
                return;
            }
        }
        hull.insert(temp);
        it = hull.find(temp);
        if (useless(it)) {
            hull.erase(it);
            return;
        }
        while (hasleft(it) && useless(prev(it))) {
            hull.erase(prev(it));
        }
        while (hasright(it) && useless(next(it))) {
            hull.erase(next(it));
        }
        updateborder(it);
    }
    ll getbest(ll x) {
        line query(0, 0);
        query.xleft = x;
        query.type = 1;
        ite it = hull.lower_bound(query);
        it = prev(it);
        return it->a * x + it->b;
    }
};
int main() {
    int TC;
    scanf("%d", &TC);
    cht dp;
    while (TC--) {
        dp.hull.clear();
        int n;
        scanf("%d", &n);
        ll a, b, c;
        scanf("%lld %lld %lld", &a, &b, &c);
        dp.addline(0LL, 0LL);
        ll davez, soma = 0;
        for (int i = 1; i < n; i++) {
            getll(davez);
            soma += davez;
            ll best = -dp.getbest(soma) + a * soma * soma + b * soma + c;
            dp.addline(-(-2 * a * soma), -(best + a * soma * soma - b * soma));
        }
        scanf("%lld", &davez);
        soma += davez;
        ll best = -dp.getbest(soma) + a * soma * soma + b * soma + c;
        printf("%lld\n", best);
    }
    return 0;
}