CSES Subarray Squares
// compile: make data
// run: time ./data < data.in
#include <bits/stdc++.h>
using namespace std;
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#ifdef LOCAL
#include <debug/codeforces.h>
#define debug(x...) _debug_print(#x, x);
#define Debug(x...) _debug_print_format(#x, x);
std::ifstream terminal("/dev/tty");
#define PP cerr<<"\033[1;30mpause...\e[0m",terminal.ignore();
#else
#define debug(x...)
#define Debug(x...)
#define PP
#endif
template<typename...Args> void print_(Args...args){((cout<<args<<" "),...)<<endl;}
#define rep(i,a,b) for(int i=(a);i<(int)(b);++i)
#define sz(v) ((int)(v).size())
#define print(...) print_(__VA_ARGS__);
#define FIND(a, x) ((find(a.begin(),a.end(),(x))!=a.end())?1:0)
#define cmin(x,...) x=min({(x),__VA_ARGS__})
#define cmax(x,...) x=max({(x),__VA_ARGS__})
#define INTMAX (int)(9223372036854775807)
#define INF (int)(1152921504606846976)
#define NaN (int)(0x8b88e1d0595d51d1)
#define double long double
#define int long long
#define uint unsigned long long
#define SQR(x) ((x)*(x))
#define MAXN 200010

template <typename T> struct point2d {
    T x, y;
    point2d() {}
    point2d(int X, int Y): x(X), y(Y) {}
    point2d<T> operator+(const point2d<T> &rhs) const {return point2d<T>(x + rhs.x, y + rhs.y); }
    point2d<T> operator-(const point2d<T> &rhs) const {return point2d<T>(x - rhs.x, y - rhs.y); }
    bool operator==(const point2d<T> &rhs) const {return x == rhs.x && y == rhs.y; }
    T operator*(const point2d<T> &rhs) const {return x * rhs.y - y * rhs.x; }
};

struct cht {
    vector<point2d<int>> p;
    int start = 0;
    void insert(int x, int y) {
        point2d<int> now(x, y);
        while (sz(p) > 1 && (p[sz(p)-1] - p[sz(p)-2]) * (now - p[sz(p)-1]) < 0) p.pop_back();
        cmin(start, max(sz(p)-1, 0ll));
        p.emplace_back(now);
    }
    int findmin(int k) {
        if (p.empty()) return INF;
        if (p.size() == 1) return p[0].y - k*p[0].x;
        for (; start < sz(p)-1 && (p[start+1] - p[start]) * point2d<int>(1, k) >= 0; ++start);
        return p[start].y - k*p[start].x;
    }
};

int32_t main() {
    ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);

    int n, k; cin >> n >> k;
    vector<int> a(n+1), sum(n+1);
    rep(i, 1, n+1) cin >> a[i], sum[i] = sum[i-1] + a[i];
    auto calc = [&](int l, int r) {
        return (sum[r] - sum[l-1]) * (sum[r] - sum[l-1]);
    };
    vector<int> pre(n+1), dp(n+1);
    rep(i, 1, n+1) pre[i] = calc(1, i);
    rep(it, 1, k) {
        fill(dp.begin(), dp.end(), INF);
        cht plane;
        plane.insert(sum[it], pre[it] + SQR(sum[it]));
        rep(i, it+1, n+1) {
            dp[i] = plane.findmin(2 * sum[i]) + SQR(sum[i]);
            plane.insert(sum[i], pre[i] + SQR(sum[i]));
        }
        pre = dp;
    }
    cout << dp[n] << endl;

    return 0;
}
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Source: github.com/k4yt3x/flowerhd
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