// 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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