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#define PROBLEM "https://yukicoder.me/problems/no/952" #include "../../algorithm/enumerate_monge_d_edge_shortest_path.hpp" #include "../../template/template.hpp" namespace ebi { void main_() { int n; std::cin >> n; std::vector<i64> a(n); std::cin >> a; a.insert(a.begin(), 0); n++; std::vector<i64> sum(n + 1, 0); rep(i, 0, n) sum[i + 1] = sum[i] + a[i]; auto f = [&](int i, int j) -> i64 { return (sum[j] - sum[i + 1]) * (sum[j] - sum[i + 1]); }; auto ans = enumerate_monge_d_edge_shortest_path(n + 1, f); rep(i, 1, n) { std::cout << ans[n - i] << '\n'; } } } // namespace ebi int main() { ebi::fast_io(); int t = 1; // std::cin >> t; while (t--) { ebi::main_(); } return 0; }
#line 1 "test/yuki/yuki_952.test.cpp" #define PROBLEM "https://yukicoder.me/problems/no/952" #line 2 "algorithm/enumerate_monge_d_edge_shortest_path.hpp" #include <limits> #include <utility> #include <vector> #line 2 "algorithm/monotone_minima.hpp" #include <functional> #line 6 "algorithm/monotone_minima.hpp" namespace ebi { template <class F, class T = decltype(std::declval<F>()(std::declval<int>(), std::declval<int>())), class Compare = std::less<T>> std::pair<std::vector<int>, std::vector<T>> monotone_minima( int n, int m, F f, const Compare &compare = Compare()) { std::vector<int> argmin(n); std::vector<T> min_val(n); auto dfs = [&](auto &&self, int top, int bottom, int left, int right) -> void { if (top > bottom) return; int mid = (top + bottom) >> 1; argmin[mid] = left; min_val[mid] = f(mid, left); for (int i = left + 1; i <= right; i++) { T val = f(mid, i); if (min_val[mid] == val || compare(val, min_val[mid])) { argmin[mid] = i; min_val[mid] = val; } } self(self, top, mid - 1, left, argmin[mid]); self(self, mid + 1, bottom, argmin[mid], right); }; dfs(dfs, 0, n - 1, 0, m - 1); return {argmin, min_val}; } template <class T, class F, class Compare = std::less<T>> std::pair<std::vector<int>, std::vector<T>> slide_monotone_minima( int n, int m, F f, const Compare &compare = Compare()) { std::vector<int> argmin(n); std::vector<T> min_val(n); auto dfs = [&](auto &&self, int top, int bottom, int left, int right, int depth) -> void { if (top > bottom) return; int mid = (top + bottom) >> 1; argmin[mid] = left; min_val[mid] = f(mid, left, depth); for (int i = left + 1; i <= right; i++) { T val = f(mid, i, depth); if (min_val[mid] == val || compare(val, min_val[mid])) { argmin[mid] = i; min_val[mid] = val; } } self(self, top, mid - 1, left, argmin[mid], depth + 1); self(self, mid + 1, bottom, argmin[mid], right, depth + 1); }; dfs(dfs, 0, n - 1, 0, m - 1, 0); return {argmin, min_val}; } } // namespace ebi #line 8 "algorithm/enumerate_monge_d_edge_shortest_path.hpp" namespace ebi { template <class F, class T = decltype(std::declval<F>()(std::declval<int>(), std::declval<int>()))> std::vector<T> enumerate_monge_d_edge_shortest_path(int n, F f) { const T max = std::numeric_limits<T>::max(); std::vector<T> res(n, max); std::vector<T> dp(n, max); dp[0] = 0; auto g = [&](int j, int i) -> T { if (dp[i] == max || i >= j) return max; return dp[i] + f(i, j); }; for (int d = 1; d < n; d++) { std::vector<int> argmin = monotone_minima(n, n, g).first; for (int i = n - 1; i >= d; i--) dp[i] = g(i, argmin[i]); res[d] = dp[n - 1]; } return res; } } // namespace ebi #line 1 "template/template.hpp" #include <bits/stdc++.h> #define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++) #define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--) #define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++) #define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--) #define all(v) (v).begin(), (v).end() #define rall(v) (v).rbegin(), (v).rend() #line 2 "template/debug_template.hpp" #line 4 "template/debug_template.hpp" namespace ebi { #ifdef LOCAL #define debug(...) \ std::cerr << "LINE: " << __LINE__ << " [" << #__VA_ARGS__ << "]:", \ debug_out(__VA_ARGS__) #else #define debug(...) #endif void debug_out() { std::cerr << std::endl; } template <typename Head, typename... Tail> void debug_out(Head h, Tail... t) { std::cerr << " " << h; if (sizeof...(t) > 0) std::cerr << " :"; debug_out(t...); } } // namespace ebi #line 2 "template/int_alias.hpp" #line 4 "template/int_alias.hpp" namespace ebi { using ld = long double; using std::size_t; using i8 = std::int8_t; using u8 = std::uint8_t; using i16 = std::int16_t; using u16 = std::uint16_t; using i32 = std::int32_t; using u32 = std::uint32_t; using i64 = std::int64_t; using u64 = std::uint64_t; using i128 = __int128_t; using u128 = __uint128_t; } // namespace ebi #line 2 "template/io.hpp" #line 5 "template/io.hpp" #include <optional> #line 7 "template/io.hpp" namespace ebi { template <typename T1, typename T2> std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &pa) { return os << pa.first << " " << pa.second; } template <typename T1, typename T2> std::istream &operator>>(std::istream &os, std::pair<T1, T2> &pa) { return os >> pa.first >> pa.second; } template <typename T> std::ostream &operator<<(std::ostream &os, const std::vector<T> &vec) { for (std::size_t i = 0; i < vec.size(); i++) os << vec[i] << (i + 1 == vec.size() ? "" : " "); return os; } template <typename T> std::istream &operator>>(std::istream &os, std::vector<T> &vec) { for (T &e : vec) std::cin >> e; return os; } template <typename T> std::ostream &operator<<(std::ostream &os, const std::optional<T> &opt) { if (opt) { os << opt.value(); } else { os << "invalid value"; } return os; } void fast_io() { std::cout << std::fixed << std::setprecision(15); std::cin.tie(nullptr); std::ios::sync_with_stdio(false); } } // namespace ebi #line 2 "template/utility.hpp" #line 5 "template/utility.hpp" #line 2 "graph/base.hpp" #line 5 "graph/base.hpp" #include <ranges> #line 7 "graph/base.hpp" #line 2 "data_structure/simple_csr.hpp" #line 6 "data_structure/simple_csr.hpp" namespace ebi { template <class E> struct simple_csr { simple_csr() = default; simple_csr(int n, const std::vector<std::pair<int, E>>& elements) : start(n + 1, 0), elist(elements.size()) { for (auto e : elements) { start[e.first + 1]++; } for (auto i : std::views::iota(0, n)) { start[i + 1] += start[i]; } auto counter = start; for (auto [i, e] : elements) { elist[counter[i]++] = e; } } simple_csr(const std::vector<std::vector<E>>& es) : start(es.size() + 1, 0) { int n = es.size(); for (auto i : std::views::iota(0, n)) { start[i + 1] = (int)es[i].size() + start[i]; } elist.resize(start.back()); for (auto i : std::views::iota(0, n)) { std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]); } } int size() const { return (int)start.size() - 1; } const auto operator[](int i) const { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } auto operator[](int i) { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } const auto operator()(int i, int l, int r) const { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } auto operator()(int i, int l, int r) { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } private: std::vector<int> start; std::vector<E> elist; }; } // namespace ebi #line 9 "graph/base.hpp" namespace ebi { template <class T> struct Edge { int from, to; T cost; int id; }; template <class E> struct Graph { using cost_type = E; using edge_type = Edge<cost_type>; Graph(int n_) : n(n_) {} Graph() = default; void add_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); edges.emplace_back(edge_type{u, v, c, m++}); } void add_undirected_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); buff.emplace_back(v, edge_type{v, u, c, m}); edges.emplace_back(edge_type{u, v, c, m}); m++; } void read_tree(int offset = 1, bool is_weighted = false) { read_graph(n - 1, offset, false, is_weighted); } void read_parents(int offset = 1) { for (auto i : std::views::iota(1, n)) { int p; std::cin >> p; p -= offset; add_undirected_edge(p, i, 1); } build(); } void read_graph(int e, int offset = 1, bool is_directed = false, bool is_weighted = false) { for (int i = 0; i < e; i++) { int u, v; std::cin >> u >> v; u -= offset; v -= offset; if (is_weighted) { cost_type c; std::cin >> c; if (is_directed) { add_edge(u, v, c); } else { add_undirected_edge(u, v, c); } } else { if (is_directed) { add_edge(u, v, 1); } else { add_undirected_edge(u, v, 1); } } } build(); } void build() { assert(!prepared); csr = simple_csr<edge_type>(n, buff); buff.clear(); prepared = true; } int size() const { return n; } int node_number() const { return n; } int edge_number() const { return m; } edge_type get_edge(int i) const { return edges[i]; } std::vector<edge_type> get_edges() const { return edges; } const auto operator[](int i) const { return csr[i]; } auto operator[](int i) { return csr[i]; } private: int n, m = 0; std::vector<std::pair<int,edge_type>> buff; std::vector<edge_type> edges; simple_csr<edge_type> csr; bool prepared = false; }; } // namespace ebi #line 8 "template/utility.hpp" namespace ebi { template <class T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; } template <class T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; } template <class T> T safe_ceil(T a, T b) { if (a % b == 0) return a / b; else if (a >= 0) return (a / b) + 1; else return -((-a) / b); } template <class T> T safe_floor(T a, T b) { if (a % b == 0) return a / b; else if (a >= 0) return a / b; else return -((-a) / b) - 1; } constexpr i64 LNF = std::numeric_limits<i64>::max() / 4; constexpr int INF = std::numeric_limits<int>::max() / 2; const std::vector<int> dy = {1, 0, -1, 0, 1, 1, -1, -1}; const std::vector<int> dx = {0, 1, 0, -1, 1, -1, 1, -1}; } // namespace ebi #line 5 "test/yuki/yuki_952.test.cpp" namespace ebi { void main_() { int n; std::cin >> n; std::vector<i64> a(n); std::cin >> a; a.insert(a.begin(), 0); n++; std::vector<i64> sum(n + 1, 0); rep(i, 0, n) sum[i + 1] = sum[i] + a[i]; auto f = [&](int i, int j) -> i64 { return (sum[j] - sum[i + 1]) * (sum[j] - sum[i + 1]); }; auto ans = enumerate_monge_d_edge_shortest_path(n + 1, f); rep(i, 1, n) { std::cout << ans[n - i] << '\n'; } } } // namespace ebi int main() { ebi::fast_io(); int t = 1; // std::cin >> t; while (t--) { ebi::main_(); } return 0; }