// ===== monotone_minima.hpp ===== #ifndef MONOTONE_MINIMA_HPP #define MONOTONE_MINIMA_HPP #include #include template std::vector monotone_minima_sub(const F &f, const std::vector &rows, std::size_t w) { if (rows.empty()) { return std::vector(); } std::vector red; red.reserve(rows.size() / 2); for (std::size_t i = 1; i < rows.size(); i += 2) { red.push_back(rows[i]); } std::vector red_ans = monotone_minima_sub(f, red, w); std::vector ans(rows.size()); for (std::size_t i = 0; i < red.size(); ++i) { ans[2 * i + 1] = red_ans[i]; } for (std::size_t i = 0; i < rows.size(); i += 2) { std::size_t l = (i == 0 ? 0 : ans[i - 1]); std::size_t r = (i == rows.size() - 1 ? w - 1 : ans[i + 1]); auto minimum = f(rows[i], l); std::size_t index = l; for (std::size_t j = l + 1; j <= r; ++j) { auto tmp = f(rows[i], j); if (tmp < minimum) { minimum = tmp; index = j; } } ans[i] = index; } return ans; } template std::vector monotone_minima(const F &f, std::size_t h, std::size_t w) { std::vector rows(h); std::iota(rows.begin(), rows.end(), 0); return monotone_minima_sub(f, rows, w); } #endif // ===== monotone_minima.hpp ===== #include #include #include #include using usize = std::size_t; template std::vector monge_maxima(const F &f, usize h, usize w) { const auto g = [&](std::size_t i, std::size_t j) { return -f(h - 1 - i, j); }; std::vector ret = monotone_minima(g, h, w); std::reverse(ret.begin(), ret.end()); return ret; } std::vector> calc_inv(std::vector p) { usize n = p.size(); std::vector> sum(n + 1, std::vector(n + 1, 0)); for (usize i = 0; i < n; ++i) { sum[i + 1] = sum[i]; for (usize j = p[i]; j < n; ++j) { ++sum[i + 1][j + 1]; } } std::vector> inv(n, std::vector(n + 1, 0)); for (usize i = 0; i < n; ++i) { usize s = 0; for (usize j = i; j < n; ++j) { s += sum[j][n] - sum[i][n] - sum[j][p[j]] + sum[i][p[j]]; inv[i][j + 1] = s; } } return inv; } void fast_dp( const std::vector> &f, const std::vector &from, std::vector &to, usize l, usize r ) { if (l + 1 == r) { return; } usize mid = (l + r) / 2; fast_dp(f, from, to, l, mid); const auto jump = [&](usize i, usize j) -> long { i += mid; j += l; return from[j] + f[j][i]; }; std::vector max_index = monge_maxima(jump, r - mid, mid - l); for (usize i = 0; i < r - mid; ++i) { usize tmp = jump(i, max_index[i]); if (tmp > to[i + mid]) { to[i + mid] = tmp; } } fast_dp(f, from, to, mid, r); } std::vector> calc_dp(std::vector> inv) { usize n = inv.size(); std::vector> dp(n + 1, std::vector(n + 1, 0)); for (usize i = 0; i < n; ++i) { fast_dp(inv, dp[i], dp[i + 1], i, n + 1); } return dp; } int main() { usize n; std::cin >> n; std::vector p(n); for (std::size_t &ele : p) { std::cin >> ele; --ele; } std::vector> inv = calc_inv(std::move(p)); usize all_inv = inv[0][n]; std::vector> dp = calc_dp(std::move(inv)); for (usize i = 1; i <= n; ++i) { std::cout << all_inv - dp[i][n] << '\n'; } }