// need #include #include // data structure #include //#include #include #include #include #include #include #include #include //#include //#include #include #include //#include //#include // stream //#include //#include //#include // etc #include #include #include //#include #include #include #include #define INIT std::ios::sync_with_stdio(false);std::cin.tie(0); #define VAR(type, ...)type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__); template void MACRO_VAR_Scan(T& t) { std::cin >> t; } templatevoid MACRO_VAR_Scan(First& first, Rest&...rest) { std::cin >> first; MACRO_VAR_Scan(rest...); } #define VEC_ROW(type, n, ...)std::vector __VA_ARGS__;MACRO_VEC_ROW_Init(n, __VA_ARGS__); for(int i=0; i void MACRO_VEC_ROW_Init(int n, T& t) { t.resize(n); } templatevoid MACRO_VEC_ROW_Init(int n, First& first, Rest&...rest) { first.resize(n); MACRO_VEC_ROW_Init(n, rest...); } template void MACRO_VEC_ROW_Scan(int p, T& t) { std::cin >> t[p]; } templatevoid MACRO_VEC_ROW_Scan(int p, First& first, Rest&...rest) { std::cin >> first[p]; MACRO_VEC_ROW_Scan(p, rest...); } #define OUT(d) std::cout< c(n);for(auto& i:c)std::cin>>i; #define MAT(type, c, m, n) std::vector> c(m, std::vector(n));for(auto& r:c)for(auto& i:r)std::cin>>i; #define ALL(a) (a).begin(),(a).end() #define FOR(i, a, b) for(int i=(a);i<(b);++i) #define RFOR(i, a, b) for(int i=(b)-1;i>=(a);--i) #define REP(i, n) for(int i=0;i=0;--i) #define FORLL(i, a, b) for(ll i=ll(a);i=ll(a);--i) #define REPLL(i, n) for(ll i=0;i=0;--i) #define PAIR std::pair #define PAIRLL std::pair #define IN(a, x, b) (a<=x && x tmp(a);std::cerr << #a << "\t:";for(int i=0; i(a.size()); ++i){std::cerr << tmp.front() << "\n";tmp.pop();}std::cerr << "\n";} template inline T CHMAX(T& a, const T b) { return a = (a < b) ? b : a; } template inline T CHMIN(T& a, const T b) { return a = (a > b) ? b : a; } #define EXCEPTION(msg) throw std::string("Exception : " msg " [ in ") + __func__ + " : " + std::to_string(__LINE__) + " lines ]" #define TRY(cond, msg) try {if (cond) EXCEPTION(msg);}catch (std::string s) {std::cerr << s << std::endl;} void CHECKTIME(std::function f) { auto start = std::chrono::system_clock::now(); f(); auto end = std::chrono::system_clock::now(); auto res = std::chrono::duration_cast((end - start)).count(); std::cerr << "[Time:" << res << "ns (" << res / (1.0e9) << "s)]\n"; } #define int ll using ll = long long; using ull = unsigned long long; constexpr int INFINT = 1 << 30; // 1.07x10^ 9 constexpr int INFINT_LIM = (1LL << 31) - 1; // 2.15x10^ 9 constexpr ll INFLL = 1LL << 60; // 1.15x10^18 constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^19 constexpr double EPS = 1e-7; constexpr int MOD = 1000000007; constexpr double PI = 3.141592653589793238462643383279; struct LUinfo { std::vector value; std::vector index; }; // O( n^3 ), Gaussian forward elimination LUinfo LU_decomposition(std::vector> A) { const int n = A.size(); LUinfo data; for (int i = 0; i < n; ++i) { int pivot = i; for (int j = i + 1; j < n; ++j) if (std::abs(A[j][i]) > std::abs(A[pivot][i])) pivot = j; std::swap(A[pivot], A[i]); data.index.push_back(pivot); // if A[i][i] == 0, LU decomposition failed. for (int j = i + 1; j < n; ++j) { A[j][i] /= A[i][i]; for (int k = i + 1; k < n; ++k) A[j][k] -= A[i][k] * A[j][i]; data.value.push_back(A[j][i]); } } for (int i = n - 1; i >= 0; --i) { for (int j = i + 1; j < n; ++j) data.value.push_back(A[i][j]); data.value.push_back(A[i][i]); } return data; } // O( n^2 ) Gaussian backward substitution std::vector LU_backsubstitution(const LUinfo &data, std::vector b) { const int n = b.size(); int k = 0; for (int i = 0; i < n; ++i) { std::swap(b[data.index[i]], b[i]); for (int j = i + 1; j < n; ++j) b[j] -= b[i] * data.value[k++]; } for (int i = n - 1; i >= 0; --i) { for (int j = i + 1; j < n; ++j) b[i] -= b[j] * data.value[k++]; b[i] /= data.value[k++]; } return b; } double dp[102]; // iから始めたときの最小(魔法未使用) double dp2[102]; // iから始めたときの最小(魔法 使用) signed main() { INIT; VAR(int, n, m); std::vector c(n, 0); FOR(i, 1, n - 1) { std::cin >> c[i]; } std::vector> A(n-1, std::vector(n-1, 0)); std::vector B(n-1, 0); auto toPos = [&](int x) { if (x < n) return x; else return 2 * (n - 1) - x; }; REP(i, n-1) { A[i][i] = m; FOR(j, 1, m + 1) { int p = toPos(i + j); if (p == n - 1) continue; --A[i][p]; } B[i] = c[i] * m; } auto data = LU_decomposition(A); auto v = LU_backsubstitution(data, B); REP(i, n - 1) { dp[i] = v[i]; } FOR(i, n - 1 - m, n) { dp2[i] = c[i]; } RREP(i, n - m) { double min = 1e308; double sum = 0; FOR(j, i + 1, i + m + 1) { CHMIN(min, dp[j]); sum += dp2[j] / m; } dp2[i] = c[i] + std::min(min, sum); } /*REP(i, n) { FOUT(9, dp2[i]); SP; }BR;*/ FOUT(16, dp2[0])BR; return 0; }