#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; } template bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #else #define dbg(x) (x) #endif /* MinCostFlow: Minimum-cost flow problem solver WITH NO NEGATIVE CYCLE (just negative cost edge is allowed) Verified by SRM 770 Div1 Medium */ template struct MinCostFlow { const COST INF_COST = std::numeric_limits::max() / 2; struct edge { int to, rev; CAP cap; COST cost; friend std::ostream &operator<<(std::ostream &os, const edge &e) { os << '(' << e.to << ',' << e.rev << ',' << e.cap << ',' << e.cost << ')'; return os; } }; int V; std::vector> g; std::vector dist; std::vector prevv, preve; std::vector dual; // dual[V]: potential std::vector> pos; bool _calc_distance_bellman_ford(int s) { // O(VE), able to detect negative cycle dist.assign(V, INF_COST); dist[s] = 0; bool upd = true; int cnt = 0; while (upd) { upd = false; cnt++; if (cnt > V) return false; // Negative cycle existence for (int v = 0; v < V; v++) if (dist[v] != INF_COST) { for (int i = 0; i < (int)g[v].size(); i++) { edge &e = g[v][i]; COST c = dist[v] + e.cost + dual[v] - dual[e.to]; if (e.cap > 0 and dist[e.to] > c) { dist[e.to] = c, prevv[e.to] = v, preve[e.to] = i; upd = true; } } } } return true; } bool _calc_distance_dijkstra(int s) { // O(ElogV) dist.assign(V, INF_COST); dist[s] = 0; using P = std::pair; std::priority_queue, std::greater

> q; q.emplace(0, s); while (!q.empty()) { P p = q.top(); q.pop(); int v = p.second; if (dist[v] < p.first) continue; for (int i = 0; i < (int)g[v].size(); i++) { edge &e = g[v][i]; COST c = dist[v] + e.cost + dual[v] - dual[e.to]; if (e.cap > 0 and dist[e.to] > c) { dist[e.to] = c, prevv[e.to] = v, preve[e.to] = i; q.emplace(dist[e.to], e.to); } } } return true; } MinCostFlow(int V = 0) : V(V), g(V) {} void add_edge(int from, int to, CAP cap, COST cost) { assert(0 <= from and from < V); assert(0 <= to and to < V); pos.emplace_back(from, g[from].size()); g[from].emplace_back(edge{to, (int)g[to].size() + (from == to), cap, cost}); g[to].emplace_back(edge{from, (int)g[from].size() - 1, (CAP)0, -cost}); } std::pair flow(int s, int t, const CAP &f) { /* Flush amount of `f` from `s` to `t` using the Dijkstra's algorithm works for graph with no negative cycles (negative cost edges are allowed) retval: (flow, cost) */ COST ret = 0; dual.assign(V, 0); prevv.assign(V, -1); preve.assign(V, -1); CAP frem = f; while (frem > 0) { _calc_distance_dijkstra(s); if (dist[t] == INF_COST) break; for (int v = 0; v < V; v++) dual[v] = std::min(dual[v] + dist[v], INF_COST); CAP d = frem; for (int v = t; v != s; v = prevv[v]) { d = std::min(d, g[prevv[v]][preve[v]].cap); } frem -= d; ret += d * dual[t]; for (int v = t; v != s; v = prevv[v]) { edge &e = g[prevv[v]][preve[v]]; e.cap -= d; g[v][e.rev].cap += d; } } return std::make_pair(f - frem, ret); } friend std::ostream &operator<<(std::ostream &os, const MinCostFlow &mcf) { os << "[MinCostFlow]V=" << mcf.V << ":"; for (int i = 0; i < (int)mcf.g.size(); i++) for (auto &e : mcf.g[i]) { os << "\n" << i << "->" << e.to << ": cap=" << e.cap << ", cost=" << e.cost; } return os; } }; int main() { int N, K; cin >> N >> K; vector A(N), B(N); vector P(N, vector(N)); cin >> A >> B >> P; const int gs = N * 2, gt = gs + 1; MinCostFlow graph(gt + 1); lint ret = 0; REP(i, N) REP(j, N) { ret += P[i][j] * P[i][j]; REP(a, A[i]) graph.add_edge(i, j + N, 1, 2 * (a - P[i][j]) + 1); } REP(i, N) { graph.add_edge(gs, i, A[i], 0); graph.add_edge(i + N, gt, B[i], 0); } cout << ret + graph.flow(gs, gt, K).second << '\n'; }