This documentation is automatically generated by competitive-verifier/competitive-verifier
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/global_minimum_cut_of_dynamic_star_augmented_graph
#include "../../template/template.hpp"
#include "../../graph/flow/global-minimum-cut-of-dynamic-star-augmented-graph.hpp"
int main() {
int N, M, Q;
cin >> N >> M >> Q;
vector<int> A(N);
for (auto &a : A) cin >> a;
Edges<int64> es(M);
for (auto &e : es) {
cin >> e.from >> e.to >> e.cost;
}
GlobalMinimumCutofDynamicStarAugmentedGraph<int64> g(N, es);
for (int i = 0; i < N; i++) {
g.update(i, A[i]);
}
while (Q--) {
int x, y;
cin >> x >> y;
cout << g.update(x, y) << "\n";
}
}
#line 1 "test/verify/yosupo-global-minimum-cut-of-dynamic-star-augmented-graph.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/global_minimum_cut_of_dynamic_star_augmented_graph
#line 1 "template/template.hpp"
#include <bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif
using namespace std;
using int64 = long long;
const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;
struct IoSetup {
IoSetup() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(10);
cerr << fixed << setprecision(10);
}
} iosetup;
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
for (int i = 0; i < (int)v.size(); i++) {
os << v[i] << (i + 1 != v.size() ? " " : "");
}
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (T &in : v) is >> in;
return is;
}
template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
return a < b && (a = b, true);
}
template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
return a > b && (a = b, true);
}
template <typename T = int64>
vector<T> make_v(size_t a) {
return vector<T>(a);
}
template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}
template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
t = v;
}
template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
for (auto &e : t) fill_v(e, v);
}
template <typename F>
struct FixPoint : F {
explicit FixPoint(F &&f) : F(std::forward<F>(f)) {}
template <typename... Args>
decltype(auto) operator()(Args &&...args) const {
return F::operator()(*this, std::forward<Args>(args)...);
}
};
template <typename F>
inline decltype(auto) MFP(F &&f) {
return FixPoint<F>{std::forward<F>(f)};
}
#line 4 "test/verify/yosupo-global-minimum-cut-of-dynamic-star-augmented-graph.test.cpp"
#line 2 "graph/tree/heavy-light-decomposition.hpp"
#line 2 "graph/graph-template.hpp"
template <typename T = int>
struct Edge {
int from, to;
T cost;
int idx;
Edge() = default;
Edge(int from, int to, T cost = 1, int idx = -1)
: from(from), to(to), cost(cost), idx(idx) {}
operator int() const { return to; }
};
template <typename T = int>
struct Graph {
vector<vector<Edge<T> > > g;
int es;
Graph() = default;
explicit Graph(int n) : g(n), es(0) {}
size_t size() const { return g.size(); }
void add_directed_edge(int from, int to, T cost = 1) {
g[from].emplace_back(from, to, cost, es++);
}
void add_edge(int from, int to, T cost = 1) {
g[from].emplace_back(from, to, cost, es);
g[to].emplace_back(to, from, cost, es++);
}
void read(int M, int padding = -1, bool weighted = false,
bool directed = false) {
for (int i = 0; i < M; i++) {
int a, b;
cin >> a >> b;
a += padding;
b += padding;
T c = T(1);
if (weighted) cin >> c;
if (directed)
add_directed_edge(a, b, c);
else
add_edge(a, b, c);
}
}
inline vector<Edge<T> > &operator[](const int &k) { return g[k]; }
inline const vector<Edge<T> > &operator[](const int &k) const { return g[k]; }
};
template <typename T = int>
using Edges = vector<Edge<T> >;
#line 4 "graph/tree/heavy-light-decomposition.hpp"
/**
* @brief Heavy-Light-Decomposition(HL分解)
* @see https://smijake3.hatenablog.com/entry/2019/09/15/200200
*/
template <typename T = int>
struct HeavyLightDecomposition : Graph<T> {
public:
using Graph<T>::Graph;
using Graph<T>::g;
vector<int> sz, in, out, head, rev, par, dep;
void build(int root = 0) {
sz.assign(g.size(), 0);
in.assign(g.size(), 0);
out.assign(g.size(), 0);
head.assign(g.size(), 0);
rev.assign(g.size(), 0);
par.assign(g.size(), 0);
dep.assign(g.size(), 0);
dfs_sz(root, -1, 0);
int t = 0;
head[root] = root;
dfs_hld(root, -1, t);
}
/* k: 0-indexed */
int la(int v, int k) {
while (1) {
int u = head[v];
if (in[v] - k >= in[u]) return rev[in[v] - k];
k -= in[v] - in[u] + 1;
v = par[u];
}
}
int lca(int u, int v) const {
for (;; v = par[head[v]]) {
if (in[u] > in[v]) swap(u, v);
if (head[u] == head[v]) return u;
}
}
int dist(int u, int v) const { return dep[u] + dep[v] - 2 * dep[lca(u, v)]; }
template <typename E, typename Q, typename F, typename S>
E query(int u, int v, const E &ti, const Q &q, const F &f, const S &s,
bool edge = false) {
E l = ti, r = ti;
for (;; v = par[head[v]]) {
if (in[u] > in[v]) swap(u, v), swap(l, r);
if (head[u] == head[v]) break;
l = f(q(in[head[v]], in[v] + 1), l);
}
return s(f(q(in[u] + edge, in[v] + 1), l), r);
}
template <typename E, typename Q, typename F>
E query(int u, int v, const E &ti, const Q &q, const F &f,
bool edge = false) {
return query(u, v, ti, q, f, f, edge);
}
template <typename Q>
void add(int u, int v, const Q &q, bool edge = false) {
for (;; v = par[head[v]]) {
if (in[u] > in[v]) swap(u, v);
if (head[u] == head[v]) break;
q(in[head[v]], in[v] + 1);
}
q(in[u] + edge, in[v] + 1);
}
/* {parent, child} */
vector<pair<int, int> > compress(vector<int> &remark) {
auto cmp = [&](int a, int b) { return in[a] < in[b]; };
sort(begin(remark), end(remark), cmp);
remark.erase(unique(begin(remark), end(remark)), end(remark));
int K = (int)remark.size();
for (int k = 1; k < K; k++)
remark.emplace_back(lca(remark[k - 1], remark[k]));
sort(begin(remark), end(remark), cmp);
remark.erase(unique(begin(remark), end(remark)), end(remark));
vector<pair<int, int> > es;
stack<int> st;
for (auto &k : remark) {
while (!st.empty() && out[st.top()] <= in[k]) st.pop();
if (!st.empty()) es.emplace_back(st.top(), k);
st.emplace(k);
}
return es;
}
explicit HeavyLightDecomposition(const Graph<T> &g) : Graph<T>(g) {}
private:
void dfs_sz(int idx, int p, int d) {
dep[idx] = d;
par[idx] = p;
sz[idx] = 1;
if (g[idx].size() && g[idx][0] == p) swap(g[idx][0], g[idx].back());
for (auto &to : g[idx]) {
if (to == p) continue;
dfs_sz(to, idx, d + 1);
sz[idx] += sz[to];
if (sz[g[idx][0]] < sz[to]) swap(g[idx][0], to);
}
}
void dfs_hld(int idx, int p, int ×) {
in[idx] = times++;
rev[in[idx]] = idx;
for (auto &to : g[idx]) {
if (to == p) continue;
head[to] = (g[idx][0] == to ? head[idx] : to);
dfs_hld(to, idx, times);
}
out[idx] = times;
}
};
#line 1 "structure/class/range-add-range-min.hpp"
template <typename T>
struct RangeAddRangeMin {
using S = T;
using F = T;
static constexpr S op(const S &a, const S &b) { return min(a, b); }
static constexpr S e() { return numeric_limits<T>::max(); }
static constexpr F mapping(const S &x, const F &f) { return x + f; }
static constexpr F composition(const F &f, const F &g) { return f + g; }
static constexpr F id() { return {0}; }
};
#line 2 "structure/class/acted-monoid.hpp"
template <typename S2, typename Op, typename E, typename F2, typename Mapping,
typename Composition, typename Id>
struct LambdaActedMonoid {
using S = S2;
using F = F2;
S op(const S &a, const S &b) const { return _op(a, b); }
S e() const { return _e(); }
S mapping(const S &x, const F &f) const { return _mapping(x, f); }
F composition(const F &f, const F &g) const { return _composition(f, g); }
F id() const { return _id(); }
LambdaActedMonoid(Op _op, E _e, Mapping _mapping, Composition _composition,
Id _id)
: _op(_op),
_e(_e),
_mapping(_mapping),
_composition(_composition),
_id(_id) {}
private:
Op _op;
E _e;
Mapping _mapping;
Composition _composition;
Id _id;
};
template <typename Op, typename E, typename Mapping, typename Composition,
typename Id>
LambdaActedMonoid(Op _op, E _e, Mapping _mapping, Composition _composition,
Id _id)
-> LambdaActedMonoid<decltype(_e()), Op, E, decltype(_id()), Mapping,
Composition, Id>;
/*
struct ActedMonoid {
using S = ?;
using F = ?;
static constexpr S op(const S& a, const S& b) {}
static constexpr S e() {}
static constexpr S mapping(const S &x, const F &f) {}
static constexpr F composition(const F &f, const F &g) {}
static constexpr F id() {}
};
*/
#line 2 "structure/segment-tree/lazy-segment-tree.hpp"
template <typename ActedMonoid>
struct LazySegmentTree {
using S = typename ActedMonoid::S;
using F = typename ActedMonoid::F;
private:
ActedMonoid m;
int n{}, sz{}, height{};
vector<S> data;
vector<F> lazy;
inline void update(int k) {
data[k] = m.op(data[2 * k + 0], data[2 * k + 1]);
}
inline void all_apply(int k, const F &x) {
data[k] = m.mapping(data[k], x);
if (k < sz) lazy[k] = m.composition(lazy[k], x);
}
inline void propagate(int k) {
if (lazy[k] != m.id()) {
all_apply(2 * k + 0, lazy[k]);
all_apply(2 * k + 1, lazy[k]);
lazy[k] = m.id();
}
}
public:
LazySegmentTree() = default;
explicit LazySegmentTree(ActedMonoid m, int n) : m(m), n(n) {
sz = 1;
height = 0;
while (sz < n) sz <<= 1, height++;
data.assign(2 * sz, m.e());
lazy.assign(2 * sz, m.id());
}
explicit LazySegmentTree(ActedMonoid m, const vector<S> &v)
: LazySegmentTree(m, v.size()) {
build(v);
}
void build(const vector<S> &v) {
assert(n == (int)v.size());
for (int k = 0; k < n; k++) data[k + sz] = v[k];
for (int k = sz - 1; k > 0; k--) update(k);
}
void set(int k, const S &x) {
k += sz;
for (int i = height; i > 0; i--) propagate(k >> i);
data[k] = x;
for (int i = 1; i <= height; i++) update(k >> i);
}
S get(int k) {
k += sz;
for (int i = height; i > 0; i--) propagate(k >> i);
return data[k];
}
S operator[](int k) { return get(k); }
S prod(int l, int r) {
if (l >= r) return m.e();
l += sz;
r += sz;
for (int i = height; i > 0; i--) {
if (((l >> i) << i) != l) propagate(l >> i);
if (((r >> i) << i) != r) propagate((r - 1) >> i);
}
S L = m.e(), R = m.e();
for (; l < r; l >>= 1, r >>= 1) {
if (l & 1) L = m.op(L, data[l++]);
if (r & 1) R = m.op(data[--r], R);
}
return m.op(L, R);
}
S all_prod() const { return data[1]; }
void apply(int k, const F &f) {
k += sz;
for (int i = height; i > 0; i--) propagate(k >> i);
data[k] = m.mapping(data[k], f);
for (int i = 1; i <= height; i++) update(k >> i);
}
void apply(int l, int r, const F &f) {
if (l >= r) return;
l += sz;
r += sz;
for (int i = height; i > 0; i--) {
if (((l >> i) << i) != l) propagate(l >> i);
if (((r >> i) << i) != r) propagate((r - 1) >> i);
}
{
int l2 = l, r2 = r;
for (; l < r; l >>= 1, r >>= 1) {
if (l & 1) all_apply(l++, f);
if (r & 1) all_apply(--r, f);
}
l = l2, r = r2;
}
for (int i = 1; i <= height; i++) {
if (((l >> i) << i) != l) update(l >> i);
if (((r >> i) << i) != r) update((r - 1) >> i);
}
}
template <typename C>
int find_first(int l, const C &check) {
if (l >= n) return n;
l += sz;
for (int i = height; i > 0; i--) propagate(l >> i);
S sum = m.e();
do {
while ((l & 1) == 0) l >>= 1;
if (check(m.op(sum, data[l]))) {
while (l < sz) {
propagate(l);
l <<= 1;
auto nxt = m.op(sum, data[l]);
if (not check(nxt)) {
sum = nxt;
l++;
}
}
return l + 1 - sz;
}
sum = m.op(sum, data[l++]);
} while ((l & -l) != l);
return n;
}
template <typename C>
int find_last(int r, const C &check) {
if (r <= 0) return -1;
r += sz;
for (int i = height; i > 0; i--) propagate((r - 1) >> i);
S sum = m.e();
do {
r--;
while (r > 1 and (r & 1)) r >>= 1;
if (check(m.op(data[r], sum))) {
while (r < sz) {
propagate(r);
r = (r << 1) + 1;
auto nxt = m.op(data[r], sum);
if (not check(nxt)) {
sum = nxt;
r--;
}
}
return r - sz;
}
sum = m.op(data[r], sum);
} while ((r & -r) != r);
return -1;
}
};
#line 2 "graph/others/extreme-vertex-set.hpp"
template <typename T>
Graph<T> extreme_vertex_set(int n, const Edges<T> &es) {
for (auto &e : es) {
assert(0 <= e.from and e.from < n);
assert(0 <= e.to and e.to < n);
assert(e.from != e.to);
assert(0 <= e.cost);
}
using pi = pair<int, T>;
Graph<T> res(2 * n - 1);
vector<int> uf(n);
vector<T> cur(2 * n - 1);
iota(uf.begin(), uf.end(), 0);
vector<bool> leaf(2 * n - 1);
for (int i = 0; i < n; i++) {
leaf[i] = true;
}
using qi = pair<T, int>;
priority_queue<qi, vector<qi>, greater<> > que;
for (int phase = 0; phase < n - 1; phase++) {
Graph<T> g(2 * n - 1);
vector<T> cost(2 * n - 1);
for (auto e : es) {
e.from = uf[e.from];
e.to = uf[e.to];
if (e.from != e.to) {
cost[e.from] += e.cost;
cost[e.to] += e.cost;
g.add_edge(e.from, e.to, e.cost);
}
}
for (int i = 0; i < 2 * n - 1; i++) {
if (leaf[i]) {
cur[i] = cost[i];
que.emplace(cost[i], i);
}
}
int x = -1, y = -1;
while (not que.empty()) {
auto [c, v] = que.top();
que.pop();
if (cur[v] == -1) {
continue;
}
cur[v] = -1;
y = x;
x = v;
for (auto &e : g[v]) {
if (cur[e.to] != -1) {
cur[e.to] -= e.cost;
que.emplace(cur[e.to], e.to);
}
}
}
int z = n + phase;
res.add_directed_edge(z, x, cost[x]);
res.add_directed_edge(z, y, cost[y]);
for (int i = 0; i < n; i++) {
if (uf[i] == x or uf[i] == y) {
uf[i] = z;
}
}
leaf[x] = false;
leaf[y] = false;
leaf[z] = true;
}
return res;
}
#line 5 "graph/flow/global-minimum-cut-of-dynamic-star-augmented-graph.hpp"
template <typename T>
struct GlobalMinimumCutofDynamicStarAugmentedGraph {
private:
int n{};
HeavyLightDecomposition<T> hld;
vector<T> cur;
LazySegmentTree<RangeAddRangeMin<T> > seg;
public:
GlobalMinimumCutofDynamicStarAugmentedGraph() = default;
explicit GlobalMinimumCutofDynamicStarAugmentedGraph(int n,
const Edges<T> &es)
: n(n),
hld(extreme_vertex_set(n, es)),
cur(n),
seg(RangeAddRangeMin<T>(), 2 * n - 1) {
hld.build((int)hld.size() - 1);
vector<int64> vs(2 * n - 1);
for (int i = 0; i < 2 * n - 1; i++) {
for (auto &e : hld[i]) {
vs[hld.in[e.to]] = e.cost;
}
}
seg.build(vs);
}
T update(int v, T cost) {
assert(0 <= v and v < n);
hld.add(v, (int)hld.size() - 1,
[&](int l, int r) { seg.apply(l, r, cost - cur[v]); });
cur[v] = cost;
return seg.all_prod();
}
};
#line 6 "test/verify/yosupo-global-minimum-cut-of-dynamic-star-augmented-graph.test.cpp"
int main() {
int N, M, Q;
cin >> N >> M >> Q;
vector<int> A(N);
for (auto &a : A) cin >> a;
Edges<int64> es(M);
for (auto &e : es) {
cin >> e.from >> e.to >> e.cost;
}
GlobalMinimumCutofDynamicStarAugmentedGraph<int64> g(N, es);
for (int i = 0; i < N; i++) {
g.update(i, A[i]);
}
while (Q--) {
int x, y;
cin >> x >> y;
cout << g.update(x, y) << "\n";
}
}
Env | Name | Status | Elapsed | Memory |
---|---|---|---|---|
g++ | almostclique_00 | AC | 71 ms | 4 MB |
g++ | balance_00 | AC | 1398 ms | 4 MB |
g++ | balance_01 | AC | 1391 ms | 4 MB |
g++ | balance_many_00 | AC | 2290 ms | 5 MB |
g++ | balance_many_01 | AC | 2321 ms | 5 MB |
g++ | clique_00 | AC | 67 ms | 4 MB |
g++ | clique_max_00 | AC | 77 ms | 4 MB |
g++ | deep_00 | AC | 2329 ms | 5 MB |
g++ | deep_01 | AC | 2337 ms | 5 MB |
g++ | dense_00 | AC | 136 ms | 4 MB |
g++ | dense_01 | AC | 137 ms | 4 MB |
g++ | doubledeep_00 | AC | 2499 ms | 5 MB |
g++ | doubledeep_01 | AC | 2483 ms | 5 MB |
g++ | example_00 | AC | 5 ms | 3 MB |
g++ | example_01 | AC | 4 ms | 3 MB |
g++ | handmake_00 | AC | 2324 ms | 5 MB |
g++ | noedge_00 | AC | 612 ms | 5 MB |
g++ | only_00 | AC | 37 ms | 3 MB |
g++ | onlyzero_00 | AC | 2268 ms | 5 MB |
g++ | sparse_00 | AC | 2099 ms | 5 MB |
g++ | sparse_01 | AC | 2117 ms | 5 MB |
clang++ | almostclique_00 | AC | 68 ms | 4 MB |
clang++ | balance_00 | AC | 1394 ms | 4 MB |
clang++ | balance_01 | AC | 1368 ms | 4 MB |
clang++ | balance_many_00 | AC | 2210 ms | 4 MB |
clang++ | balance_many_01 | AC | 2215 ms | 5 MB |
clang++ | clique_00 | AC | 67 ms | 4 MB |
clang++ | clique_max_00 | AC | 76 ms | 4 MB |
clang++ | deep_00 | AC | 2219 ms | 5 MB |
clang++ | deep_01 | AC | 2264 ms | 5 MB |
clang++ | dense_00 | AC | 136 ms | 4 MB |
clang++ | dense_01 | AC | 134 ms | 4 MB |
clang++ | doubledeep_00 | AC | 2372 ms | 5 MB |
clang++ | doubledeep_01 | AC | 2364 ms | 5 MB |
clang++ | example_00 | AC | 5 ms | 3 MB |
clang++ | example_01 | AC | 4 ms | 3 MB |
clang++ | handmake_00 | AC | 2220 ms | 5 MB |
clang++ | noedge_00 | AC | 555 ms | 5 MB |
clang++ | only_00 | AC | 38 ms | 3 MB |
clang++ | onlyzero_00 | AC | 2217 ms | 5 MB |
clang++ | sparse_00 | AC | 1984 ms | 5 MB |
clang++ | sparse_01 | AC | 2020 ms | 5 MB |