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#include "graph/shortest_path/top2_dijkstra.hpp"
#include "graph/base.hpp"
#include "alg/monoid/min2.hpp"
// 経路復元はなしで距離と種類だけになっている
template <typename T, typename GT>
vc<typename Monoid_Min2<T, int>::Data> top2_dijkstra(GT& G, vc<int> vs) {
assert(G.is_prepared());
int N = G.N;
using Mono = Monoid_Min2<T, int>;
using Data = typename Mono::Data;
vc<Data> dist(N, Mono::unit());
pqg<tuple<T, int, int>> que; // 距離、町、色
auto upd = [&](int v, int c, T x) -> void {
if (dist[v].add_element(x, c)) que.emplace(x, v, c);
};
for (auto& v: vs) { upd(v, v, 0); }
while (len(que)) {
auto [dv, v, c] = POP(que);
bool ok = 0;
auto& e = dist[v];
if (e.min1 == dv && e.key1 == c) ok = 1;
if (e.min2 == dv && e.key2 == c) ok = 1;
if (!ok) continue;
for (auto&& e: G[v]) { upd(e.to, c, dv + e.cost); }
}
return dist;
}
#line 2 "graph/base.hpp"
template <typename T>
struct Edge {
int frm, to;
T cost;
int id;
};
template <typename T = int, bool directed = false>
struct Graph {
static constexpr bool is_directed = directed;
int N, M;
using cost_type = T;
using edge_type = Edge<T>;
vector<edge_type> edges;
vector<int> indptr;
vector<edge_type> csr_edges;
vc<int> vc_deg, vc_indeg, vc_outdeg;
bool prepared;
class OutgoingEdges {
public:
OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}
const edge_type* begin() const {
if (l == r) { return 0; }
return &G->csr_edges[l];
}
const edge_type* end() const {
if (l == r) { return 0; }
return &G->csr_edges[r];
}
private:
const Graph* G;
int l, r;
};
bool is_prepared() { return prepared; }
Graph() : N(0), M(0), prepared(0) {}
Graph(int N) : N(N), M(0), prepared(0) {}
void build(int n) {
N = n, M = 0;
prepared = 0;
edges.clear();
indptr.clear();
csr_edges.clear();
vc_deg.clear();
vc_indeg.clear();
vc_outdeg.clear();
}
void add(int frm, int to, T cost = 1, int i = -1) {
assert(!prepared);
assert(0 <= frm && 0 <= to && to < N);
if (i == -1) i = M;
auto e = edge_type({frm, to, cost, i});
edges.eb(e);
++M;
}
#ifdef FASTIO
// wt, off
void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }
void read_graph(int M, bool wt = false, int off = 1) {
for (int m = 0; m < M; ++m) {
INT(a, b);
a -= off, b -= off;
if (!wt) {
add(a, b);
} else {
T c;
read(c);
add(a, b, c);
}
}
build();
}
#endif
void build() {
assert(!prepared);
prepared = true;
indptr.assign(N + 1, 0);
for (auto&& e: edges) {
indptr[e.frm + 1]++;
if (!directed) indptr[e.to + 1]++;
}
for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; }
auto counter = indptr;
csr_edges.resize(indptr.back() + 1);
for (auto&& e: edges) {
csr_edges[counter[e.frm]++] = e;
if (!directed)
csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});
}
}
OutgoingEdges operator[](int v) const {
assert(prepared);
return {this, indptr[v], indptr[v + 1]};
}
vc<int> deg_array() {
if (vc_deg.empty()) calc_deg();
return vc_deg;
}
pair<vc<int>, vc<int>> deg_array_inout() {
if (vc_indeg.empty()) calc_deg_inout();
return {vc_indeg, vc_outdeg};
}
int deg(int v) {
if (vc_deg.empty()) calc_deg();
return vc_deg[v];
}
int in_deg(int v) {
if (vc_indeg.empty()) calc_deg_inout();
return vc_indeg[v];
}
int out_deg(int v) {
if (vc_outdeg.empty()) calc_deg_inout();
return vc_outdeg[v];
}
#ifdef FASTIO
void debug() {
print("Graph");
if (!prepared) {
print("frm to cost id");
for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id);
} else {
print("indptr", indptr);
print("frm to cost id");
FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id);
}
}
#endif
vc<int> new_idx;
vc<bool> used_e;
// G における頂点 V[i] が、新しいグラフで i になるようにする
// {G, es}
// sum(deg(v)) の計算量になっていて、
// 新しいグラフの n+m より大きい可能性があるので注意
Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) {
if (len(new_idx) != N) new_idx.assign(N, -1);
int n = len(V);
FOR(i, n) new_idx[V[i]] = i;
Graph<T, directed> G(n);
vc<int> history;
FOR(i, n) {
for (auto&& e: (*this)[V[i]]) {
if (len(used_e) <= e.id) used_e.resize(e.id + 1);
if (used_e[e.id]) continue;
int a = e.frm, b = e.to;
if (new_idx[a] != -1 && new_idx[b] != -1) {
history.eb(e.id);
used_e[e.id] = 1;
int eid = (keep_eid ? e.id : -1);
G.add(new_idx[a], new_idx[b], e.cost, eid);
}
}
}
FOR(i, n) new_idx[V[i]] = -1;
for (auto&& eid: history) used_e[eid] = 0;
G.build();
return G;
}
Graph<T, true> to_directed_tree(int root = -1) {
if (root == -1) root = 0;
assert(!is_directed && prepared && M == N - 1);
Graph<T, true> G1(N);
vc<int> par(N, -1);
auto dfs = [&](auto& dfs, int v) -> void {
for (auto& e: (*this)[v]) {
if (e.to == par[v]) continue;
par[e.to] = v, dfs(dfs, e.to);
}
};
dfs(dfs, root);
for (auto& e: edges) {
int a = e.frm, b = e.to;
if (par[a] == b) swap(a, b);
assert(par[b] == a);
G1.add(a, b, e.cost);
}
G1.build();
return G1;
}
private:
void calc_deg() {
assert(vc_deg.empty());
vc_deg.resize(N);
for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++;
}
void calc_deg_inout() {
assert(vc_indeg.empty());
vc_indeg.resize(N);
vc_outdeg.resize(N);
for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; }
}
};
#line 2 "alg/monoid/min2.hpp"
template <typename T, typename KEY>
struct Monoid_Min2 {
struct Data {
T min1, min2;
KEY key1, key2;
bool add_element(T x, KEY key) {
if (key1 == key) { return chmin(min1, x); }
if (key2 == key) {
bool upd = chmin(min2, x);
if (min1 > min2) swap(min1, min2), swap(key1, key2);
return upd;
}
if (min1 > x) {
min2 = min1, key2 = key1, min1 = x, key1 = key;
return 1;
}
elif (min2 > x) {
min2 = x, key2 = key;
return 1;
}
return 0;
}
};
using value_type = Data;
using X = value_type;
static X op(X x, X y) {
x.add_element(y.min1, y.key1);
x.add_element(y.min2, y.key2);
return x;
}
static constexpr X unit() { return {infty<T>, infty<T>, -1, -1}; }
static constexpr bool commute = true;
};
#line 3 "graph/shortest_path/top2_dijkstra.hpp"
// 経路復元はなしで距離と種類だけになっている
template <typename T, typename GT>
vc<typename Monoid_Min2<T, int>::Data> top2_dijkstra(GT& G, vc<int> vs) {
assert(G.is_prepared());
int N = G.N;
using Mono = Monoid_Min2<T, int>;
using Data = typename Mono::Data;
vc<Data> dist(N, Mono::unit());
pqg<tuple<T, int, int>> que; // 距離、町、色
auto upd = [&](int v, int c, T x) -> void {
if (dist[v].add_element(x, c)) que.emplace(x, v, c);
};
for (auto& v: vs) { upd(v, v, 0); }
while (len(que)) {
auto [dv, v, c] = POP(que);
bool ok = 0;
auto& e = dist[v];
if (e.min1 == dv && e.key1 == c) ok = 1;
if (e.min2 == dv && e.key2 == c) ok = 1;
if (!ok) continue;
for (auto&& e: G[v]) { upd(e.to, c, dv + e.cost); }
}
return dist;
}