#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "template/template.hpp"
#include "graph/graph.hpp"
#include "graph/shortest-path.hpp"
void test_bfs() {
GraphUnweighted g(6);
g.add_edge_directed(0, 1);
g.add_edge_directed(0, 2);
g.add_edge_directed(1, 3);
g.add_edge_directed(2, 3);
g.add_edge_directed(3, 4);
auto dist = ShortestPath::BFS(g, 0);
assert(dist == vector<optional<int>>({0, 1, 1, 2, 3, nullopt}));
auto [dist_with_prev, prev] = ShortestPath::BFSWithPrev(g, 0);
assert(dist_with_prev == dist);
auto path = ShortestPath::EnumeratePath(prev, 4);
assert(path.front() == 0 && path.back() == 4 && path.size() == 4);
assert(ShortestPath::EnumeratePath(prev, 0) == vector<int>({0}));
}
void test_zero_one_bfs() {
GraphWeighted<int> g(6);
g.add_edge_directed(0, 1, 1);
g.add_edge_directed(0, 2, 0);
g.add_edge_directed(2, 1, 0);
g.add_edge_directed(1, 3, 1);
g.add_edge_directed(2, 3, 1);
g.add_edge_directed(3, 4, 0);
auto dist = ShortestPath::ZeroOneBFS(g, 0);
assert(dist == vector<optional<int>>({0, 0, 0, 1, 1, nullopt}));
auto [dist_with_prev, prev] = ShortestPath::ZeroOneBFSWithPrev(g, 0);
assert(dist_with_prev == dist);
assert(ShortestPath::EnumeratePath(prev, 4) == vector<int>({0, 2, 3, 4}));
}
int main() {
test_bfs();
test_zero_one_bfs();
int a, b;
in(a, b);
out(a + b);
}
#line 1 "verify/graph/UNIT_shortest_path.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 2 "template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
#line 2 "template/macro.hpp"
#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())
#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";
#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";
#define yn(b) cout << ((b) ? "yes" : "no") << "\n";
#line 6 "template/template.hpp"
#line 2 "template/util.hpp"
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <class T>
using priority_queue_asc = priority_queue<T, vector<T>, greater<T>>;
template <class T, class S = T>
S SUM(const vector<T>& a) {
return accumulate(ALL(a), S(0));
}
template <class T1, class T2>
inline bool chmin(T1& a, T2 b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2>
inline bool chmax(T1& a, T2 b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2>
inline bool chmin_opt(optional<T1>& a, T2 b) {
if (!a || a > b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2>
inline bool chmax_opt(optional<T1>& a, T2 b) {
if (!a || a < b) {
a = b;
return true;
}
return false;
}
template <class T>
int popcnt(T x) {
return __builtin_popcountll(x);
}
template <class T>
int topbit(T x) {
return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <class T>
int lowbit(T x) {
return (x == 0 ? -1 : __builtin_ctzll(x));
}
#line 8 "template/template.hpp"
#line 2 "template/inout.hpp"
struct Fast {
Fast() {
cin.tie(nullptr);
ios_base::sync_with_stdio(false);
cout << fixed << setprecision(15);
}
} fast;
ostream& operator<<(ostream& os, __uint128_t x) {
char buf[40];
size_t k = 0;
while (x > 0) buf[k++] = (char)(x % 10 + '0'), x /= 10;
if (k == 0) buf[k++] = '0';
while (k) os << buf[--k];
return os;
}
ostream& operator<<(ostream& os, __int128_t x) {
return x < 0 ? (os << '-' << (__uint128_t)(-x)) : (os << (__uint128_t)x);
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a);
template <class T1, class T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
return is >> p.first >> p.second;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
return os << p.first << " " << p.second;
}
template <class T>
istream& operator>>(istream& is, vector<T>& a) {
for (auto& v : a) is >> v;
return is;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& a) {
for (auto it = a.begin(); it != a.end();) {
os << *it;
if (++it != a.end()) os << " ";
}
return os;
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a) {
for (auto it = a.begin(); it != a.end();) {
os << *it;
if (++it != a.end()) os << " ";
}
return os;
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& st) {
os << "{";
for (auto it = st.begin(); it != st.end();) {
os << *it;
if (++it != st.end()) os << ",";
}
os << "}";
return os;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2>& mp) {
os << "{";
for (auto it = mp.begin(); it != mp.end();) {
os << it->first << ":" << it->second;
if (++it != mp.end()) os << ",";
}
os << "}";
return os;
}
void in() {}
template <typename T, class... U>
void in(T& t, U&... u) {
cin >> t;
in(u...);
}
template <class... T>
void in_zip(int n, T&... t) {
assert(n >= 0 && ((size(t) >= static_cast<size_t>(n)) && ...));
for (int i = 0; i < n; i++) in(t[i]...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T& t, const U&... u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
template <class T, class U>
void out_opt(const optional<T>& opt, const U& fallback, ostream& os = cout) {
if (opt.has_value())
os << opt.value();
else
os << fallback;
os << "\n";
}
template <class T, class U>
void out_opt(const vector<optional<T>>& vec, const U& fallback, ostream& os = cout) {
for (auto it = vec.begin(); it != vec.end();) {
if ((*it).has_value())
os << (*it).value();
else
os << fallback;
if (++it != vec.end()) os << " ";
}
os << "\n";
}
namespace IO {
template <class T, class... U>
T read(U&&... u) {
T t = T(forward<U>(u)...);
in(t);
return t;
}
namespace Graph {
vector<vector<int>> unweighted(int n, int m, bool directed = false, int offset = 1) {
vector<vector<int>> g(n);
for (int i = 0; i < m; i++) {
int u, v;
cin >> u >> v;
u -= offset, v -= offset;
g[u].push_back(v);
if (!directed) g[v].push_back(u);
}
return g;
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, int m, bool directed = false, int offset = 1) {
vector<vector<pair<int, T>>> g(n);
for (int i = 0; i < m; i++) {
int u, v;
T w;
cin >> u >> v >> w;
u -= offset, v -= offset;
g[u].push_back({v, w});
if (!directed) g[v].push_back({u, w});
}
return g;
}
} // namespace Graph
namespace Tree {
vector<vector<int>> unweighted(int n, bool directed = false, int offset = 1) {
return Graph::unweighted(n, n - 1, directed, offset);
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, bool directed = false, int offset = 1) {
return Graph::weighted<T>(n, n - 1, directed, offset);
}
vector<vector<int>> rooted(int n, bool to_root = true, bool to_leaf = true, int offset = 1) {
vector<vector<int>> g(n);
for (int i = 1; i < n; i++) {
int p;
cin >> p;
p -= offset;
if (to_root) g[i].push_back(p);
if (to_leaf) g[p].push_back(i);
}
return g;
}
} // namespace Tree
} // namespace IO
#line 10 "template/template.hpp"
#line 2 "template/debug.hpp"
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <class T>
void _show(int, T) {
cerr << '\n';
}
template <class T1, class T2, class... T3>
void _show(int i, const T1& a, const T2& b, const T3&... c) {
for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i];
cerr << ":" << b << " ";
_show(i + 1, a, c...);
}
#line 2 "graph/graph.hpp"
#line 4 "graph/graph.hpp"
template <class E>
struct GraphBase {
public:
GraphBase() : GraphBase(0) {}
GraphBase(int size) : n(size) {
assert(size >= 0);
g.resize(size);
}
size_t size() const { return n; }
const vector<E>& operator[](int x) const {
assert(0 <= x && x < n);
return g[x];
}
vector<E>& operator[](int x) {
assert(0 <= x && x < n);
return g[x];
}
protected:
int n;
vector<vector<E>> g;
};
struct EdgeUnweighted {
int to;
};
struct GraphUnweighted : GraphBase<EdgeUnweighted> {
using base = GraphBase<EdgeUnweighted>;
public:
GraphUnweighted() : base(0) {}
GraphUnweighted(int size) : base(size) {}
GraphUnweighted(const vector<vector<int>>& graph) : base(graph.size()) {
for (int x = 0; x < n; x++) {
base::g[x].reserve(graph[x].size());
for (int y : graph[x]) base::g[x].push_back({y});
}
}
void add_edge(int x, int y) {
(*this)[x].push_back({y});
(*this)[y].push_back({x});
}
void add_edge_directed(int from, int to) { (*this)[from].push_back({to}); }
};
template <class T>
struct EdgeWeighted {
int to;
T weight;
};
template <class T>
struct GraphWeighted : GraphBase<EdgeWeighted<T>> {
using base = GraphBase<EdgeWeighted<T>>;
public:
GraphWeighted() : base(0) {}
GraphWeighted(int size) : base(size) {}
GraphWeighted(const vector<vector<pair<int, T>>>& graph) : base(graph.size()) {
for (int x = 0; x < base::n; x++) {
base::g[x].reserve(graph[x].size());
for (const auto& [y, w] : graph[x]) base::g[x].push_back({y, w});
}
}
void add_edge(int x, int y, T w) {
(*this)[x].push_back({y, w});
(*this)[y].push_back({x, w});
}
void add_edge_directed(int from, int to, T w) { (*this)[from].push_back({to, w}); }
};
inline GraphWeighted<int> GraphUnweightedToWeighted(const GraphUnweighted& g) {
GraphWeighted<int> h(g.size());
for (int x = 0; x < static_cast<int>(g.size()); x++) {
h[x].reserve(g[x].size());
for (const auto& e : g[x]) h[x].push_back({e.to, 1});
}
return h;
}
/**
* @brief Graph
* @docs docs/graph/graph.md
*/
#line 2 "graph/shortest-path.hpp"
namespace ShortestPath {
namespace Internal {
template <class G, class F>
vector<optional<int>> bfs(const G& g, int root, F on_relax) {
assert(0 <= root && root < static_cast<int>(g.size()));
vector<optional<int>> dist(g.size(), nullopt);
dist[root] = 0;
queue<int> qu;
qu.push(root);
while (!qu.empty()) {
int x = qu.front();
qu.pop();
for (const auto& e : g[x]) {
int y = e.to;
if (chmin_opt(dist[y], *dist[x] + 1)) {
on_relax(x, y);
qu.push(y);
}
}
}
return dist;
}
template <class T, class G, class F>
vector<optional<T>> zero_one_bfs(const G& g, int root, F on_relax) {
assert(0 <= root && root < static_cast<int>(g.size()));
const T zero = T(0), one = T(1);
vector<optional<T>> dist(g.size(), nullopt);
dist[root] = zero;
deque<int> deq;
deq.push_back(root);
while (!deq.empty()) {
int x = deq.front();
deq.pop_front();
for (const auto& e : g[x]) {
int y = e.to;
const T& w = e.weight;
if (w == zero) {
if (chmin_opt(dist[y], *dist[x])) {
on_relax(x, y);
deq.push_front(y);
}
} else if (w == one) {
if (chmin_opt(dist[y], *dist[x] + one)) {
on_relax(x, y);
deq.push_back(y);
}
} else {
assert(false);
}
}
}
return dist;
}
template <class T, class G, class F>
vector<optional<T>> dijkstra(const G& g, const T zero, int root, F on_relax) {
assert(0 <= root && root < static_cast<int>(g.size()));
vector<optional<T>> dist(g.size(), nullopt);
dist[root] = zero;
priority_queue_asc<pair<T, int>> pq;
pq.push({zero, root});
while (!pq.empty()) {
auto [dx, x] = pq.top();
pq.pop();
if (!dist[x] || dx != *dist[x]) continue;
for (const auto& e : g[x]) {
int y = e.to;
T nd = dx + e.weight;
if (chmin_opt(dist[y], nd)) {
on_relax(x, y);
pq.push({nd, y});
}
}
}
return dist;
}
} // namespace Internal
template <class G>
vector<optional<int>> BFS(const G& g, int root) {
return Internal::bfs(g, root, [](int, int) {});
}
template <class G>
pair<vector<optional<int>>, vector<optional<int>>> BFSWithPrev(const G& g, int root) {
vector<optional<int>> prev(g.size(), nullopt);
auto dist = Internal::bfs(g, root, [&](int x, int y) { prev[y] = x; });
return {dist, prev};
}
template <class T = int, class G>
vector<optional<T>> ZeroOneBFS(const G& g, int root) {
return Internal::zero_one_bfs<T>(g, root, [](int, int) {});
}
template <class T = int, class G>
pair<vector<optional<T>>, vector<optional<int>>> ZeroOneBFSWithPrev(const G& g, int root) {
vector<optional<int>> prev(g.size(), nullopt);
auto dist = Internal::zero_one_bfs<T>(g, root, [&](int x, int y) { prev[y] = x; });
return {dist, prev};
}
template <class T, class G>
vector<optional<T>> Dijkstra(const G& g, const T zero, int root) {
return Internal::dijkstra<T>(g, zero, root, [](int, int) {});
}
template <class T, class G>
pair<vector<optional<T>>, vector<optional<int>>> DijkstraWithPrev(const G& g, const T zero, int root) {
vector<optional<int>> prev(g.size(), nullopt);
auto dist = Internal::dijkstra<T>(g, zero, root, [&](int x, int y) { prev[y] = x; });
return {dist, prev};
}
vector<int> EnumeratePath(const vector<optional<int>>& prev, int goal) {
assert(0 <= goal && goal < static_cast<int>(prev.size()));
vector<int> path{goal};
for (int x = goal;;) {
if (!prev[x]) break;
x = *prev[x];
path.push_back(x);
}
reverse(path.begin(), path.end());
return path;
}
} // namespace ShortestPath
/**
* @brief Shortest Path
* @docs docs/graph/shortest-path.md
*/
#line 6 "verify/graph/UNIT_shortest_path.test.cpp"
void test_bfs() {
GraphUnweighted g(6);
g.add_edge_directed(0, 1);
g.add_edge_directed(0, 2);
g.add_edge_directed(1, 3);
g.add_edge_directed(2, 3);
g.add_edge_directed(3, 4);
auto dist = ShortestPath::BFS(g, 0);
assert(dist == vector<optional<int>>({0, 1, 1, 2, 3, nullopt}));
auto [dist_with_prev, prev] = ShortestPath::BFSWithPrev(g, 0);
assert(dist_with_prev == dist);
auto path = ShortestPath::EnumeratePath(prev, 4);
assert(path.front() == 0 && path.back() == 4 && path.size() == 4);
assert(ShortestPath::EnumeratePath(prev, 0) == vector<int>({0}));
}
void test_zero_one_bfs() {
GraphWeighted<int> g(6);
g.add_edge_directed(0, 1, 1);
g.add_edge_directed(0, 2, 0);
g.add_edge_directed(2, 1, 0);
g.add_edge_directed(1, 3, 1);
g.add_edge_directed(2, 3, 1);
g.add_edge_directed(3, 4, 0);
auto dist = ShortestPath::ZeroOneBFS(g, 0);
assert(dist == vector<optional<int>>({0, 0, 0, 1, 1, nullopt}));
auto [dist_with_prev, prev] = ShortestPath::ZeroOneBFSWithPrev(g, 0);
assert(dist_with_prev == dist);
assert(ShortestPath::EnumeratePath(prev, 4) == vector<int>({0, 2, 3, 4}));
}
int main() {
test_bfs();
test_zero_one_bfs();
int a, b;
in(a, b);
out(a + b);
}
verify/graph/UNIT_shortest_path.test.cpp
Graph
(graph/graph.hpp)