bfs
(src/graph/bfs.hpp)

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• Last update: 2024-11-09 01:34:39+09:00
• Include: #include "src/graph/bfs.hpp"

bfs

vector<pair<int, int>> bfs(Graph<int> g, int s = 0)

$n$ 頂点の重みなしグラフ g 上で頂点 s を始点とした最短経路探索を行います．

返り値は長さ $n$ の pair 型の配列です．
pair 型の第一要素は頂点 s から頂点 i までの最短距離を，第二要素は頂点 i にたどり着く直前にいた頂点番号を保持しています．

もし頂点 i に到達できない場合， pair 型の第一要素は numeric_limits<int>::max() で，第二要素は $-1$ です．

制約

• $0 \leq s < n$
• 辺の重みが $1$ である ( assert 等で検知されません)．

計算量

• $O(E + V)$

Depends on

• Graph (src/graph/graph_template.hpp)
• template (src/template/template.hpp)

Verified with

• verify/unit_test/graph/bfs.test.cpp

Code

#pragma once
#include "../template/template.hpp"
#include "./graph_template.hpp"
vector<pair<int, int>> bfs(const Graph<int>& g, const int s = 0) {
    const int n = g.size();
    assert(0 <= s and s < n);
    vector<pair<int, int>> d(n, {numeric_limits<int>::max(), -1});
    queue<int> q;
    d[s] = {0, -1};
    q.emplace(s);
    while(!q.empty()) {
        const int cur = q.front();
        q.pop();
        for(const Edge<int>& e : g[cur]) {
            if(d[e.to].first == numeric_limits<int>::max()) {
                d[e.to] = {d[cur].first + 1, cur};
                q.emplace(e.to);
            }
        }
    }
    return d;
}

#line 2 "src/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
    SetupIO() {
        ios::sync_with_stdio(0);
        cin.tie(0);
        cout << fixed << setprecision(30);
    }
} setup_io;
#line 3 "src/graph/graph_template.hpp"
template <typename T>
struct Edge {
    int from, to;
    T cost;
    int idx;
    Edge()
        : from(-1), to(-1), cost(-1), idx(-1) {}
    Edge(const int from, const int to, const T& cost = 1, const int idx = -1)
        : from(from), to(to), cost(cost), idx(idx) {}
    operator int() const {
        return to;
    }
};
template <typename T>
struct Graph {
    Graph(const int N)
        : n(N), es(0), g(N) {}
    int size() const {
        return n;
    }
    int edge_size() const {
        return es;
    }
    void add_edge(const int from, const int to, const T& cost = 1) {
        assert(0 <= from and from < n);
        assert(0 <= to and to < n);
        g[from].emplace_back(from, to, cost, es);
        g[to].emplace_back(to, from, cost, es++);
    }
    void add_directed_edge(const int from, const int to, const T& cost = 1) {
        assert(0 <= from and from < n);
        assert(0 <= to and to < n);
        g[from].emplace_back(from, to, cost, es++);
    }
    inline vector<Edge<T>>& operator[](const int& k) {
        assert(0 <= k and k < n);
        return g[k];
    }
    inline const vector<Edge<T>>& operator[](const int& k) const {
        assert(0 <= k and k < n);
        return g[k];
    }

   private:
    int n, es;
    vector<vector<Edge<T>>> g;
};
template <typename T>
using Edges = vector<Edge<T>>;
#line 4 "src/graph/bfs.hpp"
vector<pair<int, int>> bfs(const Graph<int>& g, const int s = 0) {
    const int n = g.size();
    assert(0 <= s and s < n);
    vector<pair<int, int>> d(n, {numeric_limits<int>::max(), -1});
    queue<int> q;
    d[s] = {0, -1};
    q.emplace(s);
    while(!q.empty()) {
        const int cur = q.front();
        q.pop();
        for(const Edge<int>& e : g[cur]) {
            if(d[e.to].first == numeric_limits<int>::max()) {
                d[e.to] = {d[cur].first + 1, cur};
                q.emplace(e.to);
            }
        }
    }
    return d;
}

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