0-1 BFS
(graph/zero_one_bfs.hpp)

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• Last update: 2026-08-13 01:41:40+09:00
• Include: #include "graph/zero_one_bfs.hpp"

Overview

0-1 BFS computes shortest paths when every edge cost is either 0 or 1. It uses a deque instead of a priority queue: relaxing a 0-cost edge pushes the next vertex to the front, and relaxing a 1-cost edge pushes it to the back.

Use it instead of Dijkstra when all costs are 0 or 1. It gives the same shortest distances for this special case in linear time.

Graph Orientation

Direction is respected. zero_one_bfs works on directed graphs as written, and also on undirected graphs built with add_edge.

Every edge cost must be exactly 0 or 1.

How to Use It

Call zero_one_bfs(g, s) for one source, or zero_one_bfs(g, sources) for multiple sources. Multi-source mode sets every source distance to 0.

The result contains these members:

Member	Type / Signature	Meaning
dist	std::vector<int>	dist[v] is the minimum total cost from the nearest source to v, or inf if unreachable.
parent	std::vector<int>	parent[v] is the previous vertex on one shortest path, or -1.
parent_edge	std::vector<int>	parent_edge[v] is the edge id used to enter v, or -1.
inf	int	The unreachable-distance sentinel used by this run.
reachable	bool reachable(int v) const	Returns whether v was reached.
path	std::vector<int> path(int t) const	Restores one shortest path from a source to t. Requires reachable(t).

Functions

Function	Signature	Description	Complexity
zero_one_bfs	template <class T> ZeroOneBfsResult zero_one_bfs(const Graph<T>& g, int s, int inf = std::numeric_limits<int>::max() / 2)	Runs 0-1 BFS from one source.	$O(N + M)$
zero_one_bfs	template <class T> ZeroOneBfsResult zero_one_bfs(const Graph<T>& g, const std::vector<int>& sources, int inf = std::numeric_limits<int>::max() / 2)	Runs multi-source 0-1 BFS.	$O(N + M)$

Example

#include "graph/graph.hpp"
#include "graph/zero_one_bfs.hpp"
#include <iostream>

int main() {
    m1une::graph::Graph<int> g(4);
    g.add_directed_edge(0, 1, 1);
    g.add_directed_edge(0, 2, 0);
    g.add_directed_edge(2, 1, 0);
    g.add_directed_edge(1, 3, 1);

    auto res = m1une::graph::zero_one_bfs(g, 0);
    std::cout << res.dist[3] << "\n";  // 1
}

Depends on

• Graph (graph/graph.hpp)

Required by

• Graph All (graph/all.hpp)
• Directed Graph Algorithms (graph/directed.hpp)
• Shortest Path (graph/shortest_path.hpp)
• Undirected Graph Algorithms (graph/undirected.hpp)

Verified with

• verify/graph/cow_game.test.cpp
• verify/graph/graph_algorithms.test.cpp
• verify/graph/range_edge_graph.test.cpp

Code

#ifndef M1UNE_GRAPH_ZERO_ONE_BFS_HPP
#define M1UNE_GRAPH_ZERO_ONE_BFS_HPP 1

#include <algorithm>
#include <cassert>
#include <deque>
#include <limits>
#include <vector>

#include "graph.hpp"

namespace m1une {
namespace graph {

struct ZeroOneBfsResult {
    std::vector<int> dist;
    std::vector<int> parent;
    std::vector<int> parent_edge;
    int inf;

    bool reachable(int v) const {
        assert(0 <= v && v < int(dist.size()));
        return dist[v] != inf;
    }

    std::vector<int> path(int t) const {
        assert(reachable(t));
        std::vector<int> result;
        for (int v = t; v != -1; v = parent[v]) result.push_back(v);
        std::reverse(result.begin(), result.end());
        return result;
    }
};

template <class T>
ZeroOneBfsResult zero_one_bfs(const Graph<T>& g, const std::vector<int>& sources,
                              int inf = std::numeric_limits<int>::max() / 2) {
    int n = g.size();
    ZeroOneBfsResult result;
    result.dist.assign(n, inf);
    result.parent.assign(n, -1);
    result.parent_edge.assign(n, -1);
    result.inf = inf;

    std::deque<int> deq;
    for (int s : sources) {
        assert(0 <= s && s < n);
        if (result.dist[s] == 0) continue;
        result.dist[s] = 0;
        deq.push_back(s);
    }

    while (!deq.empty()) {
        int v = deq.front();
        deq.pop_front();
        for (const auto& e : g[v]) {
            if (!e.alive) continue;
            int w;
            if (e.cost == T(0)) {
                w = 0;
            } else {
                assert(e.cost == T(1));
                w = 1;
            }
            int nd = result.dist[v] + w;
            if (result.dist[e.to] <= nd) continue;
            result.dist[e.to] = nd;
            result.parent[e.to] = v;
            result.parent_edge[e.to] = e.id;
            if (w == 0) {
                deq.push_front(e.to);
            } else {
                deq.push_back(e.to);
            }
        }
    }

    return result;
}

template <class T>
ZeroOneBfsResult zero_one_bfs(const Graph<T>& g, int s, int inf = std::numeric_limits<int>::max() / 2) {
    return zero_one_bfs(g, std::vector<int>{s}, inf);
}

}  // namespace graph
}  // namespace m1une

#endif  // M1UNE_GRAPH_ZERO_ONE_BFS_HPP

#line 1 "graph/zero_one_bfs.hpp"



#include <algorithm>
#include <cassert>
#include <deque>
#include <limits>
#include <vector>

#line 1 "graph/graph.hpp"



#include <array>
#line 6 "graph/graph.hpp"
#include <utility>
#line 8 "graph/graph.hpp"

namespace m1une {
namespace graph {

template <class T = int>
struct Edge {
    using cost_type = T;

    int from;
    int to;
    T cost;
    int id;
    bool alive;

    Edge() : from(-1), to(-1), cost(T()), id(-1), alive(true) {}
    Edge(int from_, int to_, T cost_ = T(1), int id_ = -1, bool alive_ = true)
        : from(from_), to(to_), cost(cost_), id(id_), alive(alive_) {}

    int other(int v) const {
        assert(v == from || v == to);
        return from ^ to ^ v;
    }
};

template <class T = int>
struct Graph {
    using edge_type = Edge<T>;
    using cost_type = T;

   private:
    struct EdgePositions {
        std::array<std::pair<int, int>, 2> value{};
        int size = 0;

        void push_back(std::pair<int, int> position) {
            assert(size < 2);
            value[size++] = position;
        }
    };

    int _n;
    int _edge_count;
    std::vector<std::vector<edge_type>> _g;
    std::vector<EdgePositions> _edge_positions;

   public:
    Graph() : _n(0), _edge_count(0) {}
    explicit Graph(int n) : _n(n), _edge_count(0), _g(n) {
        assert(0 <= n);
    }

    int size() const {
        return _n;
    }

    bool empty() const {
        return _n == 0;
    }

    int edge_count() const {
        return _edge_count;
    }

    int add_vertex() {
        _g.emplace_back();
        return _n++;
    }

    int add_directed_edge(int from, int to, T cost = T(1)) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        int id = _edge_count++;
        int idx = int(_g[from].size());
        _g[from].push_back(edge_type(from, to, cost, id));
        _edge_positions.emplace_back();
        _edge_positions.back().push_back({from, idx});
        return id;
    }

    int add_edge(int u, int v, T cost = T(1)) {
        assert(0 <= u && u < _n);
        assert(0 <= v && v < _n);
        int id = _edge_count++;
        int u_idx = int(_g[u].size());
        _g[u].push_back(edge_type(u, v, cost, id));
        int v_idx = int(_g[v].size());
        _g[v].push_back(edge_type(v, u, cost, id));
        _edge_positions.emplace_back();
        _edge_positions.back().push_back({u, u_idx});
        _edge_positions.back().push_back({v, v_idx});
        return id;
    }

    void set_edge_alive(int id, bool alive) {
        assert(0 <= id && id < _edge_count);
        for (int i = 0; i < _edge_positions[id].size; ++i) {
            auto [v, idx] = _edge_positions[id].value[i];
            _g[v][idx].alive = alive;
        }
    }

    void erase_edge(int id) {
        set_edge_alive(id, false);
    }

    void revive_edge(int id) {
        set_edge_alive(id, true);
    }

    bool is_edge_alive(int id) const {
        assert(0 <= id && id < _edge_count);
        assert(_edge_positions[id].size != 0);
        auto [v, idx] = _edge_positions[id].value[0];
        return _g[v][idx].alive;
    }

    const std::vector<edge_type>& operator[](int v) const {
        assert(0 <= v && v < _n);
        return _g[v];
    }

    std::vector<edge_type>& operator[](int v) {
        assert(0 <= v && v < _n);
        return _g[v];
    }

    const std::vector<std::vector<edge_type>>& adjacency() const {
        return _g;
    }

    std::vector<std::vector<edge_type>>& adjacency() {
        return _g;
    }

    std::vector<edge_type> edges(bool include_inactive = false) const {
        std::vector<edge_type> result;
        result.reserve(_edge_count);
        std::vector<char> used(_edge_count, false);
        for (int v = 0; v < _n; v++) {
            for (const auto& e : _g[v]) {
                if (!include_inactive && !e.alive) continue;
                if (0 <= e.id && e.id < _edge_count) {
                    if (used[e.id]) continue;
                    used[e.id] = true;
                }
                result.push_back(e);
            }
        }
        return result;
    }

    Graph reversed() const {
        Graph result(_n);
        result._edge_count = _edge_count;
        result._edge_positions.assign(_edge_count, {});
        for (int v = 0; v < _n; v++) {
            for (const auto& e : _g[v]) {
                int idx = int(result._g[e.to].size());
                result._g[e.to].push_back(edge_type(e.to, e.from, e.cost, e.id, e.alive));
                if (0 <= e.id && e.id < _edge_count) result._edge_positions[e.id].push_back({e.to, idx});
            }
        }
        return result;
    }
};

}  // namespace graph
}  // namespace m1une


#line 11 "graph/zero_one_bfs.hpp"

namespace m1une {
namespace graph {

struct ZeroOneBfsResult {
    std::vector<int> dist;
    std::vector<int> parent;
    std::vector<int> parent_edge;
    int inf;

    bool reachable(int v) const {
        assert(0 <= v && v < int(dist.size()));
        return dist[v] != inf;
    }

    std::vector<int> path(int t) const {
        assert(reachable(t));
        std::vector<int> result;
        for (int v = t; v != -1; v = parent[v]) result.push_back(v);
        std::reverse(result.begin(), result.end());
        return result;
    }
};

template <class T>
ZeroOneBfsResult zero_one_bfs(const Graph<T>& g, const std::vector<int>& sources,
                              int inf = std::numeric_limits<int>::max() / 2) {
    int n = g.size();
    ZeroOneBfsResult result;
    result.dist.assign(n, inf);
    result.parent.assign(n, -1);
    result.parent_edge.assign(n, -1);
    result.inf = inf;

    std::deque<int> deq;
    for (int s : sources) {
        assert(0 <= s && s < n);
        if (result.dist[s] == 0) continue;
        result.dist[s] = 0;
        deq.push_back(s);
    }

    while (!deq.empty()) {
        int v = deq.front();
        deq.pop_front();
        for (const auto& e : g[v]) {
            if (!e.alive) continue;
            int w;
            if (e.cost == T(0)) {
                w = 0;
            } else {
                assert(e.cost == T(1));
                w = 1;
            }
            int nd = result.dist[v] + w;
            if (result.dist[e.to] <= nd) continue;
            result.dist[e.to] = nd;
            result.parent[e.to] = v;
            result.parent_edge[e.to] = e.id;
            if (w == 0) {
                deq.push_front(e.to);
            } else {
                deq.push_back(e.to);
            }
        }
    }

    return result;
}

template <class T>
ZeroOneBfsResult zero_one_bfs(const Graph<T>& g, int s, int inf = std::numeric_limits<int>::max() / 2) {
    return zero_one_bfs(g, std::vector<int>{s}, inf);
}

}  // namespace graph
}  // namespace m1une

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