Add 0-1-bfs. (#3285)

* Add 0-1-bfs.

* fixup! Add 0-1-bfs.

* fixup! Add 0-1-bfs.

* Check edge weights.

* Check edge vertecies.

graphs/bfs_zero_one_shortest_path.py

+from collections import deque
+from dataclasses import dataclass
+from typing import Iterator, List
+
+"""
+Finding the shortest path in 0-1-graph in O(E + V) which is faster than dijkstra.
+0-1-graph is the weighted graph with the weights equal to 0 or 1.
+Link: https://codeforces.com/blog/entry/22276
+"""
+
+
+@dataclass
+class Edge:
+    """Weighted directed graph edge."""
+
+    destination_vertex: int
+    weight: int
+
+
+class AdjacencyList:
+    """Graph adjacency list."""
+
+    def __init__(self, size: int):
+        self._graph: List[List[Edge]] = [[] for _ in range(size)]
+        self._size = size
+
+    def __getitem__(self, vertex: int) -> Iterator[Edge]:
+        """Get all the vertices adjacent to the given one."""
+        return iter(self._graph[vertex])
+
+    @property
+    def size(self):
+        return self._size
+
+    def add_edge(self, from_vertex: int, to_vertex: int, weight: int):
+        """
+        >>> g = AdjacencyList(2)
+        >>> g.add_edge(0, 1, 0)
+        >>> g.add_edge(1, 0, 1)
+        >>> list(g[0])
+        [Edge(destination_vertex=1, weight=0)]
+        >>> list(g[1])
+        [Edge(destination_vertex=0, weight=1)]
+        >>> g.add_edge(0, 1, 2)
+        Traceback (most recent call last):
+            ...
+        ValueError: Edge weight must be either 0 or 1.
+        >>> g.add_edge(0, 2, 1)
+        Traceback (most recent call last):
+            ...
+        ValueError: Vertex indexes must be in [0; size).
+        """
+        if weight not in (0, 1):
+            raise ValueError("Edge weight must be either 0 or 1.")
+
+        if to_vertex < 0 or to_vertex >= self.size:
+            raise ValueError("Vertex indexes must be in [0; size).")
+
+        self._graph[from_vertex].append(Edge(to_vertex, weight))
+
+    def get_shortest_path(self, start_vertex: int, finish_vertex: int) -> int:
+        """
+        Return the shortest distance from start_vertex to finish_vertex in 0-1-graph.
+              1                  1         1
+         0--------->3        6--------7>------->8
+         |          ^        ^        ^         |1
+         |          |        |        |0        v
+        0|          |0      1|        9-------->10
+         |          |        |        ^    1
+         v          |        |        |0
+         1--------->2<-------4------->5
+              0         1        1
+        >>> g = AdjacencyList(11)
+        >>> g.add_edge(0, 1, 0)
+        >>> g.add_edge(0, 3, 1)
+        >>> g.add_edge(1, 2, 0)
+        >>> g.add_edge(2, 3, 0)
+        >>> g.add_edge(4, 2, 1)
+        >>> g.add_edge(4, 5, 1)
+        >>> g.add_edge(4, 6, 1)
+        >>> g.add_edge(5, 9, 0)
+        >>> g.add_edge(6, 7, 1)
+        >>> g.add_edge(7, 8, 1)
+        >>> g.add_edge(8, 10, 1)
+        >>> g.add_edge(9, 7, 0)
+        >>> g.add_edge(9, 10, 1)
+        >>> g.add_edge(1, 2, 2)
+        Traceback (most recent call last):
+            ...
+        ValueError: Edge weight must be either 0 or 1.
+        >>> g.get_shortest_path(0, 3)
+        0
+        >>> g.get_shortest_path(0, 4)
+        Traceback (most recent call last):
+            ...
+        ValueError: No path from start_vertex to finish_vertex.
+        >>> g.get_shortest_path(4, 10)
+        2
+        >>> g.get_shortest_path(4, 8)
+        2
+        >>> g.get_shortest_path(0, 1)
+        0
+        >>> g.get_shortest_path(1, 0)
+        Traceback (most recent call last):
+            ...
+        ValueError: No path from start_vertex to finish_vertex.
+        """
+        queue = deque([start_vertex])
+        distances = [None for i in range(self.size)]
+        distances[start_vertex] = 0
+
+        while queue:
+            current_vertex = queue.popleft()
+            current_distance = distances[current_vertex]
+
+            for edge in self[current_vertex]:
+                new_distance = current_distance + edge.weight
+                if (
+                    distances[edge.destination_vertex] is not None
+                    and new_distance >= distances[edge.destination_vertex]
+                ):
+                    continue
+                distances[edge.destination_vertex] = new_distance
+                if edge.weight == 0:
+                    queue.appendleft(edge.destination_vertex)
+                else:
+                    queue.append(edge.destination_vertex)
+
+        if distances[finish_vertex] is None:
+            raise ValueError("No path from start_vertex to finish_vertex.")
+
+        return distances[finish_vertex]
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()