Move files to various folders (#4286)

* Move files to cellular_automata

* Rename other/davis–putnam–logemann–loveland.py to backtracking/davis–putnam–logemann–loveland.py

* Rename other/markov_chain.py to graphs/markov_chain.py

* undid rename: need to fix mypy first

graphs/markov_chain.py

@@ -0,0 +1,83 @@
+from __future__ import annotations
+
+from collections import Counter
+from random import random
+
+
+class MarkovChainGraphUndirectedUnweighted:
+    """
+    Undirected Unweighted Graph for running Markov Chain Algorithm
+    """
+
+    def __init__(self):
+        self.connections = {}
+
+    def add_node(self, node: str) -> None:
+        self.connections[node] = {}
+
+    def add_transition_probability(
+        self, node1: str, node2: str, probability: float
+    ) -> None:
+        if node1 not in self.connections:
+            self.add_node(node1)
+        if node2 not in self.connections:
+            self.add_node(node2)
+        self.connections[node1][node2] = probability
+
+    def get_nodes(self) -> list[str]:
+        return list(self.connections)
+
+    def transition(self, node: str) -> str:
+        current_probability = 0
+        random_value = random()
+
+        for dest in self.connections[node]:
+            current_probability += self.connections[node][dest]
+            if current_probability > random_value:
+                return dest
+
+
+def get_transitions(
+    start: str, transitions: list[tuple[str, str, float]], steps: int
+) -> dict[str, int]:
+    """
+    Running Markov Chain algorithm and calculating the number of times each node is
+    visited
+
+    >>> transitions = [
+    ... ('a', 'a', 0.9),
+    ... ('a', 'b', 0.075),
+    ... ('a', 'c', 0.025),
+    ... ('b', 'a', 0.15),
+    ... ('b', 'b', 0.8),
+    ... ('b', 'c', 0.05),
+    ... ('c', 'a', 0.25),
+    ... ('c', 'b', 0.25),
+    ... ('c', 'c', 0.5)
+    ... ]
+
+    >>> result = get_transitions('a', transitions, 5000)
+
+    >>> result['a'] > result['b'] > result['c']
+    True
+    """
+
+    graph = MarkovChainGraphUndirectedUnweighted()
+
+    for node1, node2, probability in transitions:
+        graph.add_transition_probability(node1, node2, probability)
+
+    visited = Counter(graph.get_nodes())
+    node = start
+
+    for _ in range(steps):
+        node = graph.transition(node)
+        visited[node] += 1
+
+    return visited
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()