master > master: src-py tarjan alg

code/python/src/graphs/tarjan.py

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+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# IMPORTS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+from enum import Enum;
+
+from src.local.typing import *;
+
+from src.stacks.stack import *;
+from src.graphs.graph import *
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# EXPORTS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+__all__ = [
+    'tarjan_algorithm',
+];
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# CONSTANTS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+class State(Enum):
+    UNTOUCHED = 0;
+    PENDING = 1;
+    FINISHED = 2;
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# Tarjan Algorithm
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+class NodeInformation:
+    root: int;
+    index: int;
+    state: State;
+
+    def __init__(self):
+        self.root = self.index = 0;
+        self.state = State.UNTOUCHED;
+
+def tarjan_algorithm(G: Graph) -> List[Any]:
+    '''
+    runs the Tarjan-Algorithm to compute the strongly connected components
+    '''
+
+    # sonst Stack erstellen und Bearbeitungszustand der Knoten im Speicher notieren:
+    S = Stack();
+    index = 0;
+    infos = { u: NodeInformation() for u in G.nodes };
+    components = [];
+
+    def tarjan_visit(v: Any):
+        '''
+        recursive depth-first search algorithm to compute components
+        '''
+        nonlocal G, S, index, components;
+
+        if not(infos[v].state == State.UNTOUCHED):
+            return;
+
+        index += 1;
+        infos[v].index = infos[v].root = index;
+        S.push(v);
+
+        infos[v].state = State.PENDING;
+        # depth first search:
+        for u in G.successor(v):
+            tarjan_visit(u);
+            # remains relevant for v, provided u still in Stack:
+            if u in S:
+                infos[v].root = min(infos[v].root, infos[u].root);
+        infos[v].state = State.FINISHED;
+
+        # if at root of component pop everything from stack up to root and add component:
+        if infos[v].index == infos[v].root:
+            component = [];
+            condition_reached_root = False;
+            while not condition_reached_root:
+                u = S.pop();
+                component.append(u);
+                condition_reached_root = (u == v);
+            components.append(component);
+        return;
+
+    for v in G.nodes:
+        tarjan_visit(v);
+    return components;