62 lines
1.3 KiB
Python
62 lines
1.3 KiB
Python
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import random
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from heapq import heappush, heappop
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from collections import deque
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# A topological sort returns the vertices of a graph sorted in an ascending
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# order by the number of incoming edges each vertex has.
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#
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# A few algorithms for solving this exist, and at the time of this writing, I
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# know none. I'm going to focus on two:
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# 1. Kahn's
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# 2. DFS (TODO)
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def count_in_edges(graph):
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result = {k: 0 for k in graph.keys()}
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for xs in graph.values():
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for x in xs:
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result[x] += 1
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return result
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# Kahn's algorithm for returning a topological sorting of the vertices in
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# `graph`.
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def kahns_sort(graph):
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result = []
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q = deque()
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in_edges = count_in_edges(graph)
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for x in [k for k, v in in_edges.items() if v == 0]:
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q.append(x)
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while q:
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x = q.popleft()
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result.append(x)
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for c in graph[x]:
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in_edges[c] -= 1
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if in_edges[c] == 0:
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q.append(c)
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return result
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graphs = [
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{
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0: [],
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1: [],
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2: [3],
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3: [1],
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4: [0, 1],
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5: [0, 2],
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},
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{
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'A': ['C', 'D'],
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'B': ['D', 'E'],
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'C': [],
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'D': ['F', 'G'],
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'E': [],
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'F': [],
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'G': ['I'],
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'H': ['I'],
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'I': [],
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}
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]
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print("--- Kahn's --- ")
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for graph in graphs:
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print(kahns_sort(graph))
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