133 lines
3.3 KiB
Python
133 lines
3.3 KiB
Python
"""
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Dominance algorithms.
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"""
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from functools import reduce
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import networkx as nx
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from networkx.utils import not_implemented_for
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__all__ = ["immediate_dominators", "dominance_frontiers"]
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@not_implemented_for("undirected")
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def immediate_dominators(G, start):
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"""Returns the immediate dominators of all nodes of a directed graph.
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Parameters
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----------
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G : a DiGraph or MultiDiGraph
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The graph where dominance is to be computed.
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start : node
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The start node of dominance computation.
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Returns
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-------
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idom : dict keyed by nodes
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A dict containing the immediate dominators of each node reachable from
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`start`.
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Raises
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------
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NetworkXNotImplemented
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If `G` is undirected.
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NetworkXError
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If `start` is not in `G`.
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Notes
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-----
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Except for `start`, the immediate dominators are the parents of their
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corresponding nodes in the dominator tree.
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Examples
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--------
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>>> G = nx.DiGraph([(1, 2), (1, 3), (2, 5), (3, 4), (4, 5)])
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>>> sorted(nx.immediate_dominators(G, 1).items())
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[(1, 1), (2, 1), (3, 1), (4, 3), (5, 1)]
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References
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----------
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.. [1] K. D. Cooper, T. J. Harvey, and K. Kennedy.
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A simple, fast dominance algorithm.
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Software Practice & Experience, 4:110, 2001.
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"""
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if start not in G:
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raise nx.NetworkXError("start is not in G")
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idom = {start: start}
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order = list(nx.dfs_postorder_nodes(G, start))
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dfn = {u: i for i, u in enumerate(order)}
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order.pop()
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order.reverse()
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def intersect(u, v):
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while u != v:
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while dfn[u] < dfn[v]:
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u = idom[u]
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while dfn[u] > dfn[v]:
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v = idom[v]
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return u
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changed = True
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while changed:
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changed = False
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for u in order:
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new_idom = reduce(intersect, (v for v in G.pred[u] if v in idom))
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if u not in idom or idom[u] != new_idom:
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idom[u] = new_idom
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changed = True
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return idom
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def dominance_frontiers(G, start):
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"""Returns the dominance frontiers of all nodes of a directed graph.
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Parameters
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----------
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G : a DiGraph or MultiDiGraph
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The graph where dominance is to be computed.
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start : node
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The start node of dominance computation.
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Returns
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-------
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df : dict keyed by nodes
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A dict containing the dominance frontiers of each node reachable from
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`start` as lists.
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Raises
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------
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NetworkXNotImplemented
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If `G` is undirected.
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NetworkXError
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If `start` is not in `G`.
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Examples
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--------
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>>> G = nx.DiGraph([(1, 2), (1, 3), (2, 5), (3, 4), (4, 5)])
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>>> sorted((u, sorted(df)) for u, df in nx.dominance_frontiers(G, 1).items())
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[(1, []), (2, [5]), (3, [5]), (4, [5]), (5, [])]
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References
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----------
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.. [1] K. D. Cooper, T. J. Harvey, and K. Kennedy.
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A simple, fast dominance algorithm.
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Software Practice & Experience, 4:110, 2001.
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"""
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idom = nx.immediate_dominators(G, start)
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df = {u: set() for u in idom}
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for u in idom:
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if len(G.pred[u]) >= 2:
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for v in G.pred[u]:
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if v in idom:
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while v != idom[u]:
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df[v].add(u)
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v = idom[v]
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return df
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