Clean up explicit-stack recursion
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fc31657a56
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@ -1137,37 +1137,15 @@ class _MatchingContext:
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self.blossom[b] = None
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self.unused_blossoms.append(b)
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def expand_zero_dual_blossoms(self) -> None:
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"""Expand all blossoms with zero dual variable (recursively).
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def expand_blossom_rec(self, b: int, stack: list[int]) -> None:
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"""Expand blossom "b" and recursively expand any sub-blossoms that
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have dual variable zero.
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Note that this function runs at the end of a stage.
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Blossoms are not labeled. Least-slack edges are not tracked.
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This function takes time O(n).
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Use the stack object instead of making direct recursive calls.
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"""
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num_vertex = self.graph.num_vertex
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# TODO : clean up explicit stack
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# Find top-level blossoms with zero slack.
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stack: list[int] = []
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for b in range(num_vertex, 2 * num_vertex):
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blossom = self.blossom[b]
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if (blossom is not None) and (self.blossom_parent[b] == -1):
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# We typically expand only S-blossoms that were created after
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# the most recent delta step. Those blossoms have _exactly_
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# zero dual. So this comparison is reliable, even in case
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# of floating point edge weights.
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if blossom.dual_var == 0:
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stack.append(b)
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# Use an explicit stack to avoid deep recursion.
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while stack:
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b = stack.pop()
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# Expand blossom "b".
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blossom = self.blossom[b]
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assert blossom is not None
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assert self.blossom_parent[b] == -1
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@ -1197,29 +1175,54 @@ class _MatchingContext:
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self.blossom[b] = None
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self.unused_blossoms.append(b)
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def augment_blossom(self, b: int, sub: int) -> None:
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"""Augment along an alternating path through blossom "b",
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from sub-blossom "sub" to the base vertex of the blossom.
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def expand_zero_dual_blossoms(self) -> None:
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"""Expand all blossoms with zero dual variable (recursively).
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Note that this function runs at the end of a stage.
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Blossoms are not labeled. Least-slack edges are not tracked.
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This function takes time O(n).
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"""
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num_vertex = self.graph.num_vertex
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# TODO : cleanup explicit stack
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# Use an explicit stack to avoid deep recursion.
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stack = [(b, sub)]
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# The stack contains a list of blossoms to be expanded.
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stack: list[int] = []
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# Find top-level blossoms with zero slack.
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for b in range(num_vertex, 2 * num_vertex):
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blossom = self.blossom[b]
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if (blossom is not None) and (self.blossom_parent[b] == -1):
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# We typically expand only S-blossoms that were created after
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# the most recent delta step. Those blossoms have _exactly_
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# zero dual. So this comparison is reliable, even in case
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# of floating point edge weights.
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if blossom.dual_var == 0:
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stack.append(b)
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# Expand blossoms.
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while stack:
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(top_blossom, sub) = stack.pop()
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b = self.blossom_parent[sub]
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b = stack.pop()
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self.expand_blossom_rec(b, stack)
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if b != top_blossom:
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# Set up to continue augmenting through the parent of "b".
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stack.append((top_blossom, b))
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def augment_blossom_rec(
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self,
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b: int,
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sub: int,
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stack: list[tuple[int, int]]
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) -> None:
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"""Augment along an alternating path through blossom "b",
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from sub-blossom "sub" to the base vertex of the blossom.
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# Augment blossom "b" from subblossom "sub" to the base of the
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# blossom. Afterwards, "sub" contains the new base vertex.
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Modify the blossom to reflect that sub-blossom "sub" contains
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the base vertex after augmenting.
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Recursively augment any sub-blossoms on the alternating path,
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except for sub-blossom "sub" which has already been augmented.
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Use the stack object instead of making direct recursive calls.
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"""
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num_vertex = self.graph.num_vertex
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blossom = self.blossom[b]
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assert blossom is not None
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@ -1268,6 +1271,36 @@ class _MatchingContext:
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else:
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blossom.base_vertex = self.get_blossom(sub).base_vertex
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def augment_blossom(self, b: int, sub: int) -> None:
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"""Augment along an alternating path through blossom "b",
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from sub-blossom "sub" to the base vertex of the blossom.
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This function takes time O(n).
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"""
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# Use an explicit stack to avoid deep recursion.
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stack = [(b, sub)]
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while stack:
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(outer_blossom, sub) = stack.pop()
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b = self.blossom_parent[sub]
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if b != outer_blossom:
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# Sub-blossom "sub" is an indirect (nested) child of
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# the blossom we are supposed to be augmenting.
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#
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# Blossom "b" is the direct parent of "sub".
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# Let's first augment "b" from "sub" to its base vertex.
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# Then continue bay augmenting the parent of "b" from
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# "b" to its base vertex, and so on until we get to the
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# outer blossom.
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#
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# Set up to continue augmenting through the parent of "b".
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stack.append((outer_blossom, b))
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# Augment blossom "b" from "sub" to the base vertex of "b".
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self.augment_blossom_rec(b, sub, stack)
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def augment_matching(self, path: _AlternatingPath) -> None:
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"""Augment the matching through the specified augmenting path.
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@ -1440,7 +1473,7 @@ class _MatchingContext:
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# This loop runs through O(m) iterations per stage.
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for e in adjacent_edges[x]:
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(p, q, _w) = edges[e]
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y = p if p != x else q # TODO : consider abstracting this
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y = p if p != x else q
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# Consider the edge between vertices "x" and "y".
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# Try to pull this edge into an alternating tree.
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