177 lines
4.3 KiB
Python
177 lines
4.3 KiB
Python
import math
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class Node:
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__slots__ = ('key', 'dist', 'left', 'right', 'parent', 'child', 'degree', 'lost')
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def __init__(self, key, dist):
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self.key = key
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self.dist = dist
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self.left = self
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self.right = self
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self.parent = None
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self.child = None
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self.degree = 0
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self.lost = False
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def connect_right(self, new_right):
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old_right = self.right
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new_left = new_right.left
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new_right.left = self
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new_left.right = old_right
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old_right.left = new_left
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self.right = new_right
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def remove(self):
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self.left.right = self.right
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self.right.left = self.left
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self.left = self
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self.right = self
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def connect_child(self, child):
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child.parent = self
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child.lost = False
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if self.child is None:
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self.child = child
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else:
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self.child.connect_right(child)
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self.degree += 1
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class FiboHeap:
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def __init__(self, nodes):
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self.min = None
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self.n = 0
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self.pos = [None] * nodes
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def cut(self, cur):
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p = cur.parent
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if p.child is cur:
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if cur.right is cur:
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p.child = None
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else:
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p.child = cur.right
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cur.remove()
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p.degree -= 1
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cur.parent = None
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cur.lost = False
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self.min.connect_right(cur)
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if cur.dist < self.min.dist:
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self.min = cur
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def cascading_cut(self, cur):
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while True:
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p = cur.parent
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if p is None:
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return
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if not cur.lost:
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cur.lost = True
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return
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self.cut(cur)
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cur = p
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def add(self, key, dist):
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cur = Node(key, dist)
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if self.min is None:
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self.min = cur
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else:
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self.min.connect_right(cur)
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if cur.dist < self.min.dist:
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self.min = cur
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self.n += 1
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self.pos[key] = cur
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def extract_min(self):
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# 1. Find min node
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min_node = self.min
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self.n -= 1
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# 2. Make min node's child into individual tree
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c = min_node.child
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if c is not None:
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start = c
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cur = c
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while True:
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cur.parent = None
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cur.lost = False
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cur = cur.right
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if cur == start:
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break
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min_node.connect_right(start)
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if min_node.right is min_node:
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self.min = None
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return (min_node.key, min_node.dist)
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nxt = min_node.right
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min_node.remove()
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self.min = nxt
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min_node.child = None
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min_node.degree = 0
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self.pos[min_node.key] = None
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# 3. Make into binomial tree
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roots = []
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start = self.min
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cur = start
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while True:
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roots.append(cur)
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cur = cur.right
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if cur == start:
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break
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max_deg = int(math.log2(self.n)) + 2 if self.n > 0 else 1 # 여기서 +2 하는 이유는 사실은 log2가 아니라 fibonacci 수열 기반이기 때문에 +1 더 해주는 거임.
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A = [None] * (max_deg + 1)
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for cur in roots:
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x = cur
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d = x.degree
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while A[d] is not None:
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y = A[d]
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if y.dist < x.dist:
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x, y = y, x
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y.remove()
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x.connect_child(y)
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A[d] = None
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d = x.degree
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A[d] = x
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# 4. Find new min
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self.min = None
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for cur in A:
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if cur is None:
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continue
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if self.min is None:
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self.min = cur
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else:
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if cur.dist < self.min.dist:
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self.min = cur
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return (min_node.key, min_node.dist)
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def decrease_key(self, key, new_dist):
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cur = self.pos[key]
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if cur is None or new_dist >= cur.dist:
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return
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cur.dist = new_dist
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p = cur.parent
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if p is not None and cur.dist < p.dist:
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self.cut(cur)
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self.cascading_cut(p)
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if cur.dist < self.min.dist:
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self.min = cur |