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import math | |
class WinnerTree: | |
def __init__(self, ext): | |
self.ext = ext | |
self.N = len(ext) | |
self.k = math.ceil(math.log(self.N, 2)) | |
print(self.k, ", bottom layer node ", pow(2, self.k)) | |
def get_v(self, tree_id): | |
return self.ext[self.tree[tree_id]] | |
def build_tree(self): | |
# append bottom layer later | |
self.tree = [-1] * (pow(2, self.k) - 1) | |
self.bottom_start = len(self.tree) | |
# tree node stores id of ext | |
# so we append [0:N) | |
self.tree += range(0, self.N) | |
# print(self.tree) | |
for i in range(self.bottom_start - 1, -1, -1): | |
# print(i) | |
left = 2 * i + 1 | |
right = 2 * i + 2 | |
if left < len(self.tree): | |
self.tree[i] = self.tree[left] | |
if right < len(self.tree): | |
if self.get_v(right) < self.get_v(i): | |
self.tree[i] = self.tree[right] | |
# print(tree) | |
return self.tree | |
def rebuild_tree(self, new_id): | |
update_node = self.bottom_start + new_id | |
while update_node > 0: | |
parent = (update_node - 1) // 2 | |
bro = update_node + 1 if update_node % 2 == 1 else update_node - 1 | |
# update_node may be not the old winner | |
self.tree[parent] = self.tree[update_node] | |
if bro < len(self.tree) and self.get_v(update_node) >= self.get_v(bro): | |
self.tree[parent] = self.tree[bro] | |
update_node = parent | |
return self.tree | |
ext = [5, 3, 2, 4, 7] | |
wt = WinnerTree(ext) | |
winner_tree = wt.build_tree() | |
print(winner_tree, ", min v is ", ext[winner_tree[0]]) | |
# pop min, and push a new item | |
# winner tree can update any item in ext | |
ext[4] = -100 | |
# rebuild winner tree, start from min_id(the node id is the ) | |
winner_tree = wt.rebuild_tree(4) | |
print(winner_tree, ", min v is ", ext[winner_tree[0]]) | |
ext = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1] | |
wt = WinnerTree(ext) | |
winner_tree = wt.build_tree() | |
print(winner_tree, ", min v is ", ext[winner_tree[0]]) | |
ext[8] = -100 | |
winner_tree = wt.rebuild_tree(8) | |
print(winner_tree, ", min v is ", ext[winner_tree[0]]) | |
class LoserTree: | |
def __init__(self, ext): | |
self.ext = ext | |
self.N = len(ext) | |
self.k = math.ceil(math.log(self.N, 2)) | |
print(self.k, ", bottom layer node ", pow(2, self.k)) | |
def get_v(self, tree_id): | |
return self.ext[self.tree[tree_id]] | |
def build_tree(self): | |
# winner use [0], [1:x] is the loser tree | |
self.tree = [-1] * (pow(2, self.k)) | |
self.bottom_start = len(self.tree) - 1 | |
self.tree += range(0, self.N) | |
# hard copy. leaf winner is itself, loser is whatever | |
winners = list(self.tree) | |
# print(id(self.tree), id(winners)) | |
for i in range(self.bottom_start - 1, 0, -1): | |
left = 2 * i | |
right = 2 * i + 1 | |
if left < len(self.tree): | |
winners[i] = winners[left] | |
# loser is whatever | |
if right < len(self.tree): | |
if winners[right] < self.ext[winners[i]]: | |
# loser | |
self.tree[i] = winners[i] | |
# new winner | |
winners[i] = winners[right] | |
# print(self.tree) | |
self.tree[0] = winners[1] | |
return self.tree | |
def rebuild_tree(self, new_id): | |
print(self.ext) | |
update_node = self.bottom_start + new_id | |
temp_winner = new_id # use ext[] to get value | |
while update_node > 0: | |
parent = update_node // 2 | |
loser = self.get_v(parent) | |
if self.ext[temp_winner] >= loser: | |
temp_winner = self.tree[parent] | |
self.tree[parent] = temp_winner | |
# temp_winner goes on | |
update_node = parent | |
if update_node == 0: | |
self.tree[0] = temp_winner | |
return self.tree | |
ext = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1] | |
wt = LoserTree(ext) | |
loser_tree = wt.build_tree() | |
print("winner of loser tree ", loser_tree, " is ", ext[loser_tree[0]]) | |
# must update the winner in ext | |
ext[0] = -200 | |
loser_tree = wt.rebuild_tree(0) | |
print("winner of loser tree ", loser_tree, " is ", ext[loser_tree[0]]) |
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