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# Min heap data structure

# with decrease key functionality - in O(log(n)) time

class Node:

def __init__(self, name, val):

self.name = name

self.val = val

def __str__(self):

return f"{self.__class__.__name__}({self.name}, {self.val})"

def __lt__(self, other):

return self.val < other.val

class MinHeap:

"""

>>> r = Node("R", -1)

>>> b = Node("B", 6)

>>> a = Node("A", 3)

>>> x = Node("X", 1)

>>> e = Node("E", 4)

>>> print(b)

Node(B, 6)

>>> myMinHeap = MinHeap([r, b, a, x, e])

>>> myMinHeap.decrease_key(b, -17)

>>> print(b)

Node(B, -17)

>>> print(myMinHeap["B"])

-17

"""

def __init__(self, array):

self.idx_of_element = {}

self.heap_dict = {}

self.heap = self.build_heap(array)

def __getitem__(self, key):

return self.get_value(key)

def get_parent_idx(self, idx):

return (idx - 1) // 2

def get_left_child_idx(self, idx):

return idx * 2 + 1

def get_right_child_idx(self, idx):

return idx * 2 + 2

def get_value(self, key):

return self.heap_dict[key]

def build_heap(self, array):

lastIdx = len(array) - 1

startFrom = self.get_parent_idx(lastIdx)

for idx, i in enumerate(array):

self.idx_of_element[i] = idx

self.heap_dict[i.name] = i.val

for i in range(startFrom, -1, -1):

self.sift_down(i, array)

return array

# this is min-heapify method

def sift_down(self, idx, array):

while True:

l = self.get_left_child_idx(idx) # noqa: E741

r = self.get_right_child_idx(idx)

smallest = idx

if l < len(array) and array[l] < array[idx]:

smallest = l

if r < len(array) and array[r] < array[smallest]:

smallest = r

if smallest != idx:

array[idx], array[smallest] = array[smallest], array[idx]

(

self.idx_of_element[array[idx]],

self.idx_of_element[array[smallest]],

) = (

self.idx_of_element[array[smallest]],

self.idx_of_element[array[idx]],

)

idx = smallest

else:

break

def sift_up(self, idx):

p = self.get_parent_idx(idx)

while p >= 0 and self.heap[p] > self.heap[idx]:

self.heap[p], self.heap[idx] = self.heap[idx], self.heap[p]

self.idx_of_element[self.heap[p]], self.idx_of_element[self.heap[idx]] = (

self.idx_of_element[self.heap[idx]],

self.idx_of_element[self.heap[p]],

)

idx = p

p = self.get_parent_idx(idx)

def peek(self):

return self.heap[0]

def remove(self):

self.heap[0], self.heap[-1] = self.heap[-1], self.heap[0]

self.idx_of_element[self.heap[0]], self.idx_of_element[self.heap[-1]] = (

self.idx_of_element[self.heap[-1]],

self.idx_of_element[self.heap[0]],

)

x = self.heap.pop()

del self.idx_of_element[x]

self.sift_down(0, self.heap)

return x

def insert(self, node):

self.heap.append(node)

self.idx_of_element[node] = len(self.heap) - 1

self.heap_dict[node.name] = node.val

self.sift_up(len(self.heap) - 1)

def is_empty(self):

return True if len(self.heap) == 0 else False

def decrease_key(self, node, newValue):

assert (

self.heap[self.idx_of_element[node]].val > newValue

), "newValue must be less that current value"

node.val = newValue

self.heap_dict[node.name] = newValue

self.sift_up(self.idx_of_element[node])

# USAGE

r = Node("R", -1)

b = Node("B", 6)

a = Node("A", 3)

x = Node("X", 1)

e = Node("E", 4)

# Use one of these two ways to generate Min-Heap

# Generating Min-Heap from array

myMinHeap = MinHeap([r, b, a, x, e])

# Generating Min-Heap by Insert method

# myMinHeap.insert(a)

# myMinHeap.insert(b)

# myMinHeap.insert(x)

# myMinHeap.insert(r)

# myMinHeap.insert(e)

# Before

print("Min Heap - before decrease key")

for i in myMinHeap.heap:

print(i)

print("Min Heap - After decrease key of node [B -> -17]")

myMinHeap.decrease_key(b, -17)

# After

for i in myMinHeap.heap:

print(i)

if __name__ == "__main__":

import doctest

doctest.testmod()

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