From 6ac7b1387f9b2c2fa428bbe2bd26d3e087e41b23 Mon Sep 17 00:00:00 2001
From: Raj <raj1998211@gmail.com>
Date: Wed, 25 Sep 2019 15:03:31 -0700
Subject: [PATCH] Min head with decrease key functionality (#1202)

* Min head with decrease key functionality

* doctest added

* __str__ changed as per Python convention

* edits in doctest

* get_value by key added

* __getitem__ added
---
 data_structures/heap/min_heap.py | 169 +++++++++++++++++++++++++++++++
 1 file changed, 169 insertions(+)
 create mode 100644 data_structures/heap/min_heap.py

diff --git a/data_structures/heap/min_heap.py b/data_structures/heap/min_heap.py
new file mode 100644
index 000000000..6184d83be
--- /dev/null
+++ b/data_structures/heap/min_heap.py
@@ -0,0 +1,169 @@
+# Min head 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)
+            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()