Added Binary Heap (#46)

AUTHORS

@@ -1,3 +1,4 @@
 Gagandeep Singh<[email protected]>
 Kartikei Mittal<[email protected]>
+Umesh<[email protected]>
 

pydatastructs/linear_data_structures/arrays.py

@@ -248,6 +248,8 @@ def delete(self, idx):
             self[idx] != None:
             self[idx] = None
             self._num -= 1
+            if self._last_pos_filled == idx:
+                self._last_pos_filled -= 1
             return self._modify()
 
     @property

pydatastructs/trees/__init__.py

@@ -14,3 +14,8 @@
     OneDimensionalSegmentTree
 )
 __all__.extend(space_partitioning_trees.__all__)
+
+from .heaps import (
+    BinaryHeap
+)
+__all__.extend(heaps.__all__)

pydatastructs/trees/heaps.py

@@ -0,0 +1,180 @@
+from pydatastructs.utils.misc_util import _check_type, NoneType, TreeNode
+from pydatastructs.linear_data_structures.arrays import ArrayForTrees
+
+__all__ = [
+    'BinaryHeap'
+]
+
+class Heap:
+    """
+    Abstract class for representing heaps.
+    """
+    pass
+
+class BinaryHeap:
+    """
+    Represents Binary Heap.
+
+    Parameters
+    ==========
+
+    elements : list, tuple
+        Optional, by default 'None'.
+        List/tuple of initial elements in Heap.
+
+    heap_property : str
+        The property of binary heap.
+        If the key stored in each node is
+        either greater than or equal to
+        the keys in the node's children
+        then pass 'max'.
+        If the key stored in each node is
+        either less than or equal to
+        the keys in the node's children
+        then pass 'min'.
+        By default, the heap property is
+        set to 'min'.
+
+    Examples
+    ========
+
+    >>> from pydatastructs.trees.heaps import BinaryHeap
+    >>> min_heap = BinaryHeap(heap_property="min")
+    >>> min_heap.insert(1, 1)
+    >>> min_heap.insert(5, 5)
+    >>> min_heap.insert(7, 7)
+    >>> min_heap.extract().key
+    1
+    >>> min_heap.insert(4, 4)
+    >>> min_heap.extract().key
+    4
+
+    >>> max_heap = BinaryHeap(heap_property='max')
+    >>> max_heap.insert(1, 1)
+    >>> max_heap.insert(5, 5)
+    >>> max_heap.insert(7, 7)
+    >>> max_heap.extract().key
+    7
+    >>> max_heap.insert(6, 6)
+    >>> max_heap.extract().key
+    6
+
+    References
+    ==========
+
+    .. [1] https://en.m.wikipedia.org/wiki/Binary_heap
+    """
+    __slots__ = ['_comp', 'heap', 'heap_property', '_last_pos_filled']
+
+    def __new__(cls, elements=None, heap_property="min"):
+        obj = object.__new__(cls)
+        obj.heap_property = heap_property
+        if heap_property == "min":
+            obj._comp = lambda key_parent, key_child: key_parent <= key_child
+        elif heap_property == "max":
+            obj._comp = lambda key_parent, key_child: key_parent >= key_child
+        else:
+            raise ValueError("%s is invalid heap property"%(heap_property))
+        if elements is None:
+            elements = []
+        obj.heap = elements
+        obj._last_pos_filled = len(elements) - 1
+        obj._build()
+        return obj
+
+    def _build(self):
+        for i in range(self._last_pos_filled + 1):
+            self.heap[i].left, self.heap[i].right = \
+                2*i + 1, 2*i + 2
+        for i in range((self._last_pos_filled + 1)//2, -1, -1):
+            self._heapify(i)
+
+    def _swap(self, idx1, idx2):
+        idx1_key, idx1_data = \
+            self.heap[idx1].key, self.heap[idx1].data
+        self.heap[idx1].key, self.heap[idx1].data = \
+            self.heap[idx2].key, self.heap[idx2].data
+        self.heap[idx2].key, self.heap[idx2].data = \
+            idx1_key, idx1_data
+
+    def _heapify(self, i):
+        target = i
+        l = 2*i + 1
+        r = 2*i + 2
+
+        if l <= self._last_pos_filled:
+            target = l if self._comp(self.heap[l].key, self.heap[target].key) \
+                        else i
+        if r <= self._last_pos_filled:
+            target = r if self._comp(self.heap[r].key, self.heap[target].key) \
+                        else target
+
+        if target != i:
+            self._swap(target, i)
+            i = target
+            self._heapify(i)
+
+    def insert(self, key, data):
+        """
+        Insert a new element to the heap according to heap property.
+
+        Parameters
+        ==========
+
+        key
+            The key for comparison.
+        data
+            The data to be inserted.
+
+        Returns
+        =======
+
+        None
+        """
+        new_node = TreeNode(key, data)
+        self.heap.append(new_node)
+        self._last_pos_filled += 1
+        i = self._last_pos_filled
+        self.heap[i].left, self.heap[i].right = 2*i + 1, 2*i + 2
+
+        while True:
+            parent = (i - 1)//2
+            if i == 0 or self._comp(self.heap[parent].key, self.heap[i].key):
+                break
+            else:
+                self._swap(i, parent)
+                i = parent
+
+    def extract(self):
+        """
+        Extract root element of the Heap.
+
+        Returns
+        =======
+
+        root_element : TreeNode
+            The TreeNode at the root of the heap,
+            if the heap is not empty.
+        None
+            If the heap is empty.
+        """
+        if self._last_pos_filled == -1:
+            return None
+        else:
+            element_to_be_extracted = TreeNode(self.heap[0].key, self.heap[0].data)
+            self._swap(0, self._last_pos_filled)
+            self.heap[self._last_pos_filled] = TreeNode(float('inf') if self.heap_property == 'min'
+                                                                else float('-inf'), None)
+            self._heapify(0)
+            self.heap.pop()
+            self._last_pos_filled -= 1
+            return element_to_be_extracted
+
+    def __str__(self):
+        to_be_printed = ['' for i in range(self._last_pos_filled + 1)]
+        for i in range(self._last_pos_filled + 1):
+            node = self.heap[i]
+            to_be_printed[i] = (node.left if node.left <= self._last_pos_filled else None,
+                                node.key, node.data,
+                                node.right if node.right <= self._last_pos_filled else None)
+        return str(to_be_printed)

pydatastructs/trees/tests/test_binary_trees.py

@@ -33,7 +33,7 @@ def test_BinarySearchTree():
     assert b.delete(13) == None
     assert str(b) == \
     ("[(1, 8, 8, 7), (3, 4, 4, 4), '', (None, 1, 1, None), "
-    "(None, 6, 6, 6), '', (None, 7, 7, None), (None, 14, 14, None), '']")
+    "(None, 6, 6, 6), '', (None, 7, 7, None), (None, 14, 14, None)]")
     b.delete(7)
     b.delete(6)
     b.delete(1)

pydatastructs/trees/tests/test_heaps.py

@@ -0,0 +1,46 @@
+from pydatastructs.trees.heaps import BinaryHeap
+from pydatastructs.utils.misc_util import TreeNode
+from pydatastructs.utils.raises_util import raises
+
+def test_BinaryHeap():
+
+    max_heap = BinaryHeap(heap_property="max")
+
+    assert max_heap.extract() is None
+
+    max_heap.insert(100, 100)
+    max_heap.insert(19, 19)
+    max_heap.insert(36, 36)
+    max_heap.insert(17, 17)
+    max_heap.insert(3, 3)
+    max_heap.insert(25, 25)
+    max_heap.insert(1, 1)
+    max_heap.insert(2, 2)
+    max_heap.insert(7, 7)
+    assert str(max_heap) == \
+    ("[(1, 100, 100, 2), (3, 19, 19, 4), "
+    "(5, 36, 36, 6), (7, 17, 17, 8), "
+    "(None, 3, 3, None), (None, 25, 25, None), "
+    "(None, 1, 1, None), (None, 2, 2, None), (None, 7, 7, None)]")
+
+    expected_extracted_element = max_heap.heap[0].key
+    assert max_heap.extract().key == expected_extracted_element
+
+    expected_sorted_elements = [36, 25, 19, 17, 7, 3, 2, 1]
+    sorted_elements = []
+    for _ in range(8):
+        sorted_elements.append(max_heap.extract().key)
+    assert expected_sorted_elements == sorted_elements
+
+    elements = [
+                TreeNode(7, 7), TreeNode(25, 25), TreeNode(100, 100),
+                TreeNode(1, 1), TreeNode(2, 2), TreeNode(3, 3),
+                TreeNode(17, 17), TreeNode(19, 19), TreeNode(36, 36)
+            ]
+    min_heap = BinaryHeap(elements = elements, heap_property="min")
+    expected_extracted_element = min_heap.heap[0].key
+    assert min_heap.extract().key == expected_extracted_element
+
+    expected_sorted_elements = [2, 3, 7, 17, 19, 25, 36, 100]
+    sorted_elements = [min_heap.extract().key for _ in range(8)]
+    assert expected_sorted_elements == sorted_elements