add a generic heap (#906)

* add a generic heap

* Delete __init__.py

* Rename data_structures/Heap/heap_generic.py to data_structures/heap/heap_generic.py

* Add doctests

* Fix doctests

* Fix doctests again

Author: SaurabhGoyal

data_structures/data_structures/heap/heap_generic.py

@@ -0,0 +1,162 @@
+class Heap(object):
+    """A generic Heap class, can be used as min or max by passing the key function accordingly.
+    """
+
+    def __init__(self, key=None):
+        # Stores actual heap items.
+        self.arr = list()
+        # Stores indexes of each item for supporting updates and deletion.
+        self.pos_map = {}
+        # Stores current size of heap.
+        self.size = 0
+        # Stores function used to evaluate the score of an item on which basis ordering will be done.
+        self.key = key or (lambda x: x)
+
+    def _parent(self, i):
+        """Returns parent index of given index if exists else None"""
+        return int((i - 1) / 2) if i > 0 else None
+
+    def _left(self, i):
+        """Returns left-child-index of given index if exists else None"""
+        left = int(2 * i + 1)
+        return left if 0 < left < self.size else None
+
+    def _right(self, i):
+        """Returns right-child-index of given index if exists else None"""
+        right = int(2 * i + 2)
+        return right if 0 < right < self.size else None
+
+    def _swap(self, i, j):
+        """Performs changes required for swapping two elements in the heap"""
+        # First update the indexes of the items in index map.
+        self.pos_map[self.arr[i][0]], self.pos_map[self.arr[j][0]] = (
+            self.pos_map[self.arr[j][0]], self.pos_map[self.arr[i][0]]
+        )
+        # Then swap the items in the list.
+        self.arr[i], self.arr[j] = self.arr[j], self.arr[i]
+
+    def _cmp(self, i, j):
+        """Compares the two items using default comparison"""
+        return self.arr[i][1] < self.arr[j][1]
+
+    def _get_valid_parent(self, i):
+        """Returns index of valid parent as per desired ordering among given index and both it's children"""
+        left = self._left(i)
+        right = self._right(i)
+        valid_parent = i
+
+        if left is not None and not self._cmp(left, valid_parent):
+            valid_parent = left
+        if right is not None and not self._cmp(right, valid_parent):
+            valid_parent = right
+
+        return valid_parent
+
+    def _heapify_up(self, index):
+        """Fixes the heap in upward direction of given index"""
+        parent = self._parent(index)
+        while parent is not None and not self._cmp(index, parent):
+            self._swap(index, parent)
+            index, parent = parent, self._parent(parent)
+
+    def _heapify_down(self, index):
+        """Fixes the heap in downward direction of given index"""
+        valid_parent = self._get_valid_parent(index)
+        while valid_parent != index:
+            self._swap(index, valid_parent)
+            index, valid_parent = valid_parent, self._get_valid_parent(valid_parent)
+
+    def update_item(self, item, item_value):
+        """Updates given item value in heap if present"""
+        if item not in self.pos_map:
+            return
+        index = self.pos_map[item]
+        self.arr[index] = [item, self.key(item_value)]
+        # Make sure heap is right in both up and down direction.
+        # Ideally only one of them will make any change.
+        self._heapify_up(index)
+        self._heapify_down(index)
+
+    def delete_item(self, item):
+        """Deletes given item from heap if present"""
+        if item not in self.pos_map:
+            return
+        index = self.pos_map[item]
+        del self.pos_map[item]
+        self.arr[index] = self.arr[self.size - 1]
+        self.pos_map[self.arr[self.size - 1][0]] = index
+        self.size -= 1
+        # Make sure heap is right in both up and down direction.
+        # Ideally only one of them will make any change- so no performance loss in calling both.
+        if self.size > index:
+            self._heapify_up(index)
+            self._heapify_down(index)
+
+    def insert_item(self, item, item_value):
+        """Inserts given item with given value in heap"""
+        arr_len = len(self.arr)
+        if arr_len == self.size:
+            self.arr.append([item, self.key(item_value)])
+        else:
+            self.arr[self.size] = [item, self.key(item_value)]
+        self.pos_map[item] = self.size
+        self.size += 1
+        self._heapify_up(self.size - 1)
+
+    def get_top(self):
+        """Returns top item tuple (Calculated value, item) from heap if present"""
+        return self.arr[0] if self.size else None
+
+    def extract_top(self):
+        """Returns top item tuple (Calculated value, item) from heap and removes it as well if present"""
+        top_item_tuple = self.get_top()
+        if top_item_tuple:
+            self.delete_item(top_item_tuple[0])
+        return top_item_tuple
+
+
+def test_heap() -> None:
+    """
+    >>> h = Heap()  # Max-heap
+    >>> h.insert_item(5, 34)
+    >>> h.insert_item(6, 31)
+    >>> h.insert_item(7, 37)
+    >>> h.get_top()
+    [7, 37]
+    >>> h.extract_top()
+    [7, 37]
+    >>> h.extract_top()
+    [5, 34]
+    >>> h.extract_top()
+    [6, 31]
+    >>> h = Heap(key=lambda x: -x)  # Min heap
+    >>> h.insert_item(5, 34)
+    >>> h.insert_item(6, 31)
+    >>> h.insert_item(7, 37)
+    >>> h.get_top()
+    [6, -31]
+    >>> h.extract_top()
+    [6, -31]
+    >>> h.extract_top()
+    [5, -34]
+    >>> h.extract_top()
+    [7, -37]
+    >>> h.insert_item(8, 45)
+    >>> h.insert_item(9, 40)
+    >>> h.insert_item(10, 50)
+    >>> h.get_top()
+    [9, -40]
+    >>> h.update_item(10, 30)
+    >>> h.get_top()
+    [10, -30]
+    >>> h.delete_item(10)
+    >>> h.get_top()
+    [9, -40]
+    """
+    pass
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()