Merge pull request #34 from alberthu16/day48

Day 48: check if an array is a min heap

Author: Albert Hu

day48/README.md

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+Question of the day: http://www.techiedelight.com/check-given-array-represents-min-heap-not/
+
+Given an array of integers, check if it represents a Min-Heap
+or not.
+
+For example, this array represents a min heap:  
+`[2, 3, 4, 5, 10, 15]`
+
+While this array doesn't:  
+`[2, 10, 4, 5, 3, 15]`
+
+## Ideas
+
+A min heap is a binary tree in which every parent node has two children
+that have values greater than the parent. The second array failed the heap
+check because the parent node with value `10` has children `5` and `3`, both
+of which are smaller than it.
+
+I think we can do a linear time check across all parent-children node
+relationships in the heap.
+
+Basically, check if the left sub-tree is a heap, check if the right sub-tree
+is a heap, and then check if this node has the correct relationship with its
+children.
+
+I wonder if I can get a recursive solution to work with array and index
+manipulation..
+
+## Code
+
+[Python](./day48.py)
+
+## Follow up

day48/isMinHeap.py

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+def isMinHeap(arr):
+    def subTreeIsHeap(index, arr, arraySize):
+        if index >= arraySize:
+            return True
+
+        left, right = index*2 + 1, index*2 + 2
+        leftBigger, rightBigger = True, True
+        if left < arraySize:
+            leftBigger = (arr[index] <= arr[left])
+        if right < arraySize:
+            rightBigger = (arr[index] <= arr[right])
+
+        return leftBigger and rightBigger and subTreeIsHeap(left, arr, size) and subTreeIsHeap(right, arr, size)
+
+    size = len(arr)
+    return arr[0] <= arr[1] and arr[0] <= arr[2] and subTreeIsHeap(1, arr, size) and subTreeIsHeap(2, arr, size)
+
+def testIsMinHeap():
+    assert isMinHeap([2, 3, 4, 5, 10, 15])
+    assert not isMinHeap([2, 10, 4, 5, 3, 15])
+
+def tests():
+    testIsMinHeap()
+
+if __name__ == "__main__":
+    tests()