CS241: Data Structures & Algorithms II

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Pocketoption omni 11 binary options. Applications : A heap has many applications, including the most efficient implementation of priority queues, which are useful in many applications. In particular, heaps are crucial in several efficient graph algorithms. 2-3 heap Binary heap Many many others. Binary heap storage rules — A heap implemented with a binary tree in which the following two rules are followed: The element contained by each node is greater than or forex equal to the elements of that node’s children.

The tree is a complete binary tree. Example: which one is a heap? Example: forex We want to insert a node with value 42 to the heap on the left. The above process is called reheapification upward . Place the new element in the heap in the first available location. This keeps the structure as a complete binary tree, but it might no longer be a heap since the new element might have a greater value than its parent. while (the new element has a greater value than its parent) swap the new element with its parent.

Notice that Step 2 will stop when the new element reaches the root or when the new element’s parent has a value greater than or equal to the new element’s value. Removing the Root of a Heap. The procedure for deleting the root from the heap — effectively extracting the maximum element in a max-heap or the minimum element in a min-heap. The above process is called reheapification downward . Copy the element at the root of the heap to the variable used to return a value. Copy the last element in the deepest level to the root and then take this last node out of the tree.

This element is called the "out-of-place" element. while (the out-of-place element has a value that is lower than one of its children) swap the out-of-place element with its greatest-value child. Return the answer that was saved in Step 1. Notice that Step 3 will stop when the out-of-place element reaches a leaf or it has a value that is greater or equal to all its children. Now, think about how to build a heap. Check out the example of inserting 27, 35, 23, binary options strategy 22, 4, 45, 21, 5, 42 and 19 to an empty heap.

A more common approach is to store the heap in an array. Since heap is always a complete binary tree, it can be stored compactly. No space is required for pointers; instead, binary options the parent and children of each node can be found by simple arithmetic on array indices. The rules (assume the root is stored in arr [0]): For each index i , element arr [ i ] has children at arr [2 i + 1] and arr [2 i + 2], and forex the parent at arr [floor( ( i – 1 )/2 )].

This implementation is particularly useful in the heapsort algorithm, where it allows the space in the input array to be reused to store the heap (i.e., the algorithm is in-place). However it requires allocating the array before filling it, which makes this method not that useful in priority queues implementation, where the number of elements is unknown.

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