0
Still curious? Ask our experts.
Chat with our AI personalities
Taiga
Rene
ProfessorAdd your answer:
Earn +20 pts
Is an array that is in sorted order a min-heap?
Yes, an array that is in sorted order is considered a min-heap because the smallest item in the array is the root. Also, the rest of the items in the array will gradually get bigger from the root until the end of the array.
How do you sort the given contents of an array?
You would sort the given elements of an array by a bubble sort or heap sort code!!
What is the running time of heapsort on an array A of length n that is already sorted in increasing order?
The running time of HEAPSORT on an array A of length n that is already sorted in increasing order is (n lg n) because even though it is already sorted, it will be transformed back into a heap andsorted.The running time of HEAPSORT on an array A of length n that is sorted in decreasing order willbe (n lg n). This occurs because even though the heap will be built in linear time, every time themax element is removed and the HEAPIFY is called it will cover the full height of the tree
Implementation of priority Queue using Heap?
Now let's consider how to implement priority queues using a heap. The standard approach is to use an array (or an ArrayList), starting at position 1 (instead of 0), where each item in the array corresponds to one node in the heap:The root of the heap is always in array[1].Its left child is in array[2].Its right child is in array[3].In general, if a node is in array[k], then its left child is in array[k*2], and its right child is in array[k*2 + 1].If a node is in array[k], then its parent is in array[k/2] (using integer division, so that if k is odd, then the result is truncated; e.g., 3/2 = 1).Here's an example, showing both the conceptual heap (the binary tree), and its array representation: Note that the heap's "shape" property guarantees that there are never any "holes" in the array.The operations that create an empty heap and return the size of the heap are quite straightforward; below we discuss the insert and removeMax operations.Implementing insertWhen a new value is inserted into a priority queue, we need to: Add the value so that the heap still has the order and shape properties, andDo it efficiently!The way to achieve these goals is as follows: Add the new value at the end of the array; that corresponds to adding it as a new rightmost leaf in the tree (or, if the tree was a complete binary tree, i.e., all leaves were at the same depth d, then that corresponds to adding a new leaf at depth d+1).Step 1 above ensures that the heap still has the shapeproperty; however, it may not have the order property. We can check that by comparing the new value to the value in its parent. If the parent is smaller, we swap the values, and we continue this check-and-swap procedure up the tree until we find that the order property holds, or we get to the root.Here's a series of pictures to illustrate inserting the value 34 into a heap:
What will be the difference in running time of the heap sort algorithm if you start to apply heap sort with an array elements rather than max heap elements?
The heap sort algorithm is as follows: 1. Call the build_max_heap() function. 2. Swap the first and last elements of the max heap. 3. Reduce the heap by one element (elements that follow the heap are in sorted order). 4. Call the sift_down() function. 5. Goto step 2 unless the heap has one element. The build_max_heap() function creates the max heap and takes linear time, O(n). The sift_down() function moves the first element in the heap into its correct index, thus restoring the max heap property. This takes O(log(n)) and is called n times, so takes O(n * log(n)). The complete algorithm therefore equates to O(n + n * log(n)). If you start with a max heap rather than an unsorted array, there will be no difference in the runtime because the build_max_heap() function will still take O(n) time to complete. However, the mere fact you are starting with a max heap means you must have built that heap prior to calling the heap sort algorithm, so you've actually increased the overall runtime by an extra O(n), thus taking O(2n * log(n)) in total.
What is the running time of heap sort algorithm?
The running time of the heap sort algorithm is O(n log n), where n is the number of elements in the input array.
Is an array that is in sorted order a min heap?
Yes, an array that is in sorted order is considered a min-heap because the smallest item in the array is the root. Also, the rest of the items in the array will gradually get bigger from the root until the end of the array.
What is the array representation of a d-ary heap?
In a d-ary heap, the elements are stored in an array where each element at index i has children at indices (di1) to (did).
How can I implement an array-based heap in Java?
To implement an array-based heap in Java, you can create an array to store the heap elements and use methods to maintain the heap property. The root element is stored at index 0, and for any element at index i, its left child is at index 2i1 and its right child is at index 2i2. You can then implement methods like insert, delete, and heapify to maintain the heap structure.
Is an array that is in sorted order a min-heap?
Yes, an array that is in sorted order is considered a min-heap because the smallest item in the array is the root. Also, the rest of the items in the array will gradually get bigger from the root until the end of the array.
How do you sort the given contents of an array?
You would sort the given elements of an array by a bubble sort or heap sort code!!
What is the running time of heapsort on an array A of length n that is already sorted in increasing order?
The running time of HEAPSORT on an array A of length n that is already sorted in increasing order is (n lg n) because even though it is already sorted, it will be transformed back into a heap andsorted.The running time of HEAPSORT on an array A of length n that is sorted in decreasing order willbe (n lg n). This occurs because even though the heap will be built in linear time, every time themax element is removed and the HEAPIFY is called it will cover the full height of the tree
How do you locate memory in array?
The array name is a reference to the start address of the array, so simply take its address. int a[10]; int* p1 = &a; If the array is allocated on the heap, then there is no name (all allocations on the heap are anonymous). However, you don't need a name since you already know the address: int* p2 = malloc (10 * sizeof (int));
How can I implement an arrayheap in Java for efficient data storage and retrieval?
To implement an ArrayHeap in Java for efficient data storage and retrieval, you can create a class that represents the heap structure using an array. The array should be organized in a way that maintains the heap property, where the parent node is always greater (or smaller) than its children. You can then implement methods to insert elements into the heap and remove elements efficiently by adjusting the array structure to maintain the heap property. This will allow for quick access to the top element of the heap, making data storage and retrieval efficient.
Implementation of priority Queue using Heap?
Now let's consider how to implement priority queues using a heap. The standard approach is to use an array (or an ArrayList), starting at position 1 (instead of 0), where each item in the array corresponds to one node in the heap:The root of the heap is always in array[1].Its left child is in array[2].Its right child is in array[3].In general, if a node is in array[k], then its left child is in array[k*2], and its right child is in array[k*2 + 1].If a node is in array[k], then its parent is in array[k/2] (using integer division, so that if k is odd, then the result is truncated; e.g., 3/2 = 1).Here's an example, showing both the conceptual heap (the binary tree), and its array representation: Note that the heap's "shape" property guarantees that there are never any "holes" in the array.The operations that create an empty heap and return the size of the heap are quite straightforward; below we discuss the insert and removeMax operations.Implementing insertWhen a new value is inserted into a priority queue, we need to: Add the value so that the heap still has the order and shape properties, andDo it efficiently!The way to achieve these goals is as follows: Add the new value at the end of the array; that corresponds to adding it as a new rightmost leaf in the tree (or, if the tree was a complete binary tree, i.e., all leaves were at the same depth d, then that corresponds to adding a new leaf at depth d+1).Step 1 above ensures that the heap still has the shapeproperty; however, it may not have the order property. We can check that by comparing the new value to the value in its parent. If the parent is smaller, we swap the values, and we continue this check-and-swap procedure up the tree until we find that the order property holds, or we get to the root.Here's a series of pictures to illustrate inserting the value 34 into a heap:
What is the runtime complexity of the heap sort algorithm?
The runtime complexity of the heap sort algorithm is O(n log n), where n is the number of elements in the input array.
What is the time complexity of heap sort algorithm?
The time complexity of the heap sort algorithm is O(n log n), where n is the number of elements in the input array.
