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Wiki › Algorithms › 01. Searching and Sorting › 7. Divide and Conquer Sorting ›

Bottom Up Heapsort

Bottom Up Heapsort Bottom up heapsort improves the heapify operation used in heapsort. Instead of repeatedly comparing and swapping down the heap, it first follows a path to a leaf, then moves upward to place the element in its correct position. This reduces the number of comparisons and improves performance while keeping the same asymptotic complexity. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0]...
algorithms sorting heapsort heap
Wiki › Algorithms › 01. Searching and Sorting › 7. Divide and Conquer Sorting ›

Ternary Heapsort

Ternary Heapsort Ternary heapsort replaces the binary heap with a ternary heap, where each node has up to three children instead of two. This reduces the height of the heap, which can reduce the number of levels traversed during heap operations. The tradeoff is that each step may require more comparisons to select the largest child. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0]...
algorithms sorting heapsort heap
Wiki › Algorithms › 01. Searching and Sorting › 7. Divide and Conquer Sorting ›

Weak Heapsort

Weak Heapsort Weak heapsort is a heapsort variant that uses a weak heap instead of an ordinary binary heap. A weak heap stores elements in an implicit array and uses one extra reverse bit per node to define a modified tree structure. The main advantage is comparison efficiency. Weak heapsort can use fewer comparisons than standard binary heapsort while still sorting in place. Problem Given an array $A$ of length...
algorithms sorting heapsort weak-heap
Wiki › Algorithms › 01. Searching and Sorting › 7. Divide and Conquer Sorting ›

Heapsort

Heapsort Heapsort is a comparison based sorting algorithm that uses a binary heap. It first transforms the array into a heap, then repeatedly extracts the maximum element and places it at the end of the array. It provides a strict worst case guarantee of $O(n \log n)$ and uses constant extra space. Problem Given an array $A$ of length $n$, reorder it such that: $$ A[0] \le A[1] \le \dots...
algorithms sorting heapsort heap