Heap Sort
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Heap Sort Algorithm: A Step-by-Step Guide, Lecture notes of Data Structures and Algorithms
This document offers a detailed, step-by-step explanation of the heap sort algorithm, a widely used efficient sorting algorithm. it guides the reader through the process of heapifying an array and then sorting it using a series of swaps and recursive calls to maintain the heap property. The explanation is thorough and includes illustrative examples, making it suitable for students learning about sorting algorithms and data structures.
Typology: Lecture notes
2023/2024
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0 1 2 3 4 5 6 7 8 8 3 1 9 4 7 2 5 6 0 1 2 3 4 5 6 7 8 8 3 1 9 4 7 2 5 6 0 1 2 3 4 5 6 7 8 8 3 1 9 4 7 2 5 6 0 1 2 3 4 5 6 7 8 Children of index k are at index 2k+1 and 2k+ This is NOT a max-heap, as not all parents are larger than their children.
Heapify the Array
0 1 2 3 4 5 6 7 8 8 3 7 9 4 1 2 5 6 0 1 2 3 4 5 6 7 8 Consider the value at index 2 and its children. Because 1 is smaller than its children, we select the larger of the children 7 and swap it into position. Because there was a swap, we may need to check recursively to restore the heap property. Move on to the next lower index.
Heapify the Array
0 1 2 3 4 5 6 7 8 8 9 7 3 4 1 2 5 6 0 1 2 3 4 5 6 7 8 Consider the value at index 1 and its children. Because 1 is smaller than its children, we select the larger of the children 9 and swap it into position. Because there was a swap, we may need to check recursively to restore the heap property.
Heapify the Array
0 1 2 3 4 5 6 7 8 9 8 7 6 4 1 2 5 3 0 1 2 3 4 5 6 7 8 Consider the value at index 0 and its children. Because 8 is smaller than its child 9, we swap these values. Because there was a swap, we may need to check recursively to restore the heap property.
0 1 2 3 4 5 6 7 8 3 8 7 6 4 1 2 5 9 0 1 2 3 4 5 6 7 8 The array is now a heap and we can begin the sort. Begin by swapping the value at index 0 with the last unsorted value in the array. Mark the value sorted in the array. Restore the heap property.
0 1 2 3 4 5 6 7 8 8 6 7 3 4 1 2 5 9 0 1 2 3 4 5 6 7 8 Compare the value to its children and swap. Continue recursively as needed to restore the heap property.
0 1 2 3 4 5 6 7 8 8 6 7 5 4 1 2 3 9 0 1 2 3 4 5 6 7 8 Compare the value to its children and swap. Reaching the end of the recursion, we continue the sorting with the next value.
0 1 2 3 4 5 6 7 8 7 6 3 5 4 1 2 8 9 0 1 2 3 4 5 6 7 8 Compare the value to its children and swap. Continue recursively as needed to restore the heap property.
0 1 2 3 4 5 6 7 8 7 6 3 5 4 1 2 8 9 0 1 2 3 4 5 6 7 8 Compare the value to its children and swap. No swap is needed. Reaching the end of the recursion, we continue the sorting with the next value.
0 1 2 3 4 5 6 7 8 6 2 3 5 4 1 7 8 9 0 1 2 3 4 5 6 7 8 Compare the value to its children and swap. Continue recursively as needed to restore the heap property.
0 1 2 3 4 5 6 7 8 6 5 3 2 4 1 7 8 9 0 1 2 3 4 5 6 7 8 Compare the value to its children and swap. Reaching the end of the recursion, we continue the sorting with the next value.
0 1 2 3 4 5 6 7 8 5 1 3 2 4 6 7 8 9 0 1 2 3 4 5 6 7 8 Compare the value to its children and swap. Continue recursively as needed to restore the heap property.
0 1 2 3 4 5 6 7 8 5 4 3 2 1 6 7 8 9 0 1 2 3 4 5 6 7 8 Compare the value to its children and swap. Reaching the end of the recursion, we continue the sorting with the next value.