<s>[INST] Explain bubble sort [/INST] Bubble sort is a sorting algorithm to sort arrays of numbers or other comparable things. It works by swapping two elements that are next to each other so that the bigger one is on the right afterwards. This process is repeated for each position from left to right. After this the biggest number in the array is at the last position. Next, the algorithm starts at the very left again and swaps neighbours going to the right, but this time it can stop before the last position, as the biggest number is already there. It is called bubble sort as the biggest number always "bubbles" up.
Here is an example:
```
4 8 3 6 1
# don't swap 4, 8 as 8 > 4
4 8 3 6 1
# swap 8, 3
4 3 8 6 1
# swap 8, 6
4 3 6 8 1
# swap 8, 1; 8 is now correct
4 3 6 1 8
# swap 4, 3
3 4 6 1 8
# don't swap 4, 6 as 6 > 4
3 4 6 1 8
# swap 1, 6; 6 is now correct
3 4 1 6 8
# don't swap 3, 4 as 4 > 3
3 4 1 6 8
# swap 4, 1; 4 is now correct
3 1 4 6 8
# swap 3, 1; 3 is now correct
1 3 4 6 8
# array is sorted
```</s>\ <s>[INST] Explain heap sort and heapify. [/INST] Heap sort is a sorting algorithm that works by using a binary heap data structure to sort elements. It is an in-place algorithm, meaning that it sorts the elements within the original array without creating a new array.

The algorithm works by first creating a binary heap from the input array using a process called "heapify". Once the binary heap is created, the algorithm repeatedly removes the root element from the heap and places it at the end of the array. This process continues until all elements have been removed from the heap and placed in the correct order in the array.

The "heapify" process involves rearranging the elements in the input array so that they form a binary heap. A binary heap is a tree-based data structure in which each parent node is greater than or equal to its children (in the case of a max heap), or less than or equal to its children (in the case of a min heap). To heapify an array, the algorithm starts by finding the last parent node in the tree and then repeatedly "sinks" each parent node down the tree until it is in the correct position.

The process of sinking a node involves comparing the node to its children and swapping it with the larger (or smaller, depending on whether it is a max or min heap) child if necessary. This process is repeated until the node is in the correct position in the heap. The algorithm then moves on to the next parent node in the tree and repeats the sinking process.

Once the heapify process is complete, the input array will be sorted in ascending order if it is a max heap, or descending order if it is a min heap. The heap sort algorithm then proceeds with the step of repeatedly removing the root element from the heap and placing it at the end of the array until all elements have been placed in the correct order.</s>