Compare merge sort and quick sort algorithms in terms of storage space and time required to execute them. What is min heap? Create the min heap for the given data set: 6, 15, 50, 3, 33, 45, 40, 80, 10

Comparison of Merge Sort and Quick Sort Algorithms:

Merge Sort:

• Storage Space: O(n), additional space is required for merging the sorted runs.
• Time Complexity:
  • Worst Case: O(n log n)
  • Average Case: O(n log n)
  • Best Case: O(n log n)

Quick Sort:

• Storage Space: O(log n), only the stack space is required for storing the recursive calls.
• Time Complexity:
  • Worst Case: O(n^2)
  • Average Case: O(n log n)
  • Best Case: O(n log n)

Conclusion: Merge Sort is generally considered to be more stable than Quick Sort, meaning it always produces the same sorted output for the same input, even if the input contains duplicate elements. Quick Sort, on the other hand, can produce different sorted outputs for the same input, depending on the order in which the elements are chosen as pivots.

Min Heap:

A min heap is a complete binary tree where the value of each node is less than or equal to the value of its parent node. Min heaps are used in a variety of applications, such as priority queues and sorting algorithms.

To create a min heap for the given data set:

1. Create a binary tree with the given data set as the nodes.
2. For each node, compare its value to the value of its children.
3. If the node's value is greater than the value of any of its children, swap the node's value with the value of the smallest child.
4. Repeat steps 2 and 3 until the tree is a min heap.

The following is the min heap for the given data set:

           6
        /     \
      3       15
    /   \    /  \
   10   50  33   45
    \      \
     80     40

Time Complexity:

The time complexity to build a min heap is O(n log n).