Question

Write and test python recursive function to solve the following problems: Assume you are allowed to use at most two extra stacks.

1. A stack contains integers in a sorted ascending sequence, i.e. the largest integer is at the top. Push val into the correct position in the given stack, such that the stack remains sorted after insertion.
2. Given a stack containing integer elements, sort its elements in ascending order, i.e. largest integer at the top. You may use the insert() method in (b).

Answer 1

To insert a value into a sorted stack, compare the value with the elements of the stack and recursively pop elements until the correct position is found. To sort a stack, divide it into smaller subproblems and merge them in a sorted manner.

Step-by-step explanation:

1. Inserting an Element into a Sorted Stack:

To insert a value into a sorted stack while maintaining the sorted order, we can recursively compare the value with the elements of the stack. If the value is greater than the top element, we can push the value onto the stack. Otherwise, we can recursively pop elements from the stack until we find a smaller element or the stack becomes empty. Then, we can push the value onto the stack at the correct position.

2. Sorting a Stack:

To sort a stack in ascending order, we can divide the problem into smaller subproblems. Firstly, we can recursively divide the stack into two halves until only single elements remain. Then, we can merge the two halves in a sorted manner. We repeat this process until the entire stack is sorted.