### stack using recursion

# Reverse a stack using recursion

You are not allowed to use loop constructs like while, for..etc, and you can only use the following ADT functions on Stack S:

isEmpty(S)

push(S)

pop(S)

isEmpty(S)

push(S)

pop(S)

**Solution:**

The idea of the solution is to hold all values in Function Call Stack until the stack becomes empty. When the stack becomes empty, insert all held items one by one at the bottom of the stack.

For example, let the input stack be

1 <-- top 2 3 4

First 4 is inserted at the bottom. 4 <-- top Then 3 is inserted at the bottom 4 <-- top 3 Then 2 is inserted at the bottom 4 <-- top 3 2 Then 1 is inserted at the bottom 4 <-- top 3 2 1

So we need a function that inserts at the bottom of a stack using the above given basic stack function.

**void insertAtBottom(():**First pops all stack items and stores the popped item in function call stack using recursion. And when stack becomes empty, pushes new item and all items stored in call stack.

**void reverse():**This function mainly uses insertAtBottom() to pop all items one by one and insert the popped items at the bottom.

`// Below is a recursive function that inserts an element`

`// at the bottom of a stack.`

`void`

`insertAtBottom(`

`struct`

`sNode** top_ref, `

`int`

`item)`

`{`

` `

`if`

`(isEmpty(*top_ref))`

` `

`push(top_ref, item);`

` `

`else`

` `

`{`

` `

`/* Hold all items in Function Call Stack until we`

` `

`reach end of the stack. When the stack becomes`

` `

`empty, the isEmpty(*top_ref)becomes true, the`

` `

`above if part is executed and the item is inserted`

` `

`at the bottom */`

` `

`int`

`temp = pop(top_ref);`

` `

`insertAtBottom(top_ref, item);`

` `

`/* Once the item is inserted at the bottom, push all`

` `

`the items held in Function Call Stack */`

` `

`push(top_ref, temp);`

` `

`}`

`}`

`// Below is the function that reverses the given stack using`

`// insertAtBottom()`

`void`

`reverse(`

`struct`

`sNode** top_ref)`

`{`

` `

`if`

`(!isEmpty(*top_ref))`

` `

`{`

` `

`/* Hold all items in Function Call Stack until we`

` `

`reach end of the stack */`

` `

`int`

`temp = pop(top_ref);`

` `

`reverse(top_ref);`

` `

`/* Insert all the items (held in Function Call Stack)`

` `

`one by one from the bottom to top. Every item is`

` `

`inserted at the bottom */`

` `

`insertAtBottom(top_ref, temp);`

` `

`}`

`}`

`Output:` Original Stack
1 2 3 4
Reversed Stack
4 3 2 1

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