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)

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.

C

// C program to reverse a stack using recursion
#include<stdio.h>
#include<stdlib.h>
#define bool int

/* structure of a stack node */
struct sNode
{
    char data;
    struct sNode *next;
};

/* Function Prototypes */
void push(struct sNode** top_ref, int new_data);
int pop(struct sNode** top_ref);
bool isEmpty(struct sNode* top);
void print(struct sNode* top);

// 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);
    }
}

/* Driveer program to test above functions */
int main()
{
    struct sNode *s = NULL;
    push(&s, 4);
    push(&s, 3);
    push(&s, 2);
    push(&s, 1);

    printf("\n Original Stack ");
    print(s);
    reverse(&s);
    printf("\n Reversed Stack ");
    print(s);
    return 0;
}

/* Function to check if the stack is empty */
bool isEmpty(struct sNode* top)
{
    return (top == NULL)? 1 : 0;
}

/* Function to push an item to stack*/
void push(struct sNode** top_ref, int new_data)
{
    /* allocate node */
    struct sNode* new_node =
        (struct sNode*) malloc(sizeof(struct sNode));

    if (new_node == NULL)
    {
        printf("Stack overflow \n");
        exit(0);
    }

    /* put in the data  */
    new_node->data  = new_data;

    /* link the old list off the new node */
    new_node->next = (*top_ref);

    /* move the head to point to the new node */
    (*top_ref)    = new_node;
}

/* Function to pop an item from stack*/
int pop(struct sNode** top_ref)
{
    char res;
    struct sNode *top;

    /*If stack is empty then error */
    if (*top_ref == NULL)
    {
        printf("Stack overflow \n");
        exit(0);
    }
    else
    {
        top = *top_ref;
        res = top->data;
        *top_ref = top->next;
        free(top);
        return res;
    }
}

/* Functrion to pront a linked list */
void print(struct sNode* top)
{
    printf("\n");
    while (top != NULL)
    {
        printf(" %d ", top->data);
        top =  top->next;
    }
}

Python

# Python program to reverse a stack using recursion

# Below is a recursive function that inserts an element
# at the bottom of a stack.
def insertAtBottom(stack, item):
	if isEmpty(stack):
		push(stack, item)
	else:
		temp = pop(stack)
		insertAtBottom(stack, item)
		push(stack, temp)

# Below is the function that reverses the given stack
# using insertAtBottom()
def reverse(stack):
	if not isEmpty(stack):
		temp = pop(stack)
		reverse(stack)
		insertAtBottom(stack, temp)

# Below is a complete running program for testing above
# functions.

# Function to create a stack. It initializes size of stack
# as 0
def createStack():
	stack = []
	return stack

# Function to check if the stack is empty
def isEmpty( stack ):
	return len(stack) == 0

#Function to push an item to stack
def push( stack, item ):
	stack.append( item )

# Function to pop an item from stack
def pop( stack ):

	#If stack is empty then error
	if(isEmpty( stack )):
		print("Stack Underflow ")
		exit(1)

	return stack.pop()

# Function to print the stack
def prints(stack):
	for i in range(len(stack)-1, -1, -1):
		print(stack[i], end = ' ')
	print()

# Driver program to test above functions

stack = createStack()
push( stack, str(4) )
push( stack, str(3) )
push( stack, str(2) )
push( stack, str(1) )
print("Original Stack ")
prints(stack)

reverse(stack)

print("Reversed Stack ")
prints(stack)

# This code is contributed by Sunny Karira


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

Please write comments if you find any bug in above code/algorithm, or find other ways to solve the same problem.

GATE CS Corner    Company Wise Coding Practice





Writing code in comment? Please use code.geeksforgeeks.org, generate link and share the link here.