Sort a stack using recursion
- Difficulty Level : Medium
- Last Updated : 28 Jun, 2022
Given a stack, sort it using recursion. Use of any loop constructs like while, for, etc is not allowed. We can only use the following ADT functions on Stack S:
is_empty(S) : Tests whether stack is empty or not. push(S) : Adds new element to the stack. pop(S) : Removes top element from the stack. top(S) : Returns value of the top element. Note that this function does not remove element from the stack.
Input: -3 <--- Top 14 18 -5 30 Output: 30 <--- Top 18 14 -3 -5
This problem is mainly a variant of Reverse stack using recursion.
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 in sorted order. Here sorted order is important.
We can use the below algorithm to sort stack elements:
sortStack(stack S) if stack is not empty: temp = pop(S); sortStack(S); sortedInsert(S, temp);
Below algorithm is to insert elements in sorted order:
sortedInsert(Stack S, element) if stack is empty OR element > top element push(S, elem) else temp = pop(S) sortedInsert(S, element) push(S, temp)
Let given stack be -3 <-- top of the stack 14 18 -5 30
Let us illustrate sorting of stack using the above example:
First pop all the elements from the stack and store popped element in the variable ‘temp’. After popping all the elements function’s stack frame will look like this:
temp = -3 --> stack frame #1 temp = 14 --> stack frame #2 temp = 18 --> stack frame #3 temp = -5 --> stack frame #4 temp = 30 --> stack frame #5
Now stack is empty and ‘insert_in_sorted_order()’ function is called and it inserts 30 (from stack frame #5) at the bottom of the stack. Now stack looks like the below:
30 <-- top of the stack
Now next element i.e. -5 (from stack frame #4) is picked. Since -5 < 30, -5 is inserted at the bottom of the stack. Now stack becomes:
30 <-- top of the stack -5
Next 18 (from stack frame #3) is picked. Since 18 < 30, 18 is inserted below 30. Now stack becomes:
30 <-- top of the stack 18 -5
Next 14 (from stack frame #2) is picked. Since 14 < 30 and 14 < 18, it is inserted below 18. Now stack becomes:
30 <-- top of the stack 18 14 -5
Now -3 (from stack frame #1) is picked, as -3 < 30 and -3 < 18 and -3 < 14, it is inserted below 14. Now stack becomes:
30 <-- top of the stack 18 14 -3 -5
Below is the implementation of the above algorithm.
Stack elements before sorting: -3 14 18 -5 30 Stack elements after sorting: 30 18 14 -3 -5
- Time Complexity: O(n2).
In the worst case for every sortstack(), sortedinsert() is called for ‘N’ times recursively for putting the element in the right place
- Auxiliary Space: O(N)
Use of stack data structure for storing values
Exercise: Modify the above code to reverse stack in descending order.
This article is contributed by Narendra Kangralkar. Please write comments if you find anything incorrect, or if you want to share more information about the topic discussed above.