# Merging and Sorting Two Unsorted Stacks

Given 2 input stacks with elements in an unsorted manner. Problem is to merge them into a new final stack, such that the elements become arranged in a sorted manner.

Examples:

```Input :  s1 : 9 4 2 1
s2: 8 17 3 10
Output : final stack: 1 2 3 4 8 9 10 17

Input :  s1 : 5 7 2 6 4
s2 : 12 9 3
Output : final stack: 2 3 4 5 6 7 9 12```

Create an empty stack to store result. We first insert elements of both stacks into the result. Then we sort the result stack

Implementation:

## C++

 `// C++ program to merge to unsorted stacks` `// into a third stack in sorted way.` `#include ` `using` `namespace` `std;`   `// Sorts input stack and returns sorted stack.` `stack<``int``> sortStack(stack<``int``>& input)` `{` `    ``stack<``int``> tmpStack;`   `    ``while` `(!input.empty()) {` `        ``// pop out the first element` `        ``int` `tmp = input.top();` `        ``input.pop();`   `        ``// while temporary stack is not empty and top` `        ``// of stack is greater than temp` `        ``while` `(!tmpStack.empty() && tmpStack.top() > tmp) {`   `            ``// pop from temporary stack and push` `            ``// it to the input stack` `            ``input.push(tmpStack.top());` `            ``tmpStack.pop();` `        ``}`   `        ``// push temp in temporary of stack` `        ``tmpStack.push(tmp);` `    ``}`   `    ``return` `tmpStack;` `}`   `stack<``int``> sortedMerge(stack<``int``>& s1, stack<``int``>& s2)` `{` `    ``// Push contents of both stacks in result` `    ``stack<``int``> res;` `    ``while` `(!s1.empty()) {` `        ``res.push(s1.top());` `        ``s1.pop();` `    ``}` `    ``while` `(!s2.empty()) {` `        ``res.push(s2.top());` `        ``s2.pop();` `    ``}`   `    ``// Sort the result stack.` `    ``return` `sortStack(res);` `}`   `// main function` `int` `main()` `{` `    ``stack<``int``> s1, s2;` `    ``s1.push(34);` `    ``s1.push(3);` `    ``s1.push(31);`   `    ``s2.push(1);` `    ``s2.push(12);` `    ``s2.push(23);`   `    ``// This is the temporary stack` `    ``stack<``int``> tmpStack = sortedMerge(s1, s2);` `    ``cout << ``"Sorted and merged stack :\n"``;`   `    ``while` `(!tmpStack.empty()) {` `        ``cout << tmpStack.top() << ``" "``;` `        ``tmpStack.pop();` `    ``}` `}`

## Java

 `// Java program to merge to unsorted stacks` `// into a third stack in sorted way.` `import` `java.io.*;` `import` `java.util.*;`   `public` `class` `GFG {` `    `  `    ``// This is the temporary stack` `    ``static` `Stack res = ``new` `Stack();` `    ``static` `Stack tmpStack = ``new` `Stack();` `    `  `    ``// Sorts input stack and returns ` `    ``// sorted stack.` `    ``static` `void` `sortStack(Stack input)` `    ``{` `        ``while` `(input.size() != ``0``) ` `        ``{` `            ``// pop out the first element` `            ``int` `tmp = input.peek();` `            ``input.pop();` `    `  `            ``// while temporary stack is not empty and` `            ``// top of stack is greater than temp` `            ``while` `(tmpStack.size() != ``0` `&&` `                            ``tmpStack.peek() > tmp)` `            ``{` `    `  `                ``// pop from temporary stack and push` `                ``// it to the input stack` `                ``input.push(tmpStack.peek());` `                ``tmpStack.pop();` `            ``}` `    `  `            ``// push temp in temporary of stack` `            ``tmpStack.push(tmp);` `        ``}` `    ``}` `    `  `    ``static` `void` `sortedMerge(Stack s1,` `                                ``Stack s2)` `    ``{` `        ``// Push contents of both stacks in result` `        ``while` `(s1.size() != ``0``) {` `            ``res.push(s1.peek());` `            ``s1.pop();` `        ``}` `        `  `        ``while` `(s2.size() != ``0``) {` `            ``res.push(s2.peek());` `            ``s2.pop();` `        ``}` `    `  `        ``// Sort the result stack.` `        ``sortStack(res);` `    ``}` `    `  `    ``// main function` `    ``public` `static` `void` `main(String args[])` `    ``{` `        ``Stack s1 = ``new` `Stack();` `        ``Stack s2 = ``new` `Stack();` `        ``s1.push(``34``);` `        ``s1.push(``3``);` `        ``s1.push(``31``);` `    `  `        ``s2.push(``1``);` `        ``s2.push(``12``);` `        ``s2.push(``23``);` `    `  `        ``sortedMerge(s1, s2);` `        ``System.out.println(``"Sorted and merged stack :"``);` `    `  `        ``while` `(tmpStack.size() != ``0``) {` `            ``System.out.print(tmpStack.peek() + ``" "``);` `            ``tmpStack.pop();` `        ``}` `    ``}` `}`   `// This code is contributed by Manish Shaw` `// (manishshaw1)`

## Python3

 `# Python3 program to merge to unsorted stacks` `# into a third stack in sorted way.`   `# Sorts input stack and returns ` `# sorted stack.` `def` `sortStack(``Input``):` `    ``tmpStack ``=` `[]` `  `  `    ``while` `len``(``Input``) !``=` `0``: ` `        ``# pop out the first element` `        ``tmp ``=` `Input``[``-``1``]` `        ``Input``.pop()` `  `  `        ``# while temporary stack is not empty and` `        ``# top of stack is greater than temp` `        ``while` `len``(tmpStack) !``=` `0` `and` `tmpStack[``-``1``] > tmp:` `            ``# pop from temporary stack and push` `            ``# it to the input stack` `            ``Input``.append(tmpStack[``-``1``])` `            ``tmpStack.pop()` `        ``# push temp in temporary of stack` `        ``tmpStack.append(tmp)` `    ``return` `tmpStack` `  `  `def` `sortedMerge(s1, s2):` `    ``# Push contents of both stacks in result` `    ``res ``=` `[]` `    ``while` `len``(s1) !``=``0` `:` `        ``res.append(s1[``-``1``])` `        ``s1.pop()` `    ``while` `len``(s2) !``=``0` `:` `        ``res.append(s2[``-``1``])` `        ``s2.pop()` `  `  `    ``# Sort the result stack.` `    ``return` `sortStack(res)`   `s1 ``=` `[]` `s2 ``=` `[]` `s1.append(``34``)` `s1.append(``3``)` `s1.append(``31``)`   `s2.append(``1``)` `s2.append(``12``)` `s2.append(``23``)`   `# This is the temporary stack` `tmpStack ``=` `[]` `tmpStack ``=` `sortedMerge(s1, s2)` `print``(``"Sorted and merged stack :"``)`   `while` `len``(tmpStack) !``=` `0` `:` `    ``print``(tmpStack[``-``1``], end ``=` `" "``)` `    ``tmpStack.pop()` `    `  `    ``# This code is contributed by decode2207.`

## C#

 `// C# program to merge to unsorted stacks` `// into a third stack in sorted way.` `using` `System;` `using` `System.Collections.Generic;`   `class` `GFG {` `    `  `    ``// Sorts input stack and returns ` `    ``// sorted stack.` `    ``static` `Stack<``int``> sortStack(``ref` `Stack<``int``> input)` `    ``{` `        ``Stack<``int``> tmpStack = ``new` `Stack<``int``>();` `    `  `        ``while` `(input.Count != 0) ` `        ``{` `            ``// pop out the first element` `            ``int` `tmp = input.Peek();` `            ``input.Pop();` `    `  `            ``// while temporary stack is not empty and` `            ``// top of stack is greater than temp` `            ``while` `(tmpStack.Count != 0 &&` `                              ``tmpStack.Peek() > tmp)` `            ``{` `    `  `                ``// pop from temporary stack and push` `                ``// it to the input stack` `                ``input.Push(tmpStack.Peek());` `                ``tmpStack.Pop();` `            ``}` `    `  `            ``// push temp in temporary of stack` `            ``tmpStack.Push(tmp);` `        ``}` `    `  `        ``return` `tmpStack;` `    ``}` `    `  `    ``static` `Stack<``int``> sortedMerge(``ref` `Stack<``int``> s1,` `                                  ``ref` `Stack<``int``> s2)` `    ``{` `        ``// Push contents of both stacks in result` `        ``Stack<``int``> res = ``new` `Stack<``int``>();` `        ``while` `(s1.Count!=0) {` `            ``res.Push(s1.Peek());` `            ``s1.Pop();` `        ``}` `        ``while` `(s2.Count!=0) {` `            ``res.Push(s2.Peek());` `            ``s2.Pop();` `        ``}` `    `  `        ``// Sort the result stack.` `        ``return` `sortStack(``ref` `res);` `    ``}` `    `  `    ``// main function` `    ``static` `void` `Main()` `    ``{` `        ``Stack<``int``> s1 = ``new` `Stack<``int``>();` `        ``Stack<``int``> s2 = ``new` `Stack<``int``>();` `        ``s1.Push(34);` `        ``s1.Push(3);` `        ``s1.Push(31);` `    `  `        ``s2.Push(1);` `        ``s2.Push(12);` `        ``s2.Push(23);` `    `  `        ``// This is the temporary stack` `        ``Stack<``int``> tmpStack = ``new` `Stack<``int``>();` `        ``tmpStack = sortedMerge(``ref` `s1,``ref` `s2);` `        ``Console.Write(``"Sorted and merged stack :\n"``);` `    `  `        ``while` `(tmpStack.Count!=0) {` `            ``Console.Write(tmpStack.Peek() + ``" "``);` `            ``tmpStack.Pop();` `        ``}` `    ``}` `}`   `// This code is contributed by Manish Shaw` `// (manishshaw1)`

## Javascript

 ``

Output

```Sorted and merged stack :
34 31 23 12 3 1 ```

Complexity Analysis:

• Time Complexity: O((n+m)2) where n and m are number of elements in both the stacks respectively.
• Auxiliary Space: O(n+m)

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