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# Merge k sorted arrays | Set 2 (Different Sized Arrays)

• Difficulty Level : Medium
• Last Updated : 09 Sep, 2022

Given k sorted arrays of possibly different sizes, merge them and print the sorted output.
Examples:

```Input: k = 3
arr[][] = { {1, 3},
{2, 4, 6},
{0, 9, 10, 11}} ;
Output: 0 1 2 3 4 6 9 10 11

Input: k = 2
arr[][] = { {1, 3, 20},
{2, 4, 6}} ;
Output: 1 2 3 4 6 20 ```

We have discussed a solution that works for all arrays of the same size in Merge k sorted arrays | Set 1.
A simple solution is to create an output array and one by one copy all k arrays to it. Finally, sort the output array. This approach takes O(N Log N) time where N is the count of all elements.
An efficient solution is to use a heap data structure. The time complexity of the heap-based solution is O(N Log k).
1. Create an output array.
2. Create a min-heap of size k and insert 1st element in all the arrays into the heap
3. Repeat the following steps while the priority queue is not empty.
…..a) Remove the minimum element from the heap (minimum is always at the root) and store it in the output array.
…..b) Insert the next element from the array from which the element is extracted. If the array doesn’t have any more elements, then do nothing.

Below is the implementation of the above approach:

## C++

 `// C++ program to merge k sorted arrays``// of size n each.``#include ``using` `namespace` `std;` `// A pair of pairs, first element is going to``// store value, second element index of array``// and third element index in the array.``typedef` `pair<``int``, pair<``int``, ``int``> > ppi;` `// This function takes an array of arrays as an``// argument and all arrays are assumed to be``// sorted. It merges them together and prints``// the final sorted output.``vector<``int``> mergeKArrays(vector > arr)``{``    ``vector<``int``> output;` `    ``// Create a min heap with k heap nodes. Every``    ``// heap node has first element of an array``    ``priority_queue, greater > pq;` `    ``for` `(``int` `i = 0; i < arr.size(); i++)``        ``pq.push({ arr[i], { i, 0 } });` `    ``// Now one by one get the minimum element``    ``// from min heap and replace it with next``    ``// element of its array``    ``while` `(pq.empty() == ``false``) {``        ``ppi curr = pq.top();``        ``pq.pop();` `        ``// i ==> Array Number``        ``// j ==> Index in the array number``        ``int` `i = curr.second.first;``        ``int` `j = curr.second.second;` `        ``output.push_back(curr.first);` `        ``// The next element belongs to same array as``        ``// current.``        ``if` `(j + 1 < arr[i].size())``            ``pq.push({ arr[i][j + 1], { i, j + 1 } });``    ``}` `    ``return` `output;``}` `// Driver program to test above functions``int` `main()``{``    ``// Change n at the top to change number``    ``// of elements in an array``    ``vector > arr{ { 2, 6, 12 },``                            ``{ 1, 9 },``                            ``{ 23, 34, 90, 2000 } };` `    ``vector<``int``> output = mergeKArrays(arr);` `    ``cout << ``"Merged array is "` `<< endl;``    ``for` `(``auto` `x : output)``        ``cout << x << ``" "``;` `    ``return` `0;``}`

## Java

 `/*package whatever //do not write package name here */` `import` `java.util.ArrayList;``import` `java.util.PriorityQueue;` `public` `class` `MergeKSortedArrays {``    ``private` `static` `class` `HeapNode``        ``implements` `Comparable {``        ``int` `x;``        ``int` `y;``        ``int` `value;` `        ``HeapNode(``int` `x, ``int` `y, ``int` `value)``        ``{``            ``this``.x = x;``            ``this``.y = y;``            ``this``.value = value;``        ``}` `        ``@Override` `public` `int` `compareTo(HeapNode hn)``        ``{``            ``if` `(``this``.value <= hn.value) {``                ``return` `-``1``;``            ``}``            ``else` `{``                ``return` `1``;``            ``}``        ``}``    ``}` `    ``// Function to merge k sorted arrays.``    ``public` `static` `ArrayList``    ``mergeKArrays(``int``[][] arr, ``int` `K)``    ``{``        ``ArrayList result``            ``= ``new` `ArrayList();``        ``PriorityQueue heap``            ``= ``new` `PriorityQueue();` `        ``// Initially add only first column of elements. First``        ``// element of every array``        ``for` `(``int` `i = ``0``; i < arr.length; i++) {``            ``heap.add(``new` `HeapNode(i, ``0``, arr[i][``0``]));``        ``}` `        ``HeapNode curr = ``null``;``        ``while` `(!heap.isEmpty()) {``            ``curr = heap.poll();``            ``result.add(curr.value);` `            ``// Check if next element of curr min exists,``            ``// then add that to heap.``            ``if` `(curr.y < (arr[curr.x].length - ``1``)) {``                ``heap.add(``                    ``new` `HeapNode(curr.x, curr.y + ``1``,``                                 ``arr[curr.x][curr.y + ``1``]));``            ``}``        ``}` `        ``return` `result;``    ``}` `    ``public` `static` `void` `main(String[] args)``    ``{` `        ``int``[][] arr = { { ``2``, ``6``, ``12` `},``                            ``{ ``1``, ``9` `},``                            ``{ ``23``, ``34``, ``90``, ``2000` `} };``        ``System.out.println(``            ``MergeKSortedArrays.mergeKArrays(arr, arr.length)``                ``.toString());``    ``}``}``// This code has been contributed by Manjunatha KB`

## Python3

 `# Python code to implement the approach` `import` `heapq` `# Merge function merge two arrays``# of different or same length``# if n = max(n1, n2)``# time complexity of merge is (o(n log(n)))` `# Function for meging k arrays``def` `mergeK(arr, k):``    ``res ``=` `[]``    ` `    ``# Declaring min heap``    ``h ``=` `[]``    ` `    ``# Inserting the first elements of each row``    ``for` `i ``in` `range``(``len``(arr)):``        ``heapq.heappush(h, (arr[i][``0``], i, ``0``))``        ` `    ``# Loop to merge all the arrays``    ``while` `h:``      ` `        ``# ap stores the row number,``        ``# vp stores the column number``        ``val, ap, vp ``=` `heapq.heappop(h)``        ``res.append(val)``        ``if` `vp``+``1` `< ``len``(arr[ap]):``            ``heapq.heappush(h, (arr[ap][vp``+``1``], ap, vp``+``1``))``    ``return` `res       ``        `  `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ``arr ``=``[[``2``, ``6``, ``12` `],``          ``[ ``1``, ``9` `],``          ``[``23``, ``34``, ``90``, ``2000` `]]``    ``k ``=` `3``    ``l ``=` `mergeK(arr, k)``    ``print``(``*``l)`

## C#

 `// C# program to merge k sorted arrays``// of size n each.``using` `System;``using` `System.Collections.Generic;``class` `GFG``{` `    ``// This function takes an array of arrays as an``    ``// argument and all arrays are assumed to be``    ``// sorted. It merges them together and prints``    ``// the final sorted output.``    ``static` `List<``int``> mergeKArrays(List> arr)``    ``{``        ``List<``int``> output = ``new` `List<``int``>();``    ` `        ``// Create a min heap with k heap nodes. Every``        ``// heap node has first element of an array``        ``List>> pq =``        ``new` `List>>();``    ` `        ``for` `(``int` `i = 0; i < arr.Count; i++)``            ``pq.Add(``new` `Tuple<``int``,``                ``Tuple<``int``,``int``>>(arr[i],``                                ``new` `Tuple<``int``,``int``>(i, 0)));``            ` `        ``pq.Sort();``    ` `        ``// Now one by one get the minimum element``        ``// from min heap and replace it with next``        ``// element of its array``        ``while` `(pq.Count > 0) {``            ``Tuple<``int``,Tuple<``int``,``int``>> curr = pq;``            ``pq.RemoveAt(0);``    ` `            ``// i ==> Array Number``            ``// j ==> Index in the array number``            ``int` `i = curr.Item2.Item1;``            ``int` `j = curr.Item2.Item2;``    ` `            ``output.Add(curr.Item1);``    ` `            ``// The next element belongs to same array as``            ``// current.``            ``if` `(j + 1 < arr[i].Count)``            ``{``                ``pq.Add(``new` `Tuple<``int``,Tuple<``int``,``int``>>(arr[i][j + 1],``                                                    ``new` `Tuple<``int``,``int``>(i, j + 1)));``                ``pq.Sort();``            ``}``        ``}``        ``return` `output;``    ``}``    ` `// Driver code``static` `void` `Main()``{``    ` `    ``// Change n at the top to change number``    ``// of elements in an array``    ``List> arr = ``new` `List>();``    ``arr.Add(``new` `List<``int``>(``new` `int``[]{2, 6, 12}));``    ``arr.Add(``new` `List<``int``>(``new` `int``[]{1, 9}));``    ``arr.Add(``new` `List<``int``>(``new` `int``[]{23, 34, 90, 2000}));` `    ``List<``int``> output = mergeKArrays(arr);` `    ``Console.WriteLine(``"Merged array is "``);``    ``foreach``(``int` `x ``in` `output)``        ``Console.Write(x + ``" "``);``}``}` `// This code is contributed by divyeshrabadiya07.`

Output

```Merged array is
1 2 6 9 12 23 34 90 2000 ```

Time Complexity: O(N Log k)
Auxiliary Space: O(N)

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