Skip to content
Related Articles

Related Articles

Merge k sorted arrays | Set 2 (Different Sized Arrays)
  • Difficulty Level : Medium
  • Last Updated : 16 Feb, 2021

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

C++




// C++ program to merge k sorted arrays
// of size n each.
#include <bits/stdc++.h>
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<vector<int> > arr)
{
    vector<int> output;
 
    // Create a min heap with k heap nodes. Every
    // heap node has first element of an array
    priority_queue<ppi, vector<ppi>, greater<ppi> > pq;
 
    for (int i = 0; i < arr.size(); i++)
        pq.push({ arr[i][0], { 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<vector<int> > 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;
}


Python




# merge function merge two arrays
# of different or same length
# if n = max(n1, n2)
# time complexity of merge is (o(n log(n)))
 
from heapq import merge
 
# function for meging k arrays
def mergeK(arr, k):
     
    l = arr[0]
    for i in range(k-1):
         
        # when k = 0 it merge arr[1]
        # with arr[0] here in l arr[0]
        # is stored
        l = list(merge(l, arr[i + 1]))
    return l
 
# for printing array
def printArray(arr):
    print(*arr)
 
 
# driver code
arr =[[2, 6, 12 ],
    [ 1, 9 ],
    [23, 34, 90, 2000 ]]
k = 3
 
l = mergeK(arr, k)
 
printArray(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<List<int>> 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<Tuple<int,Tuple<int,int>>> pq =
          new List<Tuple<int,Tuple<int,int>>>();
       
        for (int i = 0; i < arr.Count; i++)
            pq.Add(new Tuple<int,
                   Tuple<int,int>>(arr[i][0],
                                   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[0];
            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<List<int>> arr = new List<List<int>>();
    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

 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.




My Personal Notes arrow_drop_up
Recommended Articles
Page :