# Merge K Sorted Arrays and Print Sorted Output

## Given k sorted arrays of size n each, write a program to merge those arrays and prints the sorted output

### Example

INPUT :
arr[][] = {{1,5,7},{2,4,6},{3,10,13}}

OUTPUT :
{1,2,3,4,5,6,10,13}

Time Complexity : O(nklogk)

where k is the number of sorted arrays and n is the size of the array
In this method the main idea is using minheap

## Algorithm

1. Create an output array of size n*k

2. Create a min heap of size k and insert first element in all the arrays into the min heap

3. Initialize count = 0 and till count less than n*k.

1. Get the minimum element from heap(ie, root) and store it in output array ie,output[count]
2. Replace heap root with next element from the array from which the element is extracted. If the array doesn’t have any more elements, then replace root with infinite. After replacing the root, heapify the tree.

4. Print the output array.

## C++ Program

``````#include<iostream>
#include<limits.h>
#define n 3
using namespace std;

// A min heap node
struct MinHeapNode
{
int element; // The element to be stored
int i; // index of the array from which the element is taken
int j; // index of the next element to be picked from array
};

// Prototype of a utility function to swap two min heap nodes
void swap(MinHeapNode *x, MinHeapNode *y);

// A class for Min Heap
class MinHeap
{
MinHeapNode *harr; // pointer to array of elements in heap
int heap_size; // size of min heap
public:
// Constructor: creates a min heap of given size
MinHeap(MinHeapNode a[], int size);

// to heapify a subtree with root at given index
void MinHeapify(int );

// to get index of left child of node at index i
int left(int i) { return (2*i + 1); }

// to get index of right child of node at index i
int right(int i) { return (2*i + 2); }

// to get the root
MinHeapNode getMin() { return harr[0]; }

// to replace root with new node x and heapify() new root
void replaceMin(MinHeapNode x) { harr[0] = x;  MinHeapify(0); }
};

// 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.
int *mergeKSortedArrays(int arr[][n], int k)
{
int *output = new int[n*k];  // To store output array

// Create a min heap with k heap nodes.  Every heap node
// has first element of an array
MinHeapNode *harr = new MinHeapNode[k];
for (int i = 0; i < k; i++)
{
harr[i].element = arr[i][0]; // Store the first element
harr[i].i = i;  // index of array
harr[i].j = 1;  // Index of next element to be stored from array
}
MinHeap hp(harr, k); // Create the heap

// Now one by one get the minimum element from min
// heap and replace it with next element of its array
for (int count = 0; count < n*k; count++)
{
// Get the minimum element and store it in output
MinHeapNode root = hp.getMin();
output[count] = root.element;

// Find the next element that will replace current
// root of heap. The next element belongs to same
// array as the current root.
if (root.j < n)
{
root.element = arr[root.i][root.j];
root.j += 1;
}
// If root was the last element of its array
else root.element =  INT_MAX; //INT_MAX is for infinite

// Replace root with next element of array
hp.replaceMin(root);
}

return output;
}

// Standard Min Heap Methods
// Constructor: Builds a heap from a given array a[] of given size
MinHeap::MinHeap(MinHeapNode a[], int size)
{
heap_size = size;
harr = a;  // store address of array
int i = (heap_size - 1)/2;
while (i >= 0)
{
MinHeapify(i);
i--;
}
}

// A recursive method to heapify a subtree with root at given index
// This method assumes that the subtrees are already heapified
void MinHeap::MinHeapify(int i)
{
int l = left(i);
int r = right(i);
int smallest = i;
if (l < heap_size && harr[l].element < harr[i].element)
smallest = l;
if (r < heap_size && harr[r].element < harr[smallest].element)
smallest = r;
if (smallest != i)
{
swap(&harr[i], &harr[smallest]);
MinHeapify(smallest);
}
}

// A utility function to swap two elements
void swap(MinHeapNode *x, MinHeapNode *y)
{
MinHeapNode temp = *x;  *x = *y;  *y = temp;
}

// A utility function to print array elements
void printArray(int arr[], int size)
{
for (int i=0; i < size; i++)
cout << arr[i] << " ";
}

int main()
{
// Change n at the top to change number of elements
// in an array
int arr[][n] = {{1,5,7},{2,4,6},{3,10,13}} ;
int k = sizeof(arr)/sizeof(arr[0]);

int *output = mergeKSortedArrays(arr, k);

cout << "Merged array is " << endl;
printArray(output, n*k);

return 0;
}``````

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