Merge k sorted arrays | DSA | Bottom-Up Approach | C++

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Given k sorted arrays of size n each, merge them and print the sorted output. Example:

Input: k = 3, n = 4 arr[][] = { {1, 3, 5, 7}, {2, 4, 6, 8}, {0, 9, 10, 11}} ; Output: 0 1 2 3 4 5 6 7 8 9 10 11 Explanation: The output array is a sorted array that contains all the elements of the input matrix. Input: k = 3, n = 4 arr[][] = { {1, 5, 6, 8}, {2, 4, 10, 12}, {3, 7, 9, 11}, {13, 14, 15, 16}} ; Output: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Explanation: The output array is a sorted array that contains all the elements of the input matrix.

Solution:


#include<bits/stdc++.h>
using namespace std;
#define n 4

// Merge arr1[0..n1-1] and arr2[0..n2-1] into 
// arr3[0..n1+n2-1] 
void mergeArrays(int arr1[], int arr2[], int n1, 
                            int n2, int arr3[]) 
{ 
    int i = 0, j = 0, k = 0; 

    // Traverse both array 
    while (i<n1 && j <n2) 
    { 
        // Check if current element of first array is smaller than current element 
        // of second array. If yes, store first array element and increment first array index. 
        // Otherwise do same with second array 
        if (arr1[i] < arr2[j]) 
            arr3[k++] = arr1[i++]; 
        else
            arr3[k++] = arr2[j++]; 
    } 

    // Store remaining elements of first array 
    while (i < n1) 
        arr3[k++] = arr1[i++]; 

    // Store remaining elements of second array 
    while (j < n2) 
        arr3[k++] = arr2[j++]; 
}

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

// 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.
void mergeKArrays(int arr[][n],int i,int j, int output[])
{
    //if one array is in range
    if(i==j)
    {
        for(int p=0; p < n; p++)
        output[p]=arr[i][p];
        return;
    }

    //if only two arrays are left them merge them 
    if(j-i==1)
    {
        mergeArrays(arr[i],arr[j],n,n,output);
        return;
    }

    //output arrays 
    int out1[n*(((i+j)/2)-i+1)],out2[n*(j-((i+j)/2))];

    //divide the array into halves
    mergeKArrays(arr,i,(i+j)/2,out1);
    mergeKArrays(arr,(i+j)/2+1,j,out2);

    //merge the output array
    mergeArrays(out1,out2,n*(((i+j)/2)-i+1),n*(j-((i+j)/2)),output);

}


// Driver program to test above functions
int main()
{
    // Change n at the top to change number of elements
    // in an array
    int arr[][n] = {{2, 6, 12, 34},
                    {1, 9, 20, 1000},
                    {23, 34, 90, 2000}};
    int k = sizeof(arr)/sizeof(arr[0]);
    int output[n*k];
    mergeKArrays(arr,0,2, output);

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

    return 0;
}

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