# How to Merge Two Sorted Arrays

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# Problem

You are given two sorted arrays A and B of lengths m and **n**, the task is to merge the two sorted arrays in such a way that the merged array is also sorted.

# Example

InputA[] = {3, 9, 10, 18, 23}B[] = {5, 12, 15, 20, 21, 25}OutputMerged[] = {3, 5, 9, 10, 12, 15, 18, 20, 21, 23, 25}ExplanationThe merged array is of the size of n + m and contains both the elements of array A and array B in sorted orderInput:A[] = { 5, 8, 9}B[] = {4, 7, 8}Output:Merged[] = {4, 5, 7, 8, 8, 9}ExplanationThe merged array is of the size of n + m and contains both the elements of array A and array B in sorted order

# Index

- Brute Force Approach
- Insertion Sort Approach
- Efficient Approach — Using Merge Sort

# Brute Force Approach

The idea is to create a new array C[] of length m+n and put all the elements from A[] and B[] in it and then sort them using Arrays.sort().

# Algorithm

- Create an array C of n+m size to store the merged array
- Put the values of both A and B arrays using a for loop
- Sort the C array using Array..sort().

# Pseudo Code

Int[] solve(int[] A, int[] B, int n, int m) {Create a new array C of n+m sizewhile(i<n) {C[k++] = A[i++];}while(j<m) {C[k++] = B[j++];}Sort C;return C}

# Output

`Array after merging - 1 2 3 4 5 6 7 8`

**Time Complexity — **O((m+n) log(m+n))

We have sorted an array of size m+n using Arrays.sort(), and the time complexity of this operation is O(n log n) which in this case becomes O((m+n )log(m+n))

**Space Complexity — **O(m+n)

We have created a new array C of size n+m which will store the merged sorted array.