Merge Two Sorted Arrays Without Extra Space

Problem Statement

We are given two sorted arrays, our task is to merge two sorted arrays in a sorted manner.

Examples:

Input: vec1[] = { 1, 3, 4, 5}, vec2[] = {2, 4, 6, 8}
Output: vec3[] = {1, 2, 3, 4, 4, 5, 6, 8}

Input : vec1[]= {-7,12,17,29,41,56,79} , vec2[]= {-9,-3,0,5,19}
Output: {-9,-7,-3,0,5,12,17,19,29,41,56,79}
Explanation:  If we merge both arrays in a sorted fashion then the resultant array will be sorted array as above.

Method 1

INTUITION: We can see the given arrays are sorted. Now our target is to make a sorted array from merging of both the arrays so if we will put the smallest element always in the front of the final array then we can make our sorted array. So to choose which element is smaller we can just simply compare the front elements of both the arrays.

Algorithm

• Create an array vec3[] of size n1 + n2.
• Simultaneously traverse vec1[] and vec2[]. 
• Pick smaller of the current elements in vec1[] and vec2[], copy this smaller element to the next position in vec3[] and move ahead in vec3[] and the array whose element is picked.
• If there are remaining elements in vec1[] or vec2[], copy them also in vec3[].

C++ Implementation

void mergeArrays(int vec1[], int vec2[], int n1,
  int n2, int vec3[]) {
  int i = 0, j = 0, k = 0;

  while (i < n1 && j < n2) {

    if (vec1[i] < vec2[j])
      vec3[k++] = vec1[i++];
    else
      vec3[k++] = vec2[j++];
  }

  while (i < n1)
    vec3[k++] = vec1[i++];

  while (j < n2)
    vec3[k++] = vec2[j++];
}

Java Implementation

public static void mergeArrays(int[] vec1, int[] vec2, int n1,
  int n2, int[] vec3) {
  int i = 0, j = 0, k = 0;
  while (i < n1 && j < n2) {
    if (vec1[i] < vec2[j])
      vec3[k++] = vec1[i++];
    else
      vec3[k++] = vec2[j++];
  }
  while (i < n1)
    vec3[k++] = vec1[i++];
  while (j < n2)
    vec3[k++] = vec2[j++];
}

Python Implementation

def mergeArrays(vec1, vec2, n1, n2):
    vec3 = [None] * (n1 + n2)
    i = 0
    j = 0
    k = 0
    while i < n1 and j < n2:
        if vec1[i] < vec2[j]:
            vec3[k] = vec1[i]
            k = k + 1
            i = i + 1
        else:
            vec3[k] = vec2[j]
            k = k + 1
            j = j + 1
    while i < n1:
        vec3[k] = vec1[i];
        k = k + 1
        i = i + 1
    while j < n2:
        vec3[k] = vec2[j];
        k = k + 1
        j = j + 1

Time Complexity:O(n1 * n2) where n1 and n2 are the sizes of two arrays.
Space Complexity:O(n1+n2) where n1 and n2 are the sizes of two arrays.

Merging Without Using Extra Space

While iterating over the two sorted arrays parallelly, if we encounter the jth second array element is smaller than ith first array element, then the jth element is to be included and replace some kth element in the first array.

Algorithm

• Initialize i,j,k as 0,0,n-1 where n is size of vec1 
• Iterate through every element of vec1 and vec2 using two pointers i and j respectively

if vec1[i] is less than vec2[j]
        increment i
    else
        swap the vec2[j] and vec1[k]
        increment j and decrement k

• Sort both vec1 and vec2.

C++ Code

void merge(int vec1[], int vec2[], int n, int m) {
  int i = 0, j = 0, k = n - 1;
  while (i <= k && j < m) {
    if (vec1[i] < vec2[j])
      i++;
    else {
      swap(vec2[j++], vec1[k--]);
    }
  }

  sort(vec1, vec1 + n);
  sort(vec2, vec2 + m);
}

Java Code

static void merge(int m, int n)
{
    int i = 0, j = 0, k = n - 1;
    while (i <= k && j < m) {
        if (vec1[i] < vec2[j])
            i++;
        else {
            int temp = vec2[j];
            vec2[j] = vec1[k];
            vec1[k] = temp;
            j++;
            k--;
        }
    }
    Arrays.sort(vec1);
    Arrays.sort(vec2);
}

Python Code

def merge(self, nums1, m, nums2, n):
        while m > 0 and n > 0:
            if nums1[m-1] >= nums2[n-1]:
                nums1[m+n-1] = nums1[m-1]
                m -= 1
            else:
                nums1[m+n-1] = nums2[n-1]
                n -= 1
        if n > 0:
            nums1[:n] = nums2[:n]

Time Complexity:O((n+m)log(n+m)) where n and m are the sizes of two arrays.
Space Complexity:O(1).

Practice Question

Merge 2 Sorted Lists
Merge K Sorted Arrays

FAQs

Why does merge sort require extra space?
When we are merging two arrays then for merging we need one more additional space to create the array.

Is Quicksort faster than mergesort?
Merge sort is more efficient and works faster than quicksort in the case of a larger size of array. Quicksort is more efficient and works faster than merge sort in case of the smaller size of an array.