Efficiently merging two sorted arrays with O(1) extra space and O(NlogN + MlogM)
Given two sorted arrays arr1[] and arr2[], the task is to merge them in O(Nlog(N) + Mlog(M)) time with O(1) extra space into a sorted array where N is the size of the first array arr1[] and M is the size of the second array arr2[].
Examples:
Input: arr1[] = {1, 5, 9, 10, 15, 20}, arr2[] = {2, 3, 8, 13}
Output: 1 2 3 5 8 9 10 13 15 20Input: arr1[] = {4, 9, 15, 20}, arr2[] = {2, 6, 7, 13}
Output: 2 4 6 7 9 13 15 20
Approach: An approach has already been discussed in this article. In this article, an even efficient approach will be discussed.
- Form two bitonic arrays by comparing the highest element from one array to the lowest element of the second array such that both arrays contain only those elements which are to be there in after the sorting of both the array.
- Now, sort both the array separately.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach #include <iostream>using namespace std; // Reducing the gap by a factor of 2int nextGap(int gap){ if (gap <= 1) return 0; return (gap / 2) + (gap % 2);} // Function to merge two sorted// arrays with O(1) extra spaceint mergeTwoSortedArray(int* arr1, int* arr2, int n, int m){ int x = min(n, m); // Form both arrays to be bitonic for (int i = 0; i < x; i++) { if (arr1[n - i - 1] > arr2[i]) swap(arr1[n - i - 1], arr2[i]); } // Now both the arrays conatin the numbers // which should be there in the result // Sort the array indiviually by inplace algo for (int gap = nextGap(n); gap > 0; gap = nextGap(gap)) { // Comparing elements in the first array for (int i = 0; i + gap < n; i++) if (arr1[i] > arr1[i + gap]) swap(arr1[i], arr1[i + gap]); } // Sort the second array for (int gap = nextGap(m); gap > 0; gap = nextGap(gap)) { // Comparing elements in the second array for (int i = 0; i + gap < m; i++) if (arr2[i] > arr2[i + gap]) swap(arr2[i], arr2[i + gap]); } for (int i = 0; i < n; i++) cout << arr1[i] << " "; for (int j = 0; j < m; j++) cout << arr2[j] << " ";} // Driver codeint main(){ int arr1[] = { 1, 5, 9, 10, 15, 20 }; int n = sizeof(arr1) / sizeof(int); int arr2[] = { 2, 3, 8, 13 }; int m = sizeof(arr2) / sizeof(int); mergeTwoSortedArray(arr1, arr2, n, m); return 0;} |
Java
// Java implementation of the approach class GFG { // Reducing the gap by a factor of 2 static int nextGap(int gap) { if (gap <= 1) return 0; return (int)((gap / 2) + (gap % 2)); } // Function to merge two sorted // arrays with O(1) extra space static void mergeTwoSortedArray(int []arr1, int []arr2, int n, int m) { int x = Math.min(n, m); // Form both arrays to be bitonic for (int i = 0; i < x; i++) { if (arr1[n - i - 1] > arr2[i]) { // swap(arr1[n - i - 1], arr2[i]); int temp = arr1[n - i - 1]; arr1[n - i - 1] = arr2[i]; arr2[i] = temp; } } // Now both the arrays conatin the numbers // which should be there in the result // Sort the array indiviually by inplace algo for (int gap = nextGap(n); gap > 0; gap = nextGap(gap)) { // Comparing elements in the first array for (int i = 0; i + gap < n; i++) if (arr1[i] > arr1[i + gap]) { // swap(arr1[i], arr1[i + gap]); int temp = arr1[i]; arr1[i] = arr1[i + gap]; arr1[i + gap] = temp; } } // Sort the second array for (int gap = nextGap(m); gap > 0; gap = nextGap(gap)) { // Comparing elements in the second array for (int i = 0; i + gap < m; i++) if (arr2[i] > arr2[i + gap]) { // swap(arr2[i], arr2[i + gap]); int temp = arr2[i]; arr2[i] = arr2[i + gap]; arr2[i + gap] = temp; } } for (int i = 0; i < n; i++) System.out.print(arr1[i] + " "); for (int j = 0; j < m; j++) System.out.print(arr2[j] + " "); } // Driver code public static void main (String[] args) { int arr1[] = { 1, 5, 9, 10, 15, 20 }; int n = arr1.length; int arr2[] = { 2, 3, 8, 13 }; int m = arr2.length; mergeTwoSortedArray(arr1, arr2, n, m); } } // This code is contributed by AnkitRai01 |
Python3
# Python3 implementation of the approach # Reducing the gap by a factor of 2 def nextGap(gap) : if (gap <= 1) : return 0; res = (gap // 2) + (gap % 2); return res; # Function to merge two sorted # arrays with O(1) extra space def mergeTwoSortedArray(arr1, arr2, n, m) : x = min(n, m); # Form both arrays to be bitonic for i in range(x) : if (arr1[n - i - 1] > arr2[i]) : arr1[n - i - 1],arr2[i] = arr2[i], arr1[n- i - 1]; # Now both the arrays conatin the numbers # which should be there in the result # Sort the array indiviually by inplace algo gap = nextGap(n); while gap > 0 : # Comparing elements in the first array i = 0; while i + gap < n : if (arr1[i] > arr1[i + gap]) : arr1[i], arr1[i + gap] = arr1[i + gap],arr1[i]; i += 1; gap = nextGap(gap) # Sort the second array gap = nextGap(m); while gap > 0 : # Comparing elements in the second array i = 0 while i + gap < m : if (arr2[i] > arr2[i + gap]) : arr2[i], arr2[i + gap] = arr2[i + gap], arr2[i]; i += 1; gap = nextGap(gap) for i in range(n) : print(arr1[i], end = " "); for j in range(m) : print(arr2[j], end = " "); # Driver code if __name__ == "__main__" : arr1 = [ 1, 5, 9, 10, 15, 20 ]; n = len(arr1); arr2 = [ 2, 3, 8, 13 ]; m = len(arr2); mergeTwoSortedArray(arr1, arr2, n, m); # This code is contributed by AnkitRai01 |
C#
// C# implementation of the approach using System; class GFG { // Reducing the gap by a factor of 2 static int nextGap(int gap) { if (gap <= 1) return 0; return (int)((gap / 2) + (gap % 2)); } // Function to merge two sorted // arrays with O(1) extra space static void mergeTwoSortedArray(int []arr1, int []arr2, int n, int m) { int x = Math.Min(n, m); // Form both arrays to be bitonic for (int i = 0; i < x; i++) { if (arr1[n - i - 1] > arr2[i]) { int temp = arr1[n - i - 1]; arr1[n - i - 1] = arr2[i]; arr2[i] = temp; } } // Now both the arrays conatin the numbers // which should be there in the result // Sort the array indiviually by inplace algo for (int gap = nextGap(n); gap > 0; gap = nextGap(gap)) { // Comparing elements in the first array for (int i = 0; i + gap < n; i++) if (arr1[i] > arr1[i + gap]) { int temp = arr1[i]; arr1[i] = arr1[i + gap]; arr1[i + gap] = temp; } } // Sort the second array for (int gap = nextGap(m); gap > 0; gap = nextGap(gap)) { // Comparing elements in the second array for (int i = 0; i + gap < m; i++) if (arr2[i] > arr2[i + gap]) { int temp = arr2[i]; arr2[i] = arr2[i + gap]; arr2[i + gap] = temp; } } for (int i = 0; i < n; i++) Console.Write(arr1[i] + " "); for (int j = 0; j < m; j++) Console.Write(arr2[j] + " "); } // Driver code public static void Main() { int []arr1 = { 1, 5, 9, 10, 15, 20 }; int n = arr1.Length; int []arr2 = { 2, 3, 8, 13 }; int m = arr2.Length; mergeTwoSortedArray(arr1, arr2, n, m); } } // This code is contributed by AnkitRai01 |
Output:
1 2 3 5 8 9 10 13 15 20
Time Complexity: O(Nlog(N) + Mlog(M))
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.
