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:
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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 more efficient approach will be discussed.
- Form two bitonic arrays by comparing the highest element of one array to the lowest element of the second array such that both arrays contain only those elements which are to be there after the sorting of both the arrays.
- Now, sort both the arrays 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 contain 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 approachclass 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 contain 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 2def nextGap(gap) : if (gap <= 1) : return 0; res = (gap // 2) + (gap % 2); return res;# Function to merge two sorted# arrays with O(1) extra spacedef 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 contain 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 codeif __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 approachusing 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 contain 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 |
Javascript
<script> // Javascript implementation of the approach // Reducing the gap by a factor of 2 function nextGap(gap) { if (gap <= 1) return 0; return (parseInt(gap / 2, 10) + (gap % 2)); } // Function to merge two sorted // arrays with O(1) extra space function mergeTwoSortedArray(arr1, arr2, n, m) { let x = Math.min(n, m); // Form both arrays to be bitonic for (let i = 0; i < x; i++) { if (arr1[n - i - 1] > arr2[i]) { let temp = arr1[n - i - 1]; arr1[n - i - 1] = arr2[i]; arr2[i] = temp; } } // Now both the arrays contain the numbers // which should be there in the result // Sort the array indiviually by inplace algo for (let gap = nextGap(n); gap > 0; gap = nextGap(gap)) { // Comparing elements in the first array for (let i = 0; i + gap < n; i++) if (arr1[i] > arr1[i + gap]) { let temp = arr1[i]; arr1[i] = arr1[i + gap]; arr1[i + gap] = temp; } } // Sort the second array for (let gap = nextGap(m); gap > 0; gap = nextGap(gap)) { // Comparing elements in the second array for (let i = 0; i + gap < m; i++) if (arr2[i] > arr2[i + gap]) { let temp = arr2[i]; arr2[i] = arr2[i + gap]; arr2[i + gap] = temp; } } for (let i = 0; i < n; i++) document.write(arr1[i] + " "); for (let j = 0; j < m; j++) document.write(arr2[j] + " "); } let arr1 = [ 1, 5, 9, 10, 15, 20 ]; let n = arr1.length; let arr2 = [ 2, 3, 8, 13 ]; let m = arr2.length; mergeTwoSortedArray(arr1, arr2, n, m); </script> |
Output:
1 2 3 5 8 9 10 13 15 20
Time Complexity: O(Nlog(N) + Mlog(M))
