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 20

Input: arr1[] = {4, 9, 15, 20}, arr2[] = {2, 6, 7, 13}
Output: 2 4 6 7 9 13 15 20

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `using` `namespace` `std; ` ` `  `// Reducing the gap by a factor of 2 ` `int` `nextGap(``int` `gap) ` `{ ` `    ``if` `(gap <= 1) ` `        ``return` `0; ` `    ``return` `(gap / 2) + (gap % 2); ` `} ` ` `  `// Function to merge two sorted ` `// arrays with O(1) extra space ` `int` `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 code ` `int` `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))

GeeksforGeeks has prepared a complete interview preparation course with premium videos, theory, practice problems, TA support and many more features. Please refer Placement 100 for details

My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Improved By : AnkitRai01

Article Tags :
Practice Tags :

1

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.