Sort an array when two halves are sorted

Given an integer array of which both first half and second half are sorted. Task is to merge two sorted halves of array into single sorted array.

Examples:

```Input : A[] = { 2, 3, 8, -1, 7, 10 }
Output : -1, 2, 3, 7, 8, 10

Input : A[] = {-4, 6, 9, -1, 3 }
Output : -4, -1, 3, 6, 9```

Method 1: A Simple Solution is to sort the array using built in functions (generally an implementation of quick sort).
Below is the implementation of above method:

C++

 `// C++ program to Merge two sorted halves of ``// array Into Single Sorted Array ``#include ``using` `namespace` `std; `` ` `void` `mergeTwoHalf(``int` `A[], ``int` `n) ``{ ``    ``// Sort the given array using sort STL ``    ``sort(A, A + n); ``} `` ` `// Driver code ``int` `main() ``{ ``    ``int` `A[] = { 2, 3, 8, -1, 7, 10 }; ``    ``int` `n = ``sizeof``(A) / ``sizeof``(A[0]); ``    ``mergeTwoHalf(A, n); `` ` `    ``// Print sorted Array ``    ``for` `(``int` `i = 0; i < n; i++) ``        ``cout << A[i] << ``" "``; ``    ``return` `0; ``} `

Java

 `// Java program to Merge two sorted halves of ``// array Into Single Sorted Array ``import` `java.io.*; ``import` `java.util.*; `` ` `class` `GFG { `` ` `    ``static` `void` `mergeTwoHalf(``int``[] A, ``int` `n) ``    ``{ ``        ``// Sort the given array using sort STL ``        ``Arrays.sort(A); ``    ``} `` ` `    ``// Driver code ``    ``static` `public` `void` `main(String[] args) ``    ``{ ``        ``int``[] A = { ``2``, ``3``, ``8``, -``1``, ``7``, ``10` `}; ``        ``int` `n = A.length; ``        ``mergeTwoHalf(A, n); `` ` `        ``// Print sorted Array ``        ``for` `(``int` `i = ``0``; i < n; i++) ``            ``System.out.print(A[i] + ``" "``); ``    ``} ``} `` ` `// This code is contributed by vt_m . `

Python3

 `# Python program to Merge two sorted ``# halves of array Into Single Sorted Array `` ` ` ` `def` `mergeTwoHalf(A, n): `` ` `    ``# Sort the given array using sort STL ``    ``A.sort() `` ` ` ` `# Driver Code ``if` `__name__ ``=``=` `'__main__'``: ``    ``A ``=` `[``2``, ``3``, ``8``, ``-``1``, ``7``, ``10``] ``    ``n ``=` `len``(A) ``    ``mergeTwoHalf(A, n) `` ` `    ``# Print sorted Array ``    ``for` `i ``in` `range``(n): ``        ``print``(A[i], end``=``" "``) `` ` `# This code is contributed by 29AjayKumar `

C#

 `// C# program to Merge two sorted halves of ``// array Into Single Sorted Array ``using` `System; `` ` `class` `GFG { `` ` `    ``static` `void` `mergeTwoHalf(``int``[] A, ``int` `n) ``    ``{ ``        ``// Sort the given array using sort STL ``        ``Array.Sort(A); ``    ``} `` ` `    ``// Driver code ``    ``static` `public` `void` `Main() ``    ``{ ``        ``int``[] A = { 2, 3, 8, -1, 7, 10 }; ``        ``int` `n = A.Length; ``        ``mergeTwoHalf(A, n); `` ` `        ``// Print sorted Array ``        ``for` `(``int` `i = 0; i < n; i++) ``            ``Console.Write(A[i] + ``" "``); ``    ``} ``} `` ` `// This code is contributed by vt_m .`

PHP

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Javascript

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Output
`-1 2 3 7 8 10`

Time Complexity: best & average case, worst case (for quicksort)

Space Complexity: to depending on the case & implementation (for quicksort)

For more details, check out the GFG article on Quicksort.

Method 2: A more efficient solution is to use an auxiliary array which is very similar to the Merge Function of Merge sort

Below is the implementation of above approach :

C++

 `// C++ program to Merge Two Sorted Halves Of ``// Array Into Single Sorted Array ``#include ``using` `namespace` `std; `` ` `// Merge two sorted halves of Array into single ``// sorted array ``void` `mergeTwoHalf(``int` `A[], ``int` `n) ``{ ``    ``int` `half_i = 0; ``// starting index of second half `` ` `    ``// Temp Array store sorted resultant array ``    ``int` `temp[n]; `` ` `    ``// First Find the point where array is divide ``    ``// into two half ``    ``for` `(``int` `i = 0; i < n - 1; i++) { ``        ``if` `(A[i] > A[i + 1]) { ``            ``half_i = i + 1; ``            ``break``; ``        ``} ``    ``} `` ` `    ``// If Given array is all-ready sorted ``    ``if` `(half_i == 0) ``        ``return``; `` ` `    ``// Merge two sorted arrays in single sorted array ``    ``int` `i = 0, j = half_i, k = 0; ``    ``while` `(i < half_i && j < n) { ``        ``if` `(A[i] < A[j]) ``            ``temp[k++] = A[i++]; ``        ``else``            ``temp[k++] = A[j++]; ``    ``} `` ` `    ``// Copy the remaining elements of A[i to half_! ] ``    ``while` `(i < half_i) ``        ``temp[k++] = A[i++]; `` ` `    ``// Copy the remaining elements of A[ half_! to n ] ``    ``while` `(j < n) ``        ``temp[k++] = A[j++]; `` ` `    ``for` `(``int` `i = 0; i < n; i++) ``        ``A[i] = temp[i]; ``} `` ` `// Driver code ``int` `main() ``{ ``    ``int` `A[] = { 2, 3, 8, -1, 7, 10 }; ``    ``int` `n = ``sizeof``(A) / ``sizeof``(A[0]); ``    ``mergeTwoHalf(A, n); `` ` `    ``// Print sorted Array ``    ``for` `(``int` `i = 0; i < n; i++) ``        ``cout << A[i] << ``" "``; ``    ``return` `0; ``}`

Java

 `// Java program to Merge Two Sorted Halves Of ``// Array Into Single Sorted Array ``import` `java.io.*; `` ` `class` `GFG { `` ` `    ``// Merge two sorted halves of Array ``    ``// into single sorted array ``    ``static` `void` `mergeTwoHalf(``int``[] A, ``int` `n) ``    ``{ ``        ``int` `half_i = ``0``; ``// starting index of second half ``        ``int` `i; `` ` `        ``// Temp Array store sorted resultant array ``        ``int``[] temp = ``new` `int``[n]; `` ` `        ``// First Find the point where array is divide ``        ``// into two half ``        ``for` `(i = ``0``; i < n - ``1``; i++) { ``            ``if` `(A[i] > A[i + ``1``]) { ``                ``half_i = i + ``1``; ``                ``break``; ``            ``} ``        ``} `` ` `        ``// If Given array is all-ready sorted ``        ``if` `(half_i == ``0``) ``            ``return``; `` ` `        ``// Merge two sorted arrays in single sorted array ``        ``i = ``0``; ``        ``int` `j = half_i; ``        ``int` `k = ``0``; ``        ``while` `(i < half_i && j < n) { ``            ``if` `(A[i] < A[j]) ``                ``temp[k++] = A[i++]; ``            ``else``                ``temp[k++] = A[j++]; ``        ``} `` ` `        ``// Copy the remaining elements of A[i to half_! ] ``        ``while` `(i < half_i) ``            ``temp[k++] = A[i++]; `` ` `        ``// Copy the remaining elements of A[ half_! to n ] ``        ``while` `(j < n) ``            ``temp[k++] = A[j++]; `` ` `        ``for` `(i = ``0``; i < n; i++) ``            ``A[i] = temp[i]; ``    ``} `` ` `    ``// Driver code ``    ``static` `public` `void` `main(String[] args) ``    ``{ ``        ``int``[] A = { ``2``, ``3``, ``8``, -``1``, ``7``, ``10` `}; ``        ``int` `n = A.length; ``        ``mergeTwoHalf(A, n); `` ` `        ``// Print sorted Array ``        ``for` `(``int` `i = ``0``; i < n; i++) ``            ``System.out.print(A[i] + ``" "``); ``    ``} ``} `` ` `// This code is contributed by vt_m .`

Python3

 `# Python3 program to Merge Two Sorted Halves Of ``# Array Into Single Sorted Array `` ` `# Merge two sorted halves of Array into single ``# sorted array ``def` `mergeTwoHalf(A, n): ``     ` `    ``# Starting index of second half ``    ``half_i ``=` `0`    ` ` `    ``# Temp Array store sorted resultant array ``    ``temp ``=` `[``0` `for` `i ``in` `range``(n)] `` ` `    ``# First Find the point where array is  ``    ``# divide into two half ``    ``for` `i ``in` `range``(n ``-` `1``): ``        ``if` `(A[i] > A[i ``+` `1``]): ``            ``half_i ``=` `i ``+` `1``            ``break`` ` `    ``# If Given array is all-ready sorted ``    ``if` `(half_i ``=``=` `0``): ``        ``return`` ` `    ``# Merge two sorted arrays in single ``    ``# sorted array ``    ``i ``=` `0``    ``j ``=` `half_i ``    ``k ``=` `0``     ` `    ``while` `(i < half_i ``and` `j < n): ``        ``if` `(A[i] < A[j]): ``            ``temp[k] ``=` `A[i] ``            ``k ``+``=` `1``            ``i ``+``=` `1``        ``else``: ``            ``temp[k] ``=` `A[j] ``            ``k ``+``=` `1``            ``j ``+``=` `1``     ` `    ``# Copy the remaining elements of A[i to half_! ] ``    ``while` `i < half_i: ``        ``temp[k] ``=` `A[i] ``        ``k ``+``=` `1``        ``i ``+``=` `1`` ` `    ``# Copy the remaining elements of A[ half_! to n ] ``    ``while` `(j < n): ``        ``temp[k] ``=` `A[j] ``        ``k ``+``=` `1``        ``j ``+``=` `1`` ` `    ``for` `i ``in` `range``(n): ``        ``A[i] ``=` `temp[i] `` ` `# Driver code ``A ``=` `[ ``2``, ``3``, ``8``, ``-``1``, ``7``, ``10` `] ``n ``=` `len``(A) `` ` `mergeTwoHalf(A, n) `` ` `# Print sorted Array ``print``(``*``A, sep ``=` `' '``) `` ` `# This code is contributed by avanitrachhadiya2155`

C#

 `// C# program to Merge Two Sorted Halves Of ``// Array Into Single Sorted Array ``using` `System `` ` `    ``class` `GFG { `` ` `    ``// Merge two sorted halves of Array ``    ``// into single sorted array ``    ``static` `void` `mergeTwoHalf(``int``[] A, ``int` `n) ``    ``{ ``        ``int` `half_i = 0 ``            ``// starting index of second half ``            ``int` `i `` ` `            ``// Temp Array store sorted resultant array ``            ``int``[] temp ``            ``= ``new` `int``[n] `` ` `            ``// First Find the point where array is divide ``            ``// into two half ``            ``for` `(i = 0 i < n - 1 i++) ``        ``{ ``            ``if` `(A[i] > A[i + 1]) { ``                ``half_i = i + 1 ``break``            ``} ``        ``} `` ` `        ``// If Given array is all-ready sorted ``        ``if` `(half_i == 0) ``            ``return`` ` `                ``// Merge two sorted arrays in single sorted ``                ``// array ``                ``i = 0 ``int` `j = half_i ``int` `k ``                ``= 0 ``while` `(i < half_i & &j < n) ``            ``{ ``                ``if` `(A[i] < A[j]) ``                    ``temp[k++] = A[i++] ``else` `temp[k++] ``                        ``= A[j++] ``            ``} `` ` `        ``// Copy the remaining elements of A[i to half_!] ``        ``while` `(i < half_i) ``            ``temp[k++] = A[i++] `` ` `                ``// Copy the remaining elements of A[half_! ``                ``// to n] ``                ``while` `(j < n) temp[k++] ``                ``= A[j++] `` ` `                ``for` `(i = 0 i < n i++) A[i] ``                ``= temp[i] ``    ``} `` ` `    ``// Driver code ``    ``static` `public` `void` `Main() ``    ``{ ``        ``int``[] A ``            ``= { 2, ``                ``3, ``                ``8, ``                ``-1, ``                ``7, ``                ``10 } ``int` `n ``            ``= A.Length mergeTwoHalf(A, n) `` ` `              ``// Print sorted Array ``              ``for` `(``int` `i = 0 i < n i++) ``                  ``Console.Write(A[i] + ``" "``) ``    ``} ``} `` ` `// This code is contributed by vt_m .`

Javascript

 ``

Output
`-1 2 3 7 8 10`

Time Complexity:

Space Complexity:
Reference: https://www.careercup.com/question?id=8412257

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