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```

A Simple Solution is to sort the array.
Below is the implementation of above approach :

 `// 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 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 .`

 `# 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# 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 .`

 ``

Output
`-1 2 3 7 8 10`

Time Complexity O(nlogn) || Sort Given array using quick sort or merge sort

An efficient solution is to use an auxiliary array one half. Now whole process is same as the Merge Function of Merge sort

Below is the implementation of above approach :

 `// 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 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 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# 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 .`

Output
`-1 2 3 7 8 10`

Time Complexity: O(n)
Reference: https://www.careercup.com/question?id=8412257

Another efficient solution is use two pointers i and j, and compare a[i] and a[j]. Use merge need space of O(n) but this need space O(1). Below is the implementation:

 `// C++ program to Merge Two Sorted Halves Of` `// Array Into Single Sorted Array` `#include ` `using` `namespace` `std;`   `void` `SortTwoHalfSorted(``int` `A[], ``int` `n)` `{` `    ``int` `i = 0;` `    ``int` `j = n / 2;`   `    ``// loop until end of array` `    ``while` `(j < n) {`   `        ``// if two pointer is equal then go` `        ``// to next element of second half.` `        ``if` `(i == j)` `            ``j++;`   `        ``// if element of first half is bigger ` `        ``// than element of second half swap two ` `        ``// elements and go next element of first half.` `        ``if` `(j < n && A[i] > A[j]) {` `            ``swap(A[i], A[j]);` `        ``}` `        ``i++;` `    ``}` `}`   `// Driver code` `int` `main()` `{` `    ``int` `A[] = { 2, 3, 8, -1, 7, 10 };` `    ``int` `n = ``sizeof``(A) / ``sizeof``(A[0]);` `    ``SortTwoHalfSorted(A, n);`   `    ``// Print sorted Array` `    ``for` `(``int` `i = 0; i < n; i++)` `        ``cout << A[i] << ``" "``;` `    ``return` `0;` `}`

 `// Java program to Merge Two Sorted Halves Of` `// Array Into Single Sorted Array`   `import` `java.io.*;` `import` `java.util.*;` `class` `GFG {` `    ``public` `static` `void` `sortTwoHalfs(``int` `a[], ``int` `n)` `    ``{` `        ``int` `i = ``0``;` `        ``int` `j = n / ``2``;` `        ``// loop until end of array` `        ``while` `(j < n) {` `            ``// if two pointer is equal then go` `            ``// to next element of second half.` `            ``if` `(i == j)` `                ``j++;`   `            ``// if element of first half is bigger` `            ``// than element of second half swap two` `            ``// elements and go next element of first half.` `            ``if` `(j < n && a[i] > a[j]) {` `                ``// Swap elements` `                ``int` `temp = a[i];` `                ``a[i] = a[j];` `                ``a[j] = temp;` `            ``}` `            ``i++;` `        ``}` `    ``}` `  `  `    ``// Driver Code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `a[] = { ``2``, ``3``, ``8``, -``1``, ``7``, ``10` `};` `        ``int` `n = a.length;` `        ``sortTwoHalfs(a, n); ``// Call func. to sort array.` `        ``// Print sorted array` `        ``for` `(``int` `i = ``0``; i < n; i++) {` `            ``System.out.print(a[i] + ``" "``);` `        ``}` `    ``}` `}`

 `# Python3 program to Merge Two Sorted` `# Halves Of Array Into Single Sorted Array` `def` `SortTwoHalfSorted(A, n):` `    `  `    ``i ``=` `0` `    ``j ``=` `n ``/``/` `2`   `    ``# Loop until end of array` `    ``while` `(j < n):` `        `  `        ``# If two pointer is equal then go` `        ``# to next element of second half.` `        ``if` `(i ``=``=` `j):` `            ``j ``+``=` `1`   `        ``# If element of first half is bigger ` `        ``# than element of second half swap two ` `        ``# elements and go next element of first half` `        ``if` `(j < n ``and` `A[i] > A[j]):` `            ``A[i], A[j] ``=` `A[j], A[i]`   `        ``i ``+``=` `1`   `# Driver code` `A ``=` `[ ``2``, ``3``, ``8``, ``-``1``, ``7``, ``10` `]` `n ``=` `len``(A)` `SortTwoHalfSorted(A, n)`   `# Print sorted Array` `for` `i ``in` `range``(n):` `    ``print``(A[i], end ``=` `" "``)`   `# This code is contributed by divyesh072019`

 `// C# program to Merge Two Sorted Halves Of` `// Array Into Single Sorted Array` `using` `System;` `using` `System.Collections.Generic; `   `class` `GFG{`   `static` `void` `sortTwoHalfs(``int``[] a, ``int` `n)` `{` `    ``int` `i = 0;` `    ``int` `j = n / 2;` `    `  `    ``// Loop until end of array` `    ``while` `(j < n)` `    ``{` `        `  `        ``// If two pointer is equal then go` `        ``// to next element of second half.` `        ``if` `(i == j)` `            ``j++;`   `        ``// If element of first half is bigger` `        ``// than element of second half swap two` `        ``// elements and go next element of first half.` `        ``if` `(j < n && a[i] > a[j]) ` `        ``{` `            `  `            ``// Swap elements` `            ``int` `temp = a[i];` `            ``a[i] = a[j];` `            ``a[j] = temp;` `        ``}` `        ``i++;` `    ``}` `}`   `// Driver code    ` `static` `void` `Main() ` `{` `    ``int``[] a = { 2, 3, 8, -1, 7, 10 };` `    ``int` `n = a.Length;` `    `  `    ``// Call func. to sort array.` `    ``sortTwoHalfs(a, n);` `    `  `    ``// Print sorted array` `    ``for``(``int` `i = 0; i < n; i++)` `    ``{` `        ``Console.Write(a[i] + ``" "``);` `    ``}` `}` `}`   `// This code is contributed by divyeshrabadiya07`

Output
`-1 2 3 7 8 10`

Time Complexity: O(n) and Space : O(1)

This article is contributed by Nishant Singh . 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.

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