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 :

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// C++ program to Merge two sorted halves of
// array Into Single Sorted Array
#include <bits/stdc++.h>
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;
}
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// 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 .
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# 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
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// 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 .
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<?php
// PHP program to Merge two sorted halves
// of array Into Single Sorted Array
 
function mergeTwoHalf(&$A, $n)
{
    // Sort the given array using sort STL
    sort($A, 0);
}
 
// Driver Code
$A = array(2, 3, 8, -1, 7, 10);
$n = sizeof($A);
mergeTwoHalf($A, $n);
 
// Print sorted Array
for ($i = 0; $i < $n; $i++)
    echo $A[$i] . " ";
 
// This code is contributed
// by Akanksha Rai
?>
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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 : 

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// C++ program to Merge Two Sorted Halves Of
// Array Into Single Sorted Array
#include <bits/stdc++.h>
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;
}
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// 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 .
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# 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
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// 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 .
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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:

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// C++ program to Merge Two Sorted Halves Of
// Array Into Single Sorted Array
#include <bits/stdc++.h>
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;
}
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// 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] + " ");
        }
    }
}
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# 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
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// 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
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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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