Sort an array when two halves are sorted

Given an integer array of which both the first half and second half are sorted. The task is to merge two sorted halves of the array into a 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 a quick sort). 

Below is the implementation of the above method:

C++

// 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;
}

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

<?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
?>

Javascript

<script>

// Javascript program to Merge two sorted halves of
// array Into Single Sorted Array

function mergeTwoHalf(A, n)
{
    // Sort the given array using sort function
    A.sort((a,b) => a-b);
}

// Driver code
var A = [ 2, 3, 8, -1, 7, 10 ];
var n = A.length;
mergeTwoHalf(A, n);

// Print sorted Array
for (var i = 0; i < n; i++)
    document.write( A[i] + " ");

// This code is contributed by itsok.
</script>

Output

-1 2 3 7 8 10 

Time Complexity: best & average case, worst case (for quicksort)
Space Complexity: 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 the above approach : 

C++

// 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;
}

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

<script>

    // JavaScript program to Merge Two Sorted Halves Of
    // Array Into Single Sorted Array

    // Merge two sorted halves of Array into single
    // sorted array
    function mergeTwoHalf(A, n)
    {
        let half_i = 0; // starting index of second half

        // Temp Array store sorted resultant array
        let temp = new Array(n);
        temp.fill(0);

        // First Find the point where array is divide
        // into two half
        for (let 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
        let 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 (let i = 0; i < n; i++)
            A[i] = temp[i];
    }

    let A = [ 2, 3, 8, -1, 7, 10 ];
    let n = A.length;
    mergeTwoHalf(A, n);

    // Print sorted Array
    for (let i = 0; i < n; i++)
        document.write(A[i] + " ");

</script>

Output

-1 2 3 7 8 10 

Time Complexity: O(n)
Space Complexity: 

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*** Error message:
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O(n)

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