Split an array into two equal Sum subarrays

Given an array of integers greater than zero, find if it is possible to split it in two subarrays (without reordering the elements), such that the sum of the two subarrays is the same. Print the two subarrays.

Examples :

Input : Arr[] = { 1 , 2 , 3 , 4 , 5 , 5  }
Output :  { 1 2 3 4 } 
          { 5 , 5 }

Input : Arr[] = { 4, 1, 2, 3 }
Output : {4 1}
         {2 3}

Input : Arr[] = { 4, 3, 2, 1}
Output : Not Possible

Asked In : Facebook interview

A Simple solution is to run two loop to split array and check it is possible to split array into two parts such that sum of first_part equal to sum of second_part. 

Below is the implementation of above idea. 

C++

// C++ program to split an array into Two
// equal sum subarrays
#include<bits/stdc++.h>
using namespace std;

// Returns split point. If not possible, then
// return -1.
int findSplitPoint(int arr[], int n)
{
    int leftSum = 0 ;

    // traverse array element
    for (int i = 0; i < n; i++)
    {
        // add current element to left Sum
        leftSum += arr[i] ;

        // find sum of rest array elements (rightSum)
        int rightSum = 0 ;
        for (int j = i+1 ; j < n ; j++ )
            rightSum += arr[j] ;

        // split point index
        if (leftSum == rightSum)
            return i+1 ;
    }

    // if it is not possible to split array into
    // two parts
    return -1;
}

// Prints two parts after finding split point using
// findSplitPoint()
void printTwoParts(int arr[], int n)
{
    int splitPoint = findSplitPoint(arr, n);

    if (splitPoint == -1 || splitPoint == n )
    {
        cout << "Not Possible" <<endl;
        return;
    }
    for (int i = 0; i < n; i++)
    {
        if(splitPoint == i)
            cout << endl;
        cout << arr[i] << " " ;
    }
}

// driver program
int main()
{
    int arr[] = {1 , 2 , 3 , 4 , 5 , 5 };
    int n = sizeof(arr)/sizeof(arr[0]);
    printTwoParts(arr, n);
    return 0;
}

Java

// Java program to split an array
// into two equal sum subarrays
import java.io.*;

class GFG {

    // Returns split point. If
    // not possible, then return -1.
    static int findSplitPoint(int arr[], int n)
    {

    int leftSum = 0 ;

    // traverse array element
    for (int i = 0; i < n; i++)
    {
        // add current element to left Sum
        leftSum += arr[i] ;

        // find sum of rest array
        // elements (rightSum)
        int rightSum = 0 ;

        for (int j = i+1 ; j < n ; j++ )
            rightSum += arr[j] ;

        // split point index
        if (leftSum == rightSum)
            return i+1 ;
    }

    // if it is not possible to
    // split array into two parts
    return -1;
    }

    // Prints two parts after finding
    // split point using findSplitPoint()
    static void printTwoParts(int arr[], int n)
    {

        int splitPoint = findSplitPoint(arr, n);

        if (splitPoint == -1 || splitPoint == n )
        {
            System.out.println("Not Possible");
            return;
        }

        for (int i = 0; i < n; i++)
        {
            if(splitPoint == i)
               System.out.println();

            System.out.print(arr[i] + " ");

        }
    }

// Driver program

    public static void main (String[] args) {

    int arr[] = {1 , 2 , 3 , 4 , 5 , 5 };
    int n = arr.length;
    printTwoParts(arr, n);

    }
}

// This code is contributed by vt_m

Python3

# Python3 program to split an array into Two
# equal sum subarrays

# Returns split point. If not possible, then
# return -1.
def findSplitPoint(arr, n) :

    leftSum = 0

    # traverse array element
    for i in range(0, n) :

        # add current element to left Sum
        leftSum += arr[i]

        # find sum of rest array elements (rightSum)
        rightSum = 0
        for j in range(i+1, n) :
            rightSum += arr[j]

        # split point index
        if (leftSum == rightSum) :
            return i+1


    # if it is not possible to split array into
    # two parts
    return -1


# Prints two parts after finding split point using
# findSplitPoint()
def printTwoParts(arr, n) :

    splitPo = findSplitPoint(arr, n)

    if (splitPo == -1 or splitPo == n ) :
        print ("Not Possible")
        return

    for i in range(0, n) :
        if(splitPo == i) :
            print ("")
        print (str(arr[i]) + ' ',end='')

# driver program
arr = [1 , 2 , 3 , 4 , 5 , 5]
n = len(arr)
printTwoParts(arr, n)

# This code is contributed by Manish Shaw
# (manishshaw1)

C#

// C# program to split an array
// into two equal sum subarrays
using System;

class GFG {

    // Returns split point. If
    // not possible, then return -1.
    static int findSplitPoint(int []arr, int n)
    {

        int leftSum = 0 ;

        // traverse array element
        for (int i = 0; i < n; i++)
        {

            // add current element to left Sum
            leftSum += arr[i] ;

            // find sum of rest array
            // elements (rightSum)
            int rightSum = 0 ;

            for (int j = i+1 ; j < n ; j++ )
                rightSum += arr[j] ;

            // split point index
            if (leftSum == rightSum)
                return i+1 ;
        }

        // if it is not possible to
        // split array into two parts
        return -1;
    }

    // Prints two parts after finding
    // split point using findSplitPoint()
    static void printTwoParts(int []arr, int n)
    {

        int splitPoint = findSplitPoint(arr, n);

        if (splitPoint == -1 || splitPoint == n )
        {
            Console.Write("Not Possible");
            return;
        }

        for (int i = 0; i < n; i++)
        {
            if(splitPoint == i)
            Console.WriteLine();

            Console.Write(arr[i] + " ");
        }
    }

    // Driver program
    public static void Main ()
    {
        int []arr = {1 , 2 , 3 , 4 , 5 , 5 };
        int n = arr.Length;
        printTwoParts(arr, n);
    }
}

// This code is contributed by nitin mittal

PHP

<?php
// PHP program to split
// an array into Two
// equal sum subarrays

// Returns split point.
// If not possible, then
// return -1.
function findSplitPoint( $arr, $n)
{
    $leftSum = 0 ;

    // traverse array element
    for($i = 0; $i < $n; $i++)
    {

        // add current element
        // to left Sum
        $leftSum += $arr[$i] ;

        // find sum of rest array
        // elements (rightSum)
        $rightSum = 0 ;
        for($j = $i + 1 ; $j < $n ; $j++ )
            $rightSum += $arr[$j] ;

        // split point index
        if ($leftSum == $rightSum)
            return $i+1 ;
    }

    // if it is not possible
    // to split array into
    // two parts
    return -1;
}

// Prints two parts after
// finding split point using
// findSplitPoint()
function printTwoParts($arr, $n)
{
    $splitPoint = findSplitPoint($arr, $n);

    if ($splitPoint == -1 or $splitPoint == $n )
    {
        echo "Not Possible" ;
        return;
    }
    for ( $i = 0; $i < $n; $i++)
    {
        if($splitPoint == $i)
            echo "\n";
        echo $arr[$i] , " " ;
    }
}

    // Driver Code
    $arr = array(1 , 2 , 3 , 4 , 5 , 5);
    $n = count($arr);
    printTwoParts($arr, $n);

// This code is contributed by anuj_67.
?>

Javascript

<script>
// Java script program to split an array
// into two equal sum subarrays

    // Returns split point. If
    // not possible, then return -1.
    function findSplitPoint(arr,n)
    {

    let leftSum = 0 ;

    // traverse array element
    for (let i = 0; i < n; i++)
    {
        // add current element to left Sum
        leftSum += arr[i] ;

        // find sum of rest array
        // elements (rightSum)
        let rightSum = 0 ;

        for (let j = i+1 ; j < n ; j++ )
            rightSum += arr[j] ;

        // split point index
        if (leftSum == rightSum)
            return i+1 ;
    }

    // if it is not possible to
    // split array into two parts
    return -1;
    }

    // Prints two parts after finding
    // split point using findSplitPoint()
    function printTwoParts(arr,n)
    {

        let splitPoint = findSplitPoint(arr, n);

        if (splitPoint == -1 || splitPoint == n )
        {
            document.write("Not Possible");
            return;
        }

        for (let i = 0; i < n; i++)
        {
            if(splitPoint == i)
            document.write("<br>");

            document.write(arr[i] + " ");

        }
    }

// Driver program



    let arr = [1 , 2 , 3 , 4 , 5 , 5 ];
    let n = arr.length;
    printTwoParts(arr, n);


// contributed by sravan kumar
</script>

Output

1 2 3 4 
5 5 

Time Complexity : O(n²) 
Auxiliary Space : O(1)

An Efficient solution is to first compute the sum of the whole array from left to right. Now we traverse array from right and keep track of right sum, left sum can be computed by subtracting current element from whole sum.

Below is the implementation of above idea. 

C++

// C++ program to split an array into Two
// equal sum subarrays
#include<bits/stdc++.h>
using namespace std;

// Returns split point. If not possible, then
// return -1.
int findSplitPoint(int arr[], int n)
{
    // traverse array element and compute sum
    // of whole array
    int leftSum = 0;
    for (int i = 0 ; i < n ; i++)
        leftSum += arr[i];

    // again traverse array and compute right sum
    // and also check left_sum equal to right
    // sum or not
    int rightSum = 0;
    for (int i=n-1; i >= 0; i--)
    {
        // add current element to right_sum
        rightSum += arr[i];

        // exclude current element to the left_sum
        leftSum -=  arr[i] ;

        if (rightSum == leftSum)
            return i ;
    }

    // if it is not possible to split array
    // into two parts.
    return -1;
}

// Prints two parts after finding split point using
// findSplitPoint()
void printTwoParts(int arr[], int n)
{
    int splitPoint = findSplitPoint(arr, n);

    if (splitPoint == -1 || splitPoint == n )
    {
        cout << "Not Possible" <<endl;
        return;
    }
    for (int i = 0; i < n; i++)
    {
        if(splitPoint == i)
            cout << endl;
        cout << arr[i] << " " ;
    }
}

// driver program
int main()
{
    int arr[] = {1 , 2 , 3 , 4 , 5 , 5 };
    int n = sizeof(arr)/sizeof(arr[0]);
    printTwoParts(arr, n);
    return 0;
}

Java

// java program to split an array
// into Two equal sum subarrays
import java.io.*;

class GFG {

    // Returns split point. If not possible, then
    // return -1.
    static int findSplitPoint(int arr[], int n)
    {

    // traverse array element and compute sum
    // of whole array
    int leftSum = 0;

    for (int i = 0 ; i < n ; i++)
        leftSum += arr[i];

    // again traverse array and compute right
    // sum and also check left_sum equal to
    // right sum or not
    int rightSum = 0;

    for (int i = n-1; i >= 0; i--)
    {
        // add current element to right_sum
        rightSum += arr[i];

        // exclude current element to the left_sum
        leftSum -= arr[i] ;

        if (rightSum == leftSum)
            return i ;
    }

    // if it is not possible to split array
    // into two parts.
    return -1;
    }

    // Prints two parts after finding split
    // point using findSplitPoint()
    static void printTwoParts(int arr[], int n)
    {
        int splitPoint = findSplitPoint(arr, n);

        if (splitPoint == -1 || splitPoint == n )
        {
            System.out.println("Not Possible" );
            return;
        }
        for (int i = 0; i < n; i++)
        {
            if(splitPoint == i)
                System.out.println();

            System.out.print(arr[i] + " ");
        }
    }

    // Driver program
    public static void main (String[] args) {

    int arr[] = {1 , 2 , 3 , 4 , 5 , 5 };
    int n = arr.length;

    printTwoParts(arr, n);

    }
}

// This code is contributed by vt_m

Python3

# Python3 program to split
# an array into Two
# equal sum subarrays

# Returns split point.
# If not possible,
# then return -1.
def findSplitPoint(arr, n) :
    # traverse array element and
    # compute sum of whole array
    leftSum = 0
    for i in range(0, n) :
        leftSum += arr[i]

    # again traverse array and
    # compute right sum and also
    # check left_sum equal to
    # right sum or not
    rightSum = 0
    for i in range(n-1, -1, -1) :
        # add current element
        # to right_sum
        rightSum += arr[i]

        # exclude current element
        # to the left_sum
        leftSum -= arr[i]

        if (rightSum == leftSum) :
            return i

    # if it is not possible
    # to split array into
    # two parts.
    return -1

# Prints two parts after
# finding split point
# using findSplitPoint()
def printTwoParts(arr, n) :
    splitPoint = findSplitPoint(arr, n)

    if (splitPoint == -1 or splitPoint == n ) :
        print ("Not Possible")
        return

    for i in range (0, n) :
        if(splitPoint == i) :
            print ("")
        print (arr[i], end = " ")

# Driver Code
arr = [1, 2, 3, 4, 5, 5]
n = len(arr)
printTwoParts(arr, n)

# This code is contributed by Manish Shaw
# (manishshaw1)

C#

// C# program to split an array
// into Two equal sum subarrays
using System;

class GFG {

    // Returns split point. If not possible, then
    // return -1.
    static int findSplitPoint(int []arr, int n)
    {

    // traverse array element and compute sum
    // of whole array
    int leftSum = 0;

    for (int i = 0 ; i < n ; i++)
        leftSum += arr[i];

    // again traverse array and compute right
    // sum and also check left_sum equal to
    // right sum or not
    int rightSum = 0;

    for (int i = n-1; i >= 0; i--)
    {
        // add current element to right_sum
        rightSum += arr[i];

        // exclude current element to the left_sum
        leftSum -= arr[i] ;

        if (rightSum == leftSum)
            return i ;
    }

    // if it is not possible to split array
    // into two parts.
    return -1;
    }

    // Prints two parts after finding split
    // point using findSplitPoint()
    static void printTwoParts(int []arr, int n)
    {
        int splitPoint = findSplitPoint(arr, n);

        if (splitPoint == -1 || splitPoint == n )
        {
            Console.Write("Not Possible" );
            return;
        }
        for (int i = 0; i < n; i++)
        {
            if(splitPoint == i)
                 Console.WriteLine();

             Console.Write(arr[i] + " ");
        }
    }

    // Driver program
    public static void Main (String[] args) {

    int []arr = {1 , 2 , 3 , 4 , 5 , 5 };
    int n = arr.Length;

    printTwoParts(arr, n);

    }
}

// This code is contributed by parashar

PHP

<?php
// PHP program to split
// an array into Two
// equal sum subarrays

// Returns split point.
// If not possible,
// then return -1.
function findSplitPoint($arr, $n)
{
    // traverse array element and
    // compute sum of whole array
    $leftSum = 0;
    for ( $i = 0 ; $i < $n ; $i++)
        $leftSum += $arr[$i];

    // again traverse array and
    // compute right sum and also
    // check left_sum equal to
    // right sum or not
    $rightSum = 0;
    for ($i = $n - 1; $i >= 0; $i--)
    {
        // add current element
        // to right_sum
        $rightSum += $arr[$i];

        // exclude current element
        // to the left_sum
        $leftSum -= $arr[$i] ;

        if ($rightSum == $leftSum)
            return $i ;
    }

    // if it is not possible
    // to split array into
    // two parts.
    return -1;
}

// Prints two parts after
// finding split point
// using findSplitPoint()
function printTwoParts( $arr, $n)
{
    $splitPoint = findSplitPoint($arr, $n);

    if ($splitPoint == -1 or
        $splitPoint == $n )
    {
        echo "Not Possible" ;
        return;
    }
    for ( $i = 0; $i < $n; $i++)
    {
        if($splitPoint == $i)
            echo "\n";
        echo $arr[$i] , " " ;
    }
}

// Driver Code
$arr = array(1, 2, 3, 4, 5, 5);
$n = count($arr);
printTwoParts($arr, $n);

// This code is contributed by anuj_67.
?>

Javascript

<script>
    // Javascript program to split an array
    // into Two equal sum subarrays

    // Returns split point. If not possible, then
    // return -1.
    function findSplitPoint(arr, n)
    {

      // traverse array element and compute sum
      // of whole array
      let leftSum = 0;

      for (let i = 0 ; i < n ; i++)
          leftSum += arr[i];

      // again traverse array and compute right
      // sum and also check left_sum equal to
      // right sum or not
      let rightSum = 0;

      for (let i = n-1; i >= 0; i--)
      {
          // add current element to right_sum
          rightSum += arr[i];

          // exclude current element to the left_sum
          leftSum -= arr[i] ;

          if (rightSum == leftSum)
              return i ;
      }

      // if it is not possible to split array
      // into two parts.
      return -1;
    }

    // Prints two parts after finding split
    // point using findSplitPoint()
    function printTwoParts(arr, n)
    {
        let splitPoint = findSplitPoint(arr, n);

        if (splitPoint == -1 || splitPoint == n )
        {
            document.write("Not Possible" );
            return;
        }
        for (let i = 0; i < n; i++)
        {
            if(splitPoint == i)
                 document.write("</br>");

             document.write(arr[i] + " ");
        }
    }

    let arr = [1 , 2 , 3 , 4 , 5 , 5 ];
    let n = arr.length;

    printTwoParts(arr, n);

 // This code is contributed by rameshtravel07.
</script>

Output

1 2 3 4 
5 5 

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

Related Topic: Subarrays, Subsequences, and Subsets in Array