Find if array can be divided into two subarrays of equal sum
Given an array of integers, find if it’s possible to remove exactly one integer from the array that divides the array into two subarrays with the same sum.
Examples:
Input: arr = [6, 2, 3, 2, 1] Output: true Explanation: On removing element 2 at index 1, the array gets divided into two subarrays [6] and [3, 2, 1] having equal sum Input: arr = [6, 1, 3, 2, 5] Output: true Explanation: On removing element 3 at index 2, the array gets divided into two subarrays [6, 1] and [2, 5] having equal sum. Input: arr = [6, -2, -3, 2, 3] Output: true Explanation: On removing element 6 at index 0, the array gets divided into two sets [] and [-2, -3, 2, 3] having equal sum Input: arr = [6, -2, 3, 2, 3] Output: false
A naive solution would be to consider all elements of the array and calculate their left and right sum and return true if left and right sum are found to be equal. The time complexity of this solution would be O(n2).
The efficient solution involves calculating sum of all elements of the array in advance. Then for each element of the array, we can calculate its right sum in O(1) time by using total sum of the array elements minus sum of elements found so far. The time complexity of this solution would be O(n) and auxiliary space used by it will be O(1).
Below is the implementation of above approach:
C++
// C++ program to divide the array into two // subarrays with the same sum on removing // exactly one integer from the array #include <iostream> using namespace std; // Utility function to print the sub-array void printSubArray( int arr[], int start, int end) { cout << "[ " ; for ( int i = start; i <= end; i++) cout << arr[i] << " " ; cout << "] " ; } // Function that divides the array into two subarrays // with the same sum bool divideArray( int arr[], int n) { // sum stores sum of all elements of the array int sum = 0; for ( int i = 0; i < n; i++) sum += arr[i]; // sum stores sum till previous index of the array int sum_so_far = 0; for ( int i = 0; i < n; i++) { // If on removing arr[i], we get equals left // and right half if (2 * sum_so_far + arr[i] == sum) { cout << "The array can be divided into" "two subarrays with equal sum\nThe" " two subarrays are - " ; printSubArray(arr, 0, i - 1); printSubArray(arr, i + 1, n - 1); return true ; } // add current element to sum_so_far sum_so_far += arr[i]; } // The array cannot be divided cout << "The array cannot be divided into two " "subarrays with equal sum" ; return false ; } // Driver code int main() { int arr[] = {6, 2, 3, 2, 1}; int n = sizeof (arr)/ sizeof (arr[0]); divideArray(arr, n); return 0; } |
Java
// Java program to divide the array into two // subarrays with the same sum on removing // exactly one integer from the array import java.io.*; class GFG { // Utility function to print the sub-array static void printSubArray( int arr[], int start, int end) { System.out.print( "[ " ); for ( int i = start; i <= end; i++) System.out.print(arr[i] + " " ); System.out.print( "] " ); } // Function that divides the array into two subarrays // with the same sum static boolean divideArray( int arr[], int n) { // sum stores sum of all elements of the array int sum = 0 ; for ( int i = 0 ; i < n; i++) sum += arr[i]; // sum stores sum till previous index of the array int sum_so_far = 0 ; for ( int i = 0 ; i < n; i++) { // If on removing arr[i], we get equals left // and right half if ( 2 * sum_so_far + arr[i] == sum) { System.out.print( "The array can be divided into " + "two subarrays with equal sum\nThe" + " two subarrays are - " ); printSubArray(arr, 0 , i - 1 ); printSubArray(arr, i + 1 , n - 1 ); return true ; } // add current element to sum_so_far sum_so_far += arr[i]; } // The array cannot be divided System.out.println( "The array cannot be divided into two " + "subarrays with equal sum" ); return false ; } // Driver program public static void main (String[] args) { int arr[] = { 6 , 2 , 3 , 2 , 1 }; int n = arr.length; divideArray(arr, n); } } // This code is contributed by Pramod Kumar |
Python3
''' Python3 program to divide the array into two subarrays with the same sum on removing exactly one integer from the array''' # Utility function to print the sub-array def printSubArray(arr, start, end): print ( "[ " , end = "") for i in range (start, end + 1 ): print (arr[i], end = " " ) print ( "]" , end = "") # Function that divides the array into # two subarrays with the same sum def divideArray(arr, n): # sum stores sum of all # elements of the array sum = 0 for i in range ( 0 , n): sum + = arr[i] # sum stores sum till previous # index of the array sum_so_far = 0 for i in range ( 0 , n): # If on removing arr[i], we get # equals left and right half if 2 * sum_so_far + arr[i] = = sum : print ( "The array can be divided into" , "two subarrays with equal sum" ) print ( "two subarrays are -" , end = "") printSubArray(arr, 0 , i - 1 ) printSubArray(arr, i + 1 , n - 1 ) return True # add current element to sum_so_far sum_so_far + = arr[i] # The array cannot be divided print ( "The array cannot be divided into" "two subarrays with equal sum" , end = "") return False # Driver code arr = [ 6 , 2 , 3 , 2 , 1 ] n = len (arr) divideArray(arr, n) # This code is contributed by Shreyanshi Arun |
C#
// C# program to divide the array into two // subarrays with the same sum on removing // exactly one integer from the array using System; class GFG { // Utility function to print the sub-array static void printSubArray( int []arr, int start, int end) { Console.Write( "[ " ); for ( int i = start; i <= end; i++) Console.Write(arr[i] + " " ); Console.Write( "] " ); } // Function that divides the array into // two subarrays with the same sum static bool divideArray( int []arr, int n) { // sum stores sum of all elements of // the array int sum = 0; for ( int i = 0; i < n; i++) sum += arr[i]; // sum stores sum till previous index // of the array int sum_so_far = 0; for ( int i = 0; i < n; i++) { // If on removing arr[i], we get // equals left and right half if (2 * sum_so_far + arr[i] == sum) { Console.Write( "The array can be" + " divided into two subarrays" + " with equal sum\nThe two" + " subarrays are - " ); printSubArray(arr, 0, i - 1); printSubArray(arr, i + 1, n - 1); return true ; } // add current element to sum_so_far sum_so_far += arr[i]; } // The array cannot be divided Console.WriteLine( "The array cannot be" + " divided into two subarrays with " + "equal sum" ); return false ; } // Driver program public static void Main () { int []arr = {6, 2, 3, 2, 1}; int n = arr.Length; divideArray(arr, n); } } // This code is contributed by anuj_67. |
PHP
<?php // PHP program to divide the array into two // subarrays with the same sum on removing // exactly one integer from the array // Utility function to print the sub-array function printSubArray( $arr , $start , $end ) { echo "[ " ; for ( $i = $start ; $i <= $end ; $i ++) echo $arr [ $i ] . " " ; echo "] " ; } // Function that divides the // array into two subarrays // with the same sum function divideArray( $arr , $n ) { // sum stores sum of all // elements of the array $sum = 0; for ( $i = 0; $i < $n ; $i ++) $sum += $arr [ $i ]; // sum stores sum till previous // index of the array $sum_so_far = 0; for ( $i = 0; $i < $n ; $i ++) { // If on removing arr[i], // we get equals left // and right half if (2 * $sum_so_far + $arr [ $i ] == $sum ) { echo "The array can be divided into" . "two subarrays with equal sum\nThe" . " two subarrays are - " ; printSubArray( $arr , 0, $i - 1); printSubArray( $arr , $i + 1, $n - 1); return true; } // add current element // to sum_so_far $sum_so_far += $arr [ $i ]; } // The array cannot be divided echo "The array cannot be divided into two " . "subarrays with equal sum" ; return false; } // Driver code $arr = array (6, 2, 3, 2, 1); $n = sizeof( $arr ); divideArray( $arr , $n ); // This code is contributed by Anuj_67 ?> |
Javascript
<script> // JavaScript program to divide the array into two // subarrays with the same sum on removing // exactly one integer from the array // Utility function to print the sub-array function printSubArray(arr, start, end) { document.write( "[ " ); for (let i = start; i <= end; i++) document.write(arr[i] + " " ); document.write( "] " ); } // Function that divides the array into // two subarrays with the same sum function divideArray(arr, n) { // sum stores sum of all elements of // the array let sum = 0; for (let i = 0; i < n; i++) sum += arr[i]; // sum stores sum till previous index // of the array let sum_so_far = 0; for (let i = 0; i < n; i++) { // If on removing arr[i], we get // equals left and right half if (2 * sum_so_far + arr[i] == sum) { document.write( "The array can be" + " divided into two subarrays" + " with equal sum " + "</br>" + "The two" + " sets are - " ); printSubArray(arr, 0, i - 1); printSubArray(arr, i + 1, n - 1); return true ; } // add current element to sum_so_far sum_so_far += arr[i]; } // The array cannot be divided document.write( "The array cannot be" + " divided into two subarrays with " + "equal sum" + "</br>" ); return false ; } let arr = [6, 2, 3, 2, 1]; let n = arr.length; divideArray(arr, n); </script> |
The array can be divided intotwo subarrays with equal sum The two subarrays are - [ 6 ] [ 3 2 1 ]