Count number of ways to divide an array into two halves with same sum

30 May, 2022
Given an integer array of N elements. The task is to find the number of ways to split the array into two equal sum sub-arrays of non-zero lengths.
Examples: 
Input: arr[] = {0, 0, 0, 0}Output: 3 Explanation:All the possible ways are: { {{0}, {0, 0, 0}}, {{0, 0}, {0, 0}}, {{0, 0, 0}, {0}} Therefore, the required output is 3.
Input: {1, -1, 1, -1}Output: 1 
 
Simple Solution: A simple solution is to generate all the possible contiguous sub-arrays pairs and find there sum. If their sum is the same, we will increase the count by one.Time Complexity: O(N2)Auxiliary Space: O(1)Efficient Approach: The idea is to take an auxiliary array say, aux[] to calculate the presum of the array such that for an index i aux[i] will store the sum of all elements from index 0 to index i.By doing this we can calculate the left sum and right sum for every index of the array in constant time. So, the idea is to:  
Find the sum of all the numbers of the array and store it in a variable say, S. If the sum is odd, then the answer will be 0.Traverse the array and keep calculating the sum of elements. At ith step, we will use the variable S to maintain sum of all the elements from index 0 to i. Calculate sum upto the ith index.If this sum equals S/2, increase the count of the number of ways by 1.Do this from i=0 to i=N-2.
Find the sum of all the numbers of the array and store it in a variable say, S. If the sum is odd, then the answer will be 0.
Traverse the array and keep calculating the sum of elements. At ith step, we will use the variable S to maintain sum of all the elements from index 0 to i. Calculate sum upto the ith index.If this sum equals S/2, increase the count of the number of ways by 1.
Calculate sum upto the ith index.
If this sum equals S/2, increase the count of the number of ways by 1.
Do this from i=0 to i=N-2.
Below is the implementation of the above approach:  
C++
Java
Python3
C#
Javascript
// C++ program to count the number of ways to// divide an array into two halves// with the same sum #include <bits/stdc++.h>using namespace std; // Function to count the number of ways to// divide an array into two halves// with same sumint cntWays(int arr[], int n){    // if length of array is 1    // answer will be 0 as we have    // to split it into two    // non-empty halves    if (n == 1)        return 0;     // variables to store total sum,    // current sum and count    int tot_sum = 0, sum = 0, ans = 0;     // finding total sum    for (int i = 0; i < n; i++)        tot_sum += arr[i];     // checking if sum equals total_sum/2    for (int i = 0; i < n - 1; i++) {        sum += arr[i];        if (sum == tot_sum / 2)            ans++;    }     return ans;} // Driver Codeint main(){    int arr[] = { 1, -1, 1, -1, 1, -1 };     int n = sizeof(arr) / sizeof(int);     cout << cntWays(arr, n);     return 0;}
// Java program to count the number of ways to// divide an array into two halves// with the same sumclass GFG{     // Function to count the number of ways to    // divide an array into two halves    // with same sum    static int cntWays(int arr[], int n)    {        // if length of array is 1        // answer will be 0 as we have        // to split it into two        // non-empty halves        if (n == 1)        {            return 0;        }         // variables to store total sum,        // current sum and count        int tot_sum = 0, sum = 0, ans = 0;         // finding total sum        for (int i = 0; i < n; i++)        {            tot_sum += arr[i];        }         // checking if sum equals total_sum/2        for (int i = 0; i < n - 1; i++)        {            sum += arr[i];            if (sum == tot_sum / 2)            {                ans++;            }        }         return ans;    }     // Driver Code    public static void main(String[] args)    {        int arr[] = {1, -1, 1, -1, 1, -1};         int n = arr.length;         System.out.println(cntWays(arr, n));    }} // This code contributed by Rajput-Ji
# Python program to count the number of ways to# divide an array into two halves# with the same sum # Function to count the number of ways to# divide an array into two halves# with same sumdef cntWays(arr, n):    # if length of array is 1    # answer will be 0 as we have    # to split it into two    # non-empty halves    if (n == 1):        return 0;     # variables to store total sum,    # current sum and count    tot_sum = 0; sum = 0; ans = 0;     # finding total sum    for i in range(0,n):        tot_sum += arr[i];     # checking if sum equals total_sum/2    for i in range(0,n-1):        sum += arr[i];        if (sum == tot_sum / 2):            ans+=1;    return ans; # Driver Codearr = [1, -1, 1, -1, 1, -1 ]; n = len(arr); print(cntWays(arr, n)); # This code contributed by PrinciRaj1992
// C# program to count the number of ways to// divide an array into two halves with// the same sumusing System; class GFG{     // Function to count the number of ways to    // divide an array into two halves    // with same sum    static int cntWays(int []arr, int n)    {        // if length of array is 1        // answer will be 0 as we have        // to split it into two        // non-empty halves        if (n == 1)        {            return 0;        }         // variables to store total sum,        // current sum and count        int tot_sum = 0, sum = 0, ans = 0;         // finding total sum        for (int i = 0; i < n; i++)        {            tot_sum += arr[i];        }         // checking if sum equals total_sum/2        for (int i = 0; i < n - 1; i++)        {            sum += arr[i];            if (sum == tot_sum / 2)            {                ans++;            }        }         return ans;    }     // Driver Code    public static void Main()    {        int []arr = {1, -1, 1, -1, 1, -1};         int n = arr.Length;         Console.WriteLine(cntWays(arr, n));    }} // This code contributed by anuj_67..
<script>       // JavaScript program to count the number of ways to      // divide an array into two halves      // with the same sum       // Function to count the number of ways to      // divide an array into two halves      // with same sum      function cntWays(arr, n)      {        // if length of array is 1        // answer will be 0 as we have        // to split it into two        // non-empty halves        if (n == 1) return 0;         // variables to store total sum,        // current sum and count        var tot_sum = 0,          sum = 0,          ans = 0;         // finding total sum        for (var i = 0; i < n; i++) tot_sum += arr[i];         // checking if sum equals total_sum/2        for (var i = 0; i < n - 1; i++) {          sum += arr[i];          if (sum == tot_sum / 2)          ans++;        }         return ans;      }       // Driver Code      var arr = [1, -1, 1, -1, 1, -1];      var n = arr.length;      document.write(cntWays(arr, n));       </script>
2
 
Time Complexity: O(N), since there runs a loop from 0 to (n – 1)Auxiliary Space: O(1), since no extra space has been taken.
Rajput-Ji
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princiraj1992
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