# Smallest subset with sum greater than all other elements

Given an array of non-negative integers. Our task is to find minimum number of elements such that their sum should be greater than the sum of rest of the elements of the array.

Examples :

Input : arr[] = {3, 1, 7, 1}
Output : 1
Smallest subset is {7}. Sum of
this subset is greater than all
other elements {3, 1, 1}

Input : arr[] = {2, 1, 2}
Output : 2
In this example one element is not
enough. We can pick elements with
values 1, 2 or 2, 2. In any case,
the minimum count is 2.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

The Brute force approach is to find the sum of all the possible subsets and then compare sum with the sum of remaining elements.

The Efficient Approach is to take the largest elements. We sort values in descending order, then take elements from the largest, until we get strictly more than half of total sum of the given array.

 // CPP program to find minimum number of // elements such that their sum is greater // than sum of remaining elements of the array. #include #include using namespace std;    // function to find minimum elements needed. int minElements(int arr[], int n) {     // calculating HALF of array sum      int halfSum = 0;     for (int i = 0; i < n; i++)          halfSum = halfSum + arr[i];         halfSum = halfSum / 2;        // sort the array in descending order.     sort(arr, arr + n, greater());        int res = 0, curr_sum = 0;     for (int i = 0; i < n; i++) {            curr_sum += arr[i];          res++;            // current sum greater than sum         if (curr_sum > halfSum)                      return res;     }     return res; }    // Driver function int main() {     int arr[] = {3, 1, 7, 1};     int n = sizeof(arr) / sizeof(arr[0]);     cout << minElements(arr, n) << endl;      return 0; }

 // Java code to find minimum number of elements // such that their sum is greater than sum of // remaining elements of the array. import java.io.*; import java.util.*;    class GFG {            // Function to find minimum elements needed     static int minElements(int arr[], int n)     {         // Calculating HALF of array sum          int halfSum = 0;         for (int i = 0; i < n; i++)              halfSum = halfSum + arr[i];          halfSum = halfSum / 2;                       // Sort the array in ascending order and          // start traversing array from the ascending         // sort in descending order.         Arrays.sort(arr);                    int res = 0, curr_sum = 0;         for (int i = n-1; i >= 0; i--) {                    curr_sum += arr[i];              res++;                    // Current sum greater than sum             if (curr_sum > halfSum)                          return res;         }         return res;     }            // Driver Code     public static void main (String[] args) {         int arr[] = {3, 1, 7, 1};         int n = arr.length;         System.out.println(minElements(arr, n));     }     }        // This code is contributed by Gitanjali

 # Python3 code to find minimum number of # elements such that their sum is greater # than sum of remaining elements of the array.    # function to find minimum elements needed. def minElements(arr , n):        # calculating HALF of array sum     halfSum = 0     for i in range(n):         halfSum = halfSum + arr[i]            halfSum = int(halfSum / 2)            # sort the array in descending order.     arr.sort(reverse = True)            res = 0     curr_sum = 0     for i in range(n):                    curr_sum += arr[i]         res += 1            # current sum greater than sum         if curr_sum > halfSum:             return res            return res        # driver code arr = [3, 1, 7, 1] n = len(arr) print(minElements(arr, n) )    # This code is contributed by "Sharad_Bhardwaj".

 // C# code to find minimum number of elements // such that their sum is greater than sum of // remaining elements of the array. using System;    class GFG {            // Function to find minimum elements needed     static int minElements(int []arr, int n)     {                    // Calculating HALF of array sum          int halfSum = 0;                    for (int i = 0; i < n; i++)              halfSum = halfSum + arr[i];                         halfSum = halfSum / 2;                // Sort the array in ascending order and          // start traversing array from the ascending         // sort in descending order.         Array.Sort(arr);                    int res = 0, curr_sum = 0;         for (int i = n-1; i >= 0; i--) {                    curr_sum += arr[i];              res++;                    // Current sum greater than sum             if (curr_sum > halfSum)                      return res;         }                    return res;     }            // Driver Code     public static void Main ()     {         int []arr = {3, 1, 7, 1};         int n = arr.Length;                    Console.WriteLine(minElements(arr, n));     } }        // This code is contributed by vt_m.

 \$halfSum)                      return \$res;     }     return \$res; }    // Driver Code \$arr = array(3, 1, 7, 1); \$n = sizeof(\$arr); echo minElements(\$arr, \$n);        // This code is contributed by ihritik ?>

Output:
1

Time Complexity :
O(n Log n)

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Improved By : ihritik, nidhi_biet

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