Index with Minimum sum of prefix and suffix sums in an Array

Given an Array of integers. The task is to find the index i in the array at which the value of prefixSum(i) + suffixSum(i) is minimum.

Note:

  • PrefixSum(i) = The sum of first i numbers of the array.
  • SuffixSum(i) = the sum of last N – i + 1 numbers of the array.
  • 1-based indexing is considered for the array. That is index of the first element in array is 1.

Examples:

Input : arr[] = {3, 5, 1, 6, 6 }
Output : 3
Explanation: 
Presum[] = {3, 8, 9, 15, 21}
Postsum[] = { 21, 18, 13, 12, 6}
Presum[] + Postsum[] = {24, 26, 22, 27, 27}
It is clear that the min value of sum of
prefix and suffix sum is 22 at index 3.

Input : arr[] = { 3, 2, 5, 7, 3 }
Output : 2


Given that we need to minimize the value of PrefixSum[i] + SuffixSum[i]. That is sum of first i elements and N-i+1 elements from end.

If observed carefully, it can be seen that:

PrefixSum[i] + SuffixSum[i] = Sum of all elements in array + arr[i](Element at i-th index)

Since sum of all elements of the array will be the same for every index, therefore the value of PrefixSum[i] + SuffixSum[i] will be minimum for the minimum value of arr[i].

Therefore, the task reduces to find only the index of the minimum element of the array.

Below is the implementation of the above approach:

C++

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// C++ program to find the index with
// minimum sum of prefix and suffix
// sums in an Array
  
#include <bits/stdc++.h>
using namespace std;
  
int indexMinSum(int arr[], int n)
{
    // Initialization of the min value
    int min = arr[0];
    int index = 0;
  
    // Find minimum element in the array
    for (int i = 1; i < n; i++) {
        if (arr[i] < min) {
  
            // store the index of the
            // current minimum element
            min = arr[i];
            index = i;
        }
    }
  
    // return the index of min element
    // 1-based index
    return index + 1;
}
  
// Driver Code
int main()
{
    int arr[] = { 6, 8, 2, 3, 5 };
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << indexMinSum(arr, n);
    return 0;
}

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Java

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// Java program to find the index with
// minimum sum of prefix and suffix
// sums in an Array
  
import java.io.*;
  
class GFG {
  
static int indexMinSum(int arr[], int n)
{
    // Initialization of the min value
    int min = arr[0];
    int index = 0;
  
    // Find minimum element in the array
    for (int i = 1; i < n; i++) {
        if (arr[i] < min) {
  
            // store the index of the
            // current minimum element
            min = arr[i];
            index = i;
        }
    }
  
    // return the index of min element
    // 1-based index
    return index + 1;
}
  
// Driver Code
    public static void main (String[] args) {
    int arr[] = { 6, 8, 2, 3, 5 };
    int n =arr.length;
    System.out.println( indexMinSum(arr, n));
    }
}
// This code is contributed by inder_verma..

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Python 3

# Python 3 program to find the index with
# minimum sum of prefix and suffix
# sums in an Array

def indexMinSum(arr, n):

# Initialization of the min value
min = arr[0]
index = 0

# Find minimum element in the array
for i in range(1, n) :
if (arr[i] < min) : # store the index of the # current minimum element min = arr[i] index = i # return the index of min element # 1-based index return index + 1 # Driver Code if __name__ == "__main__": arr = [ 6, 8, 2, 3, 5 ] n = len(arr) print(indexMinSum(arr, n)) # This code is contributed by ita_c [tabby title = "C#"]

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// C# program to find the index with
// minimum sum of prefix and suffix
// sums in an Array
  
using System;
class GFG
{
    static int indexMinSum(int []arr, int n)
    {
        // Initialization of the min value
        int min = arr[0];
        int index = 0;
      
        // Find minimum element in the array
        for (int i = 1; i < n; i++) {
            if (arr[i] < min) {
      
                // store the index of the
                // current minimum element
                min = arr[i];
                index = i;
            }
        }
      
        // return the index of min element
        // 1-based index
        return index + 1;
    }
      
      
    // Driver Code
    static void Main()
    {
        int []arr = { 6, 8, 2, 3, 5 };
        int n =arr.Length;
        Console.WriteLine(indexMinSum(arr, n));
    }
    // This code is contributed by ANKITRAI1
}

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PHP

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<?php
// PHP program to find the index with 
// minimum sum of prefix and suffix 
// sums in an Array 
function indexMinSum($arr, $n
    // Initialization of the 
    // min value 
    $min = $arr[0]; 
    $index = 0; 
  
    // Find minimum element in
    // the array 
    for ($i = 1; $i < $n; $i++)
    
        if ($arr[$i] < $min
        
  
            // store the index of the 
            // current minimum element 
            $min = $arr[$i]; 
            $index = $i
        
    
  
    // return the index of min 
    // element 1-based index 
    return ($index + 1); 
  
// Driver Code 
$arr = array(6, 8, 2, 3, 5 ); 
$n = sizeof($arr); 
echo indexMinSum($arr, $n); 
  
// This code is contributed by Sachin
?>

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Output:

3


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Improved By : inderDuMCA, Ryuga, Sach_Code, Ita_c