Índice con suma mínima de sumas de prefijos y sufijos en una array

Dada una array de enteros. La tarea es encontrar el índice  en la array en el que el valor de prefixSum(i) + suffixSum(i) es mínimo.
Nota : 
 

• PrefixSum(i) = La suma de los primeros i números de la array.
• SuffixSum(i) = la suma de los últimos N – i + 1 números de la array.
• La indexación basada en 1 se considera para la array. Ese es un índice del primer elemento en la array es 1.

Ejemplos: 
 

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

Dado que necesitamos minimizar el valor de PrefixSum[i] + SuffixSum[i] . Esa es la suma de los primeros  elementos y  los elementos del final. 
Si se observa cuidadosamente, se puede ver que: 
 

PrefixSum[i] + SuffixSum[i] = Suma de todos los elementos en el arreglo + arr[i] (Elemento en el i-ésimo índice) 
 

Dado que la suma de todos los elementos de la array será la misma para cada índice, el valor de PrefixSum[i] + SuffixSum[i] será mínimo para el valor mínimo de arr[i] . 
Por lo tanto, la tarea se reduce a encontrar solo el índice del elemento mínimo de la array.
A continuación se muestra la implementación del enfoque anterior: 
 

// 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;
}

// 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..

# 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

// 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
}

<?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
?>

<script>
 
// JavaScript 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
    let min = arr[0];
    let index = 0;
   
    // Find minimum element in the array
    for (let 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
    let arr=[6, 8, 2, 3, 5];
    let n =arr.length;
    document.write( indexMinSum(arr, n));
 
// This code is contributed by avanitrachhadiya2155
 
</script>

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