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

  • Difficulty Level : Basic
  • Last Updated : 26 May, 2021

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.

 

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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++




// 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




// 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




# 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#




// 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
// 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
?>

Javascript




<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>
Output: 
3

 




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