数组中前缀和后缀和的最小总和的索引

给定一个整数数组。任务是找到索引$i$在prefixSum(i) + suffixSum(i)的值最小的数组中。
注意：

• PrefixSum(i) = 数组前 i 个数字的总和。
• SuffixSum(i) = 最后 N - i + 1 个数组的数字之和。
• 数组考虑基于 1 的索引。也就是说数组中第一个元素的索引是 1。

例子：

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

鉴于我们需要最小化PrefixSum[i] + SuffixSum[i]的值。这是第一个的总和$i$元素和$N-i+1$从头开始的元素。
如果仔细观察，可以看出：

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

由于数组中所有元素的总和对于每个索引都是相同的，因此PrefixSum[i] + SuffixSum[i]的值对于arr[i]的最小值将是最小值。
因此，任务减少到只找到数组最小元素的索引。
下面是上述方法的实现：

C++

// C++ program to find the index with
// minimum sum of prefix and suffix
// sums in an Array
 
#include 
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
}

Javascript

 
// 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
 

输出：

3

时间复杂度： O(N)

辅助空间： O(1)