数组的所有子数组的乘积| 2套

给定一个大小为N的整数数组arr[] ，任务是找到该数组所有子数组的乘积。
例子：

Input: arr[] = {2, 4} 
Output: 64 
Explanation: 
Here, subarrays are {2}, {2, 4}, and {4}. 
Products of each subarray are 2, 8, 4. 
Product of all Subarrays = 64
Input: arr[] = {1, 2, 3} 
Output: 432 
Explanation: 
Here, subarrays are {1}, {1, 2}, {1, 2, 3}, {2}, {2, 3}, {3}. 
Products of each subarray are 1, 2, 6, 2, 6, 3. 
Product of all Subarrays = 432 
 

Naive 和 Iterative 方法：请参考这篇文章了解这些方法。
方法：思路是统计所有子数组中每个元素出现的次数。为了计数，我们有以下观察结果：

• 在每个以arr[i]开头的子数组中，有(N – i) 个这样的子集，以元素arr[i]开头。
  例如：

For array arr[] = {1, 2, 3} 
N = 3 and for element 2 i.e., index = 1 
There are (N – index) = 3 – 1 = 2 subsets 
{2} and {2, 3} 
 

• 对于任何元素arr[i] ，有(N – i)*i个子数组，其中arr[i]不是第一个元素。

For array arr[] = {1, 2, 3} 
N = 3 and for element 2 i.e., index = 1 
There are (N – index)*index = (3 – 1)*1 = 2 subsets where 2 is not the first element. 
{1, 2} and {1, 2, 3} 
 

因此，根据上述观察，在每个索引 i 处的所有子数组中出现的每个元素arr[i]的总数由下式给出：

total_elements = (N - i) + (N - i)*i
total_elements = (N - i)*(i + 1) 

这个想法是将每个元素乘以(N – i)*(i + 1)次以获得所有子数组中元素的乘积。
下面是上述方法的实现：

C++

// C++ program for the above approach
#include 
using namespace std;
 
// Function to find the product of
// elements of all subarray
long int SubArrayProdct(int arr[],
                        int n)
{
    // Initialize the result
    long int result = 1;
 
    // Computing the product of
    // subarray using formula
    for (int i = 0; i < n; i++)
        result *= pow(arr[i],
                      (i + 1) * (n - i));
 
    // Return the product of all
    // elements of each subarray
    return result;
}
 
// Driver Code
int main()
{
    // Given array arr[]
    int arr[] = { 2, 4 };
    int N = sizeof(arr) / sizeof(arr[0]);
 
    // Function Call
    cout << SubArrayProdct(arr, N)
         << endl;
    return 0;
}

Java

// Java program for the above approach
import java.util.*;
 
class GFG{
 
// Function to find the product of
// elements of all subarray
static int SubArrayProdct(int arr[], int n)
{
     
    // Initialize the result
    int result = 1;
 
    // Computing the product of
    // subarray using formula
    for(int i = 0; i < n; i++)
       result *= Math.pow(arr[i], (i + 1) *
                                  (n - i));
 
    // Return the product of all
    // elements of each subarray
    return result;
}
 
// Driver code
public static void main(String[] args)
{
 
    // Given array arr[]
    int arr[] = new int[]{2, 4};
 
    int N = arr.length;
 
    // Function Call
    System.out.println(SubArrayProdct(arr, N));
}
}
 
// This code is contributed by Pratima Pandey

Python3

# Python3 program for the above approach
 
# Function to find the product of
# elements of all subarray
def SubArrayProdct(arr, n):
 
    # Initialize the result
    result = 1;
 
    # Computing the product of
    # subarray using formula
    for i in range(0, n):
        result *= pow(arr[i],
                     (i + 1) * (n - i));
 
    # Return the product of all
    # elements of each subarray
    return result;
 
# Driver Code
 
# Given array arr[]
arr = [ 2, 4 ];
N = len(arr);
 
# Function Call
print(SubArrayProdct(arr, N))
 
# This code is contributed by Code_Mech

C#

// C# program for the above approach
using System;
class GFG{
 
// Function to find the product of
// elements of all subarray
static int SubArrayProdct(int []arr, int n)
{
     
    // Initialize the result
    int result = 1;
 
    // Computing the product of
    // subarray using formula
    for(int i = 0; i < n; i++)
       result *= (int)(Math.Pow(arr[i], (i + 1) *
                                        (n - i)));
 
    // Return the product of all
    // elements of each subarray
    return result;
}
 
// Driver code
public static void Main()
{
 
    // Given array arr[]
    int []arr = new int[]{2, 4};
 
    int N = arr.Length;
 
    // Function Call
    Console.Write(SubArrayProdct(arr, N));
}
}
 
// This code is contributed by Code_Mech

Javascript

 
// JavaScript program to implement
// the above approach
 
// Function to find the product of
// elements of all subarray
function SubArrayProdct(arr, n)
{
       
    // Initialize the result
    let result = 1;
   
    // Computing the product of
    // subarray using formula
    for(let i = 0; i < n; i++)
       result *= Math.pow(arr[i], (i + 1) *
                                  (n - i));
   
    // Return the product of all
    // elements of each subarray
    return result;
}
 
// Driver code
 
     // Given array arr[]
    let arr = [2, 4];
   
    let N = arr.length;
   
    // Function Call
    document.write(SubArrayProdct(arr, N));
  
 // This code is contributed by sanjoy_62.

输出：

64

时间复杂度： O(N) ，其中 N 是元素的数量。
辅助空间： O(1)

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