Sum of product of all elements of sub-arrays of size k
Given an array and a number k, the task is to calculate the sum of the product of all elements of subarrays of size k.
Examples :
Input : arr[] = {1, 2, 3, 4, 5, 6}
k = 3
Output : 210
Consider all subarrays of size k
1*2*3 = 6
2*3*4 = 24
3*4*5 = 60
4*5*6 = 120
6 + 24 + 60 + 120 = 210
Input : arr[] = {1, -2, 3, -4, 5, 6}
k = 2
Output : -10
Consider all subarrays of size k
1*-2 = -2
-2*3 = -6
3*-4 = -12
-4*5 = -20
5*6 = 30
-2 + -6 + -12 + -20+ 30 = -10
A Naive approach is to generate all subarrays of size k and do the sum of product of all elements of subarrays.
C/C++
// C++ program to find the sum of // product of all subarrays #include <iostream> using namespace std; // Function to calculate the sum of product int calcSOP(int arr[], int n, int k) { // Initialize sum = 0 int sum = 0; // Consider every subarray of size k for (int i = 0; i <= n - k; i++) { int prod = 1; // Calculate product of all elements // of current subarray for (int j = i; j < k + i; j++) prod *= arr[j]; // Store sum of all the products sum += prod; } // Return sum return sum; } // Driver code int main() { int arr[] = { 1, 2, 3, 4, 5, 6 }; int n = sizeof(arr) / sizeof(arr[0]); int k = 3; cout << calcSOP(arr, n, k); return 0; } |
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Java
// Java program to find the sum of // product of all subarrays class GFG { // Method to calculate the sum of product static int calcSOP(int arr[], int n, int k) { // Initialize sum = 0 int sum = 0; // Consider every subarray of size k for (int i = 0; i <= n - k; i++) { int prod = 1; // Calculate product of all elements // of current subarray for (int j = i; j < k + i; j++) prod *= arr[j]; // Store sum of all the products sum += prod; } // Return sum return sum; } // Driver method public static void main(String[] args) { int arr[] = { 1, 2, 3, 4, 5, 6 }; int k = 3; System.out.println(calcSOP(arr, arr.length, k)); } } |
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Python3
# python program to find the sum of # product of all subarrays # Function to calculate the sum of product def calcSOP(arr, n, k): # Initialize sum = 0 sum = 0 # Consider every subarray of size k for i in range(0, (n-k)+1): prod = 1 # Calculate product of all elements # of current subarray for j in range(i, k+i): prod = int(prod * arr[j]) # Store sum of all the products sum = sum + prod # Return sum return sum #Driver code arr = [ 1, 2, 3, 4, 5, 6 ] n = len(arr) k = 3print(calcSOP(arr, n, k)) # This code is contributed by Sam007 |
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C#
// C# program to find the sum of // product of all subarrays using System; public class GFG { // Method to calculate the sum of product static int calcSOP(int[] arr, int n, int k) { // Initialize sum = 0 int sum = 0; // Consider every subarray of size k for (int i = 0; i <= n - k; i++) { int prod = 1; // Calculate product of all elements // of current subarray for (int j = i; j < k + i; j++) prod *= arr[j]; // Store sum of all the products sum += prod; } // Return sum return sum; } // Driver method public static void Main() { int[] arr = {1, 2, 3, 4, 5, 6}; int k = 3; Console.WriteLine(calcSOP(arr, arr.Length, k)); } } // This code is contributed by Sam007 |
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PHP
<?php // PHP program to find the sum of // product of all subarrays // Function to calculate // the sum of product function calcSOP($arr, $n, $k) { // Initialize sum = 0 $sum = 0; // Consider every subarray // of size k for ($i = 0; $i <= $n - $k; $i++) { $prod = 1; // Calculate product of all // elements of current subarray for ($j = $i; $j < $k + $i; $j++) $prod *= $arr[$j]; // Store sum of all // the products $sum += $prod; } // Return sum return $sum; } // Driver code $arr = array( 1, 2, 3, 4, 5, 6 ); $n = count($arr); $k = 3; echo calcSOP($arr, $n, $k); // This code is contributed by Sam007 ?> |
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Output:
210
Time Complexity: O(nk)
An Efficient Method is to use the concept of Sliding Window.
1- Consider first subarray/window of size k, do the product of elements and add to the total_sum.
for (i=0; i < k; i++)
prod = prod * arr[i];
2- Now, By Using sliding window concept, remove first element of window from the product and add next element to the window. i.e.
for (i =k ; i < n; i++)
{
// Removing first element from product
prod = prod / arr[i-k];
// Adding current element to the product
prod = prod * arr[i];
sum += prod;
}
3- Return sum
C/C++
// C++ program to find the sum of // product of all subarrays #include <iostream> using namespace std; // Function to calculate the sum of product int calcSOP(int arr[], int n, int k) { // Initialize sum = 0 and prod = 1 int sum = 0, prod = 1; // Consider first subarray of size k // Store the products of elements for (int i = 0; i < k; i++) prod *= arr[i]; // Add the product to the sum sum += prod; // Consider every subarray of size k // Remove first element and add current // element to the window for (int i = k; i < n; i++) { // Divide by the first element // of previous subarray/ window // and product with the current element prod = (prod / arr[i - k]) * arr[i]; // Add current product to the sum sum += prod; } // Return sum return sum; } // Drivers code int main() { int arr[] = { 1, 2, 3, 4, 5, 6 }; int n = sizeof(arr) / sizeof(arr[0]); int k = 3; cout << calcSOP(arr, n, k); return 0; } |
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Java
// Java program to find the sum of // product of all subarrays class GFG { // Method to calculate the sum of product static int calcSOP(int arr[], int n, int k) { // Initialize sum = 0 and prod = 1 int sum = 0, prod = 1; // Consider first subarray of size k // Store the products of elements for (int i = 0; i < k; i++) prod *= arr[i]; // Add the product to the sum sum += prod; // Consider every subarray of size k // Remove first element and add current // element to the window for (int i = k; i < n; i++) { // Divide by the first element // of previous subarray/ window // and product with the current element prod = (prod / arr[i - k]) * arr[i]; // Add current product to the sum sum += prod; } // Return sum return sum; } // Driver method public static void main(String[] args) { int arr[] = { 1, 2, 3, 4, 5, 6 }; int k = 3; System.out.println(calcSOP(arr, arr.length, k)); } } |
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Python3
# Python3 program to find the sum of # product of all subarrays # Function to calculate the sum of product def calcSOP(arr, n, k): # Initialize sum = 0 and prod = 1 sum = 0 prod = 1 # Consider first subarray of size k # Store the products of elements for i in range(k): prod *= arr[i] # Add the product to the sum sum += prod # Consider every subarray of size k # Remove first element and add current # element to the window for i in range(k, n, 1): # Divide by the first element of # previous subarray/ window and # product with the current element prod = (prod / arr[i - k]) * arr[i] # Add current product to the sum sum += prod # Return sum return int(sum) # Drivers code arr = [1, 2, 3, 4, 5, 6] n = len(arr) k = 3 print(calcSOP(arr, n, k)) # This code is contributed 29AjayKumar |
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C#
// C# program to find the sum of // product of all subarrays using System; public class GFG { // Method to calculate the sum of product static int calcSOP(int[] arr, int n, int k) { // Initialize sum = 0 and prod = 1 int sum = 0, prod = 1; // Consider first subarray of size k // Store the products of elements for (int i = 0; i < k; i++) prod *= arr[i]; // Add the product to the sum sum += prod; // Consider every subarray of size k // Remove first element and add current // element to the window for (int i = k; i < n; i++) { // Divide by the first element // of previous subarray/ window // and product with the current element prod = (prod / arr[i - k]) * arr[i]; // Add current product to the sum sum += prod; } // Return sum return sum; } // Driver method public static void Main() { int[] arr = { 1, 2, 3, 4, 5, 6 }; int k = 3; // Function calling Console.WriteLine(calcSOP(arr, arr.Length, k)); } } // This code is contributed by Sam007 |
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PHP
<?php // php program to find the sum of // product of all subarrays // Function to calculate the sum of product function calcSOP($arr, $n, $k) { // Initialize sum = 0 and prod = 1 $sum = 0; $prod = 1; // Consider first subarray of size k // Store the products of elements for ($i = 0; $i < $k; $i++) $prod *= $arr[$i]; // Add the product to the sum $sum += $prod; // Consider every subarray of size k // Remove first element and add current // element to the window for ($i = $k; $i < $n; $i++) { // Divide by the first element // of previous subarray/ window // and product with the current element $prod = ($prod / $arr[$i - $k]) * $arr[$i]; // Add current product to the sum $sum += $prod; } // Return sum return $sum; } // Drivers code $arr = array( 1, 2, 3, 4, 5, 6 ); $n = count($arr); $k = 3; echo calcSOP($arr, $n, $k); // This code is contributed by Sam007 ?> |
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Output:
210
Time Complexity: O(n)
This article is contributed by Sahil Chhabra. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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