Finding minimum scalar product of two vectors in Python

October 12, 2022

Minimum scalar product of two vectors in Python

Here, in this page you will find the program to find the minimum scalar product of two vectors in Python Programming Language. We will discuss different methods to find the product of given two vectors.

Methods Discussed :

Method 1 : Without Using Inbuilt sort() function.
Method 2 : Using sort() function.

Method 1 :

Sort the first array in ascending order,
Sort the second array in descending order.
Declare a variable say product = 0.
Run a loop from index 0 to n
Set product += (arrr1[i]*arr2[i])
After complete iteration print product.

Time and Space Complexity :

Time Complexity : O(n²)
Space Complexity : O(1)

Method 1 : Code in Python

Run

arr1 = [1, 2, 6, 3, 7]
arr2 = [10, 7, 45, 3, 7]

n = len(arr1)

#Sort arr1 in ascending order
for i in range(n):
    for j in range(i+1, n): 
        if arr1[i]>arr1[j] :
            arr1[i], arr1[j] = arr1[j], arr1[i]

#Sort arr2 in descending order
for i in range(n):
    for j in range(i+1, n): 
        if arr2[i]<arr2[j] :
            arr2[i], arr2[j] = arr2[j], arr2[i]

product = 0
for i in range(n):
    product += arr1[i]*arr2[i]

print(product)

Output

Finding Non Repeating elements in an Array

Removing Duplicate elements from an array

Finding Maximum scalar product of two vectors in an array

Counting the number of even and odd elements in an array

Find all Symmetric pairs in an array

Method 2 :

In this method we will use inbuilt sort function to sort the array.

For, sorting arr1 in ascending order, use arr1.sort()
For, sorting arr2 in descending order, use arr2.sort(reverse=True).

sort() function

The sort() method is a built-in Python method that, by default, sorts the list in ascending order.
However, you can modify the order from ascending to descending by specifying the sorting criteria.
On passing parameter reverse with value True, i.e, reverse-True : Then the array will get sorted in descending order

Method 2 : Code in Python

Run

arr1 = [1, 2, 6, 3, 7]
arr2 = [10, 7, 45, 3, 7]
n = len(arr1)

#Sort arr1 in ascending order
arr1.sort()

#Sort arr2 in descending order
arr2.sort(reverse=True)

product = 0
for i in range(n):
    product += arr1[i]*arr2[i]

print(product)

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