Java program to find minimum scalar of two vectors

February 9, 2022

Minimum scalar product of two vectors

In this section we will discuss the program to find the minimum scalar product of two vectors using java. We are given with two integer arrays and need to find the minimum scalar product obtained.

Example

Input :arr1[4] = [10, 30, 40, 20]
arr2[4] = [2, 4, 5, 1]
Output : 230
Explanation : 10*5 + 20*4 + 30*2 + 40*1 = 230

Here, we will discuss the two different ways for solving the problem. These two different ways are :

Method 1 : Sorting Without using inbuilt function.
Method 2 : Sorting using inbuilt 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 Java

class Main
{
    public static void main (String[] args)
    {
           int arr1[] = {1, 2, 6, 3, 7};
           int arr2[] = {10, 7, 45, 3, 7};
           int n = arr1.length;

           //Sort arr1 in ascending order
           for(int i=0; i<n; i++){
                for(int j=i+1; j<n; j++){ if(arr1[i]>arr1[j]){
                       int temp = arr1[i];
                       arr1[i] = arr1[j];
                       arr1[j] = temp;
                    }
                }
            }

           //Sort arr2 in descending order
           for(int i=0; i<n; i++){
                for(int j=i+1; j<n; j++){
                    if(arr2[i]<arr2[j]){
                        int temp = arr2[i];
                        arr2[i] = arr2[j];
                        arr2[j] = temp;
                    }
                 }
            }

          int product = 0;
          for(int i=0; i<n; i++)
              product += arr1[i]*arr2[i];

          System.out.print(product);
   }
}

Output

Method 2 :

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

For, sorting arr1 in ascending order, use Arrays.sort(arr1)
For, sorting arr2 in descending order, use Arrays.sort(arr2, Collections.reverseOrder());.

Time and Space Complexity :

Time Complexity : O(n log(n))
Space Complexity : O(1)

Method 2 : Code in Java

import java.util.Arrays;
import java.util.Collections;
class Main
{
    public static void main (String[] args)
    {
          Integer arr1[] = {1, 2, 6, 3, 7};
          Integer arr2[] = {10, 7, 45, 3, 7};
          int n = arr1.length;

          //Sort arr1 in ascending order
          Arrays.sort(arr1);

          //Sort arr2 in descending order
          Arrays.sort(arr2, Collections.reverseOrder());

          int product = 0;
          for(int i=0; i<n; i++)
              product += arr1[i]*arr2[i];

          System.out.print(product);
   }
}