Python: Compute the summation of the absolute difference of all distinct pairs in a given array

Last update on December 21 2024 07:19:17 (UTC/GMT +8 hours)

Absolute Pairwise Difference

Write a Python program to compute the summation of the absolute difference of all distinct pairs in a given array (non-decreasing order).

Sample array: [1, 2, 3]
Then all the distinct pairs will be:
1 2
1 3
2 3

Sample Solution:

Python Code:

# Define a function 'sum_distinct_pairs' that calculates the sum of distinct pairs.
def sum_distinct_pairs(arr):
    # Initialize the result variable to store the sum.
    result = 0
    
    # Initialize the index variable.
    i = 0
    
    # Iterate through the array elements.
    while i < len(arr):
        # Calculate the contribution of the current element to the sum.
        result += i * arr[i] - (len(arr) - i - 1) * arr[i]
        
        # Increment the index.
        i += 1
    
    # Return the final result.
    return result

# Test the 'sum_distinct_pairs' function with different arrays and print the results.
print(sum_distinct_pairs([1, 2, 3]))
print(sum_distinct_pairs([1, 4, 5]))

Sample Output:

4
8

Explanation:

The above Python code defines a function named "sum_distinct_pairs()" that calculates the sum of distinct pairs for a given list of numbers. Here's a brief explanation:

• Function Definition:
• def sum_distinct_pairs(arr):: Define a function named sum_distinct_pairs that takes a list of numbers 'arr' as input.
• Initialize Variables:
• result = 0: Initialize a variable 'result' to store the sum of distinct pairs.
• i = 0: Initialize an index variable to iterate through the array.
• Iterate Through Array:
• while i < len(arr):: Start a while loop to iterate through the elements of the array.
• Calculate Contribution to Sum:
• result += i arr[i] - (len(arr) - i - 1) arr[i]: Calculate the contribution of the current element to the sum based on the given formula.
• Increment Index:
• i += 1: Increment the index to move to the next element in the array.
• Return Result:
• return result: Return the final sum of distinct pairs.
• Function Testing:
• print(sum_distinct_pairs([1, 2, 3])): Test the "sum_distinct_pairs()" function with a specific array and print the result.
• print(sum_distinct_pairs([1, 4, 5])): Test the function with another array and print the result.

Visual Presentation:

Flowchart:

Python Code Editor:

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