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You are given an array of integers that has been “encrypted” by an unknown algorithm. Write a function to find the sum of the differences between consecutive integers in the array.

To clarify, you need to:

1. Iterate over the array.
2. Calculate the difference between each consecutive pair of integers.
3. Sum these differences.
4. Return the sum.

Note: The array is zero-indexed, and the length of the array is n such that n >= 2.

Clarifying Questions

• Q: Are there any constraints on the length of the array?
  • A: The array length n will be at least 2.
• Q: Should the function handle negative integers as well?
  • A: Yes, the function should handle both positive and negative integers.
• Q: Will the input array always be valid (i.e., always have at least two integers)?
  • A: Yes, you can assume the input array will always be valid.

Strategy

1. Iterate through the array from the second element to the last element.
2. For each element, calculate the difference between the current element and the previous element.
3. Sum up these differences.
4. Return the sum as the result.

Code

Here is a Python function implementing the above strategy:

def sum_of_differences(arr):
    # Initialize the sum to zero
    total_sum = 0
    
    # Iterate from the second element to the last element
    for i in range(1, len(arr)):
        # Calculate the difference between the current and previous element
        difference = arr[i] - arr[i - 1]
        # Add the difference to the sum
        total_sum += difference
    
    return total_sum

# Example usage:
# Input array
arr = [3, 6, 1, 9, 2]
# Calculating the sum of differences
result = sum_of_differences(arr)
print("The sum of differences is:", result)

Time Complexity

The time complexity of this function is O(n), where n is the length of the input array. This is because we iterate through the array exactly once to calculate the sum of differences.

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