algoadvance

Given an integer array nums, the array concatenation value is the sum of the concatenated value of all pairs of integers in the array. A concatenated value is calculated by concatenating two integers.

For example, if nums = [1, 2, 3, 4], the concatenated values of the pairs (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), and (3, 4) would be 12, 13, 14, 23, 24, and 34 respectively. The array concatenation value would be their sum: 12 + 13 + 14 + 23 + 24 + 34.

Write a function find_array_concatenation_value(nums: List[int]) -> int that computes the array concatenation value of nums.

Clarifying Questions

  1. Input Constraints: Are there any constraints on the length of the array?
  2. Data Type: Will the integers in nums always be non-negative?
  3. Output: Should the result be returned as an integer?

Strategy

  1. Iterate over Pairs:
    • Use nested loops to iterate over all unique pairs of elements in the array.
    • For each pair (nums[i], nums[j]), compute the concatenated value by converting each integer to string, concatenating them, and converting back to integer.
  2. Sum the Values:
    • Sum all these concatenated values.

Code

from typing import List

def find_array_concatenation_value(nums: List[int]) -> int:
    concatenation_value = 0
    n = len(nums)
    for i in range(n):
        for j in range(i+1, n):
            concatenated_value = int(str(nums[i]) + str(nums[j]))
            concatenation_value += concatenated_value
    return concatenation_value

# Example usage
nums = [1, 2, 3, 4]
print(find_array_concatenation_value(nums))  # Expected output: 146

Time Complexity

This algorithm efficiently computes the concatenation value by leveraging string operations and nested loops to sum the concatenated values of all unique pairs.

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