Contains Duplicate

Clarify the problem:

• The problem requires determining whether an array contains any duplicate elements.
• We need to implement a function that takes an array as input and returns a boolean indicating whether the array contains any duplicates.

Analyze the problem:

• Input: An array of integers.
• Output: A boolean value indicating whether the array contains any duplicates.
• Constraints:
  • The input array may be empty or contain multiple elements.
  • The array may contain both positive and negative integers.
  • The integers in the array can be repeated.

Design an algorithm:

• We can solve this problem using a hash set data structure.
• We will iterate through the array and add each element to the hash set.
• If we encounter an element that is already in the hash set, it means we have found a duplicate, and we return True.
• If we iterate through the entire array without finding any duplicates, we return False.

Explain your approach:

• We will implement a function called containsDuplicate that takes an array, nums, as input.
• We will create an empty hash set called seen to store the unique elements.
• We will iterate through the elements of the array and check if each element is already in the hash set.
• If an element is in the hash set, we return True.
• Otherwise, we add the element to the hash set.
• If we iterate through the entire array without finding any duplicates, we return False.

Write clean and readable code:

python

def containsDuplicate(nums):
    seen = set()

    for num in nums:
        if num in seen:
            return True
        seen.add(num)

    return False

Test your code:

python

# Test case 1
# Input: [1, 2, 3, 1]
# The array contains the duplicate element 1.
# Expected output: True
assert containsDuplicate([1, 2, 3, 1]) == True

# Test case 2
# Input: [1, 2, 3, 4]
# The array does not contain any duplicates.
# Expected output: False
assert containsDuplicate([1, 2, 3, 4]) == False

# Test case 3
# Input: [1, 1, 1, 1]
# The array contains duplicate elements (all 1's).
# Expected output: True
assert containsDuplicate([1, 1, 1, 1]) == True

Optimize if necessary:

• The current solution has a time complexity of O(n), where n is the number of elements in the array.
• It uses a hash set to efficiently check for duplicates in constant time.
• This solution is already efficient, and there is no further optimization possible in terms of time complexity.

Handle error cases:

• The code assumes that the input array is valid and contains only integers.
• It does not handle invalid input, such as empty arrays or arrays with non-integer elements.
• In such cases, the behavior of the code is undefined.

Discuss complexity analysis:

• The time complexity of the solution is O(n), where n is the number of elements in the array.
• The space complexity is O(n) in the worst case, where n is the number of elements in the array (all elements are unique).
• The best-case scenario occurs when the first two elements are duplicates, and the function returns True in constant time.
• The worst-case scenario occurs when all elements in the array are unique, and the function iterates through all n elements, taking O(n) time.
• The average-case time complexity is also O(n), assuming random inputs.