We use a hash map to store the index of each number. Every time we encounter a number that is already in the map, we check if the difference between current index and stored index is <= k.

1. Initialize seen = {}.
2. For i, num in enumerate(nums):
   • If num in seen and i - seen[num] <= k:
     • Return True.
   • seen[num] = i.
3. Return False.

• Time Complexity: O(N).
• Space Complexity: O(N).

def contains_nearby_duplicate(nums, k):
    seen = {}
    for i, n in enumerate(nums):
        if n in seen and i - seen[n] <= k:
            return True
        seen[n] = i
    return False