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Solution 15: Cardinality Constraint (Subarrays with K Different Integers)

Approach Explanation

Finding "Exactly K" directly is hard. We use Exactly K = AtMost(K) - AtMost(K-1).

Step-by-Step Logic

  1. Define at_most(k):
    • Use a sliding window and a hash map to keep track of frequency of characters.
    • while len(count) > k: shrink the window from left.
    • res += r - l + 1.
  2. Return at_most(k) - at_most(k - 1).

Complexity

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

Code

from collections import Counter

def subarrays_with_k_distinct(nums, k):
    def at_most(goal):
        count = Counter()
        res = 0
        l = 0
        for r in range(len(nums)):
            if count[nums[r]] == 0:
                goal -= 1
            count[nums[r]] += 1
            
            while goal < 0:
                count[nums[l]] -= 1
                if count[nums[l]] == 0:
                    goal += 1
                l += 1
            res += (r - l + 1)
        return res
        
    return at_most(k) - at_most(k - 1)