21. Subarrays with K Different Integers

Given an array nums of positive integers, call a (contiguous, not necessarily distinct) subarray of nums good if the number of different integers in that subarray is exactly k.

(For example, [1,2,3,1,2] has 3 different integers: 1, 2, and 3.)

Return the number of good subarrays of nums.

Example 1:

Input: nums = [1,2,1,2,3], k = 2
Output: 7
Explanation: Subarrays formed with exactly 2 different integers: [1,2], [2,1], [1,2], [2,3], [1,2,1], [2,1,2], [1,2,1,2].

Example 2:

Input: nums = [1,2,1,3,4], k = 3
Output: 3
Explanation: Subarrays formed with exactly 3 different integers: [1,2,1,3], [2,1,3], [1,3,4].

Solution: (Sliding Window)

Approach: Exact(k) = Atmost(k) - Atmost(k-1)

class Solution
{
public:
    int findAtmost(vector<int> &nums, int k)
    {
        unordered_map<int, int> m;

        int count = 0;
        int start = 0;
        int res = 0;

        for (int i = 0; i < nums.size(); i++)
        {

            if (!m[nums[i]])
            {
                count++;
            }

            m[nums[i]]++;

            while (count > k)
            {
                m[nums[start]]--;
                if (!m[nums[start]])
                {
                    count--;
                }
                start++;
            }

            res += i - start;
        }

        return res;
    }

    int subarraysWithKDistinct(vector<int> &nums, int k)
    {
        return findAtmost(nums, k) - findAtmost(nums, k - 1);
    }
};

Time Complexity: O(n)