0992 - Subarrays with K Different Integers (Hard)

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]

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].

class Solution {
public:
    int atMost(vector<int>& nums, int k) {
        // standard sliding window pattern
        int n = nums.size(), i = 0, ans = 0;
        unordered_map<int, int> m;
        for (int j = 0; j < n; j++) {
            // step 1: make the condition invalid
            k -= !m[nums[j]]++;
            // step 2: if the condition is failed,
            // it means we need to shrink the window
            // by adding k to make the condition valid
            while(k < 0) k += !(--m[nums[i++]]);
            // step 3: add the distance to ans
            ans += j - i + 1;
        }
        return ans;
    }

    int subarraysWithKDistinct(vector<int>& nums, int k) {
        // exactky k = at most k - at most (k - 1)
        return atMost(nums, k) - atMost(nums, k - 1);
    }
};