<p>Given an integer array <code>nums</code> and an integer <code>k</code>, return <em>the number of <strong>good subarrays</strong> of </em><code>nums</code>.</p>

<p>A <strong>good array</strong> is an array where the number of different integers in that array is exactly <code>k</code>.</p>

<ul>
	<li>For example, <code>[1,2,3,1,2]</code> has <code>3</code> different integers: <code>1</code>, <code>2</code>, and <code>3</code>.</li>
</ul>

<p>A <strong>subarray</strong> is a <strong>contiguous</strong> part of an array.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,1,2,3], k = 2
<strong>Output:</strong> 7
<strong>Explanation:</strong> 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]
</pre>

<p><strong class="example">Example 2:</strong></p>

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

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= nums[i], k &lt;= nums.length</code></li>
</ul>

class Solution {
public:
    int subarraysWithKDistinct(vector<int>& arr, int k) {
        int head = -1;
        int tail = 0;
        int ans = 0;
        int cnt = 0;
        int n = arr.size();
        map<int, int> mp;
        
        while (tail < n) {
            while ((head + 1 < n) && (mp[arr[head + 1]] > 0 || cnt + 1 <= k)) {
                head++;
                // cout<<mp[arr[head]]<<" ";
                mp[arr[head]]++;
                if (mp[arr[head]] == 1)
                    cnt++;
    
            }
            // cout<<"\n";
            //  update ans for [tail to head]
            int x = (head - tail + 1);
            ans += x;

            //* (x + 1) / 2;
            // eject one element
            if (tail <= head) { // for a non empty window
                mp[arr[tail]]--;
                if (mp[arr[tail]] == 0) {
                    cnt--;
                }
                tail++;
            } else {
                tail++;
                head = tail - 1;
            }
        
        }

        mp.clear();
        head = -1;
        tail = 0;
        int ans1 = 0;
        cnt = 0;
        k--;
         while (tail < n) {
            while ((head + 1 < n) && (mp[arr[head + 1]] > 0 || cnt + 1 <= k)) {
                head++;
                // cout<<mp[arr[head]]<<" ";
                mp[arr[head]]++;
                if (mp[arr[head]] == 1)
                    cnt++;
    
            }
            // cout<<"\n";
            //  update ans for [tail to head]
            int x = (head - tail + 1);
            ans1 += x;

            //* (x + 1) / 2;
            // eject one element
            if (tail <= head) { // for a non empty window
                mp[arr[tail]]--;
                if (mp[arr[tail]] == 0) {
                    cnt--;
                }
                tail++;
            } else {
                tail++;
                head = tail - 1;
            }
        
        }



        return ans-ans1;
    }
};
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