<p>You are given an integer array <code>nums</code> and two integers <code>minK</code> and <code>maxK</code>.</p>

<p>A <strong>fixed-bound subarray</strong> of <code>nums</code> is a subarray that satisfies the following conditions:</p>

<ul>
	<li>The <strong>minimum</strong> value in the subarray is equal to <code>minK</code>.</li>
	<li>The <strong>maximum</strong> value in the subarray is equal to <code>maxK</code>.</li>
</ul>

<p>Return <em>the <strong>number</strong> of fixed-bound subarrays</em>.</p>

<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 = [1,3,5,2,7,5], minK = 1, maxK = 5
<strong>Output:</strong> 2
<strong>Explanation:</strong> The fixed-bound subarrays are [1,3,5] and [1,3,5,2].
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,1,1,1], minK = 1, maxK = 1
<strong>Output:</strong> 10
<strong>Explanation:</strong> Every subarray of nums is a fixed-bound subarray. There are 10 possible subarrays.
</pre>

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

<ul>
	<li><code>2 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i], minK, maxK &lt;= 10<sup>6</sup></code></li>
</ul>

class Solution {
public:
    long long countSubarrays(vector<int>& nums, int minK, int maxK) {
        bool found_min = false;
        bool found_max = false;
        int start = 0;
        int min_idx = -1;
        int max_idx = -1;
        long long res = 0;
        for(int i = 0; i<nums.size(); i++) {
            if(nums.at(i)==minK) {
                found_min = true;
                min_idx = i;
            }
            if(nums.at(i)==maxK) {
                found_max = true;
                max_idx = i;
            }
            if(nums.at(i) > maxK || nums.at(i) < minK) {
                // invalid out of bound number.
                // we need to update start to discard this number
                // since it is asking subarray, we need to move start to i+1
                // and thus all subarray before i that includes i is discarded.
                start = i+1;
                found_min = false;
                found_max = false;
            }
            
            if(found_min && found_max) {
                // the rage from min_idx ~ max_idx is fixed (must be included)
                // the only variation is between the start and fixed array.
                res += min(min_idx, max_idx) - start + 1;
            }
        }
        return res;
    }
};
83000