<p>You may recall that an array <code>arr</code> is a <strong>mountain array</strong> if and only if:</p>

<ul>
	<li><code>arr.length &gt;= 3</code></li>
	<li>There exists some index <code>i</code> (<strong>0-indexed</strong>) with <code>0 &lt; i &lt; arr.length - 1</code> such that:
	<ul>
		<li><code>arr[0] &lt; arr[1] &lt; ... &lt; arr[i - 1] &lt; arr[i]</code></li>
		<li><code>arr[i] &gt; arr[i + 1] &gt; ... &gt; arr[arr.length - 1]</code></li>
	</ul>
	</li>
</ul>

<p>Given an integer array <code>nums</code>​​​, return <em>the <strong>minimum</strong> number of elements to remove to make </em><code>nums<em>​​​</em></code><em> </em><em>a <strong>mountain array</strong>.</em></p>

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

<pre>
<strong>Input:</strong> nums = [1,3,1]
<strong>Output:</strong> 0
<strong>Explanation:</strong> The array itself is a mountain array so we do not need to remove any elements.
</pre>

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

<pre>
<strong>Input:</strong> nums = [2,1,1,5,6,2,3,1]
<strong>Output:</strong> 3
<strong>Explanation:</strong> One solution is to remove the elements at indices 0, 1, and 5, making the array nums = [1,5,6,3,1].
</pre>

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

<ul>
	<li><code>3 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
	<li>It is guaranteed that you can make a mountain array out of <code>nums</code>.</li>
</ul>

class Solution {
public:
    void calcSubsq(vector<int>& nums, vector<int> &res)
    {
        vector<int> cur;
        cur.push_back(nums[0]);
        res.push_back(cur.size());

        for(int i=1; i<nums.size(); i++)
        {
            if(nums[i] > cur[cur.size() - 1])
                cur.push_back(nums[i]);
            else
            {
                int indx = lower_bound(cur.begin(), cur.end(), nums[i]) - cur.begin();
                cur[indx] = nums[i];
            }

            res.push_back(cur.size());            
        }
    }

    int minimumMountainRemovals(vector<int>& nums) {
        vector<int> maxIncrLeft, maxDecrRight;

        calcSubsq(nums, maxIncrLeft);
        std::reverse(nums.begin(), nums.end());
        calcSubsq(nums, maxDecrRight);
        std::reverse(maxDecrRight.begin(), maxDecrRight.end());

        int minDel = INT_MAX;

        for(int i=1; i<nums.size()-1; i++)
        {
            if(maxIncrLeft[i] <= 1 || maxDecrRight[i] <= 1)
                continue;
                
            int maxLen = maxIncrLeft[i] + maxDecrRight[i] - 1;
            minDel = min(minDel, ((int)nums.size() - maxLen));
        }

        return minDel;
    }
};
15700