<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:
 int optimal(vector<int>&arr,vector<int>&lis){
        if (arr.size() == 0) return 0;

        vector<int>ans;
        lis.push_back(1);
        ans.push_back(arr[0]);

        for(int i=1;i<arr.size();i++){
            if (arr[i] > ans.back()){
                //include
                ans.push_back(arr[i]);
                lis.push_back(ans.size());
            }
            else{
                //overwrite
                //find index of just bada 
                int index = lower_bound(ans.begin(),ans.end(),arr[i]) - ans.begin();
                ans[index] = arr[i];
                lis.push_back(index+1);
            }
        }
        return ans.size();
    }
    int minimumMountainRemovals(vector<int>& nums) {
        vector<int>lis,lds;
        optimal(nums,lis);
        reverse(nums.begin(),nums.end());
        optimal(nums,lds);

        int large = INT_MIN;
        for(int i=0;i<nums.size();i++){
            if (lis[i] == 1 || lds[nums.size()-i-1] == 1) continue;
            large = max(large,lis[i] + lds[nums.size()-i-1] - 1);
        }
        int mini = nums.size() - large;
        return mini;
    }
};
15800