<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>

const int MAX = 1000 + 1;
int memory_lds[MAX][MAX];
int memory_lis[MAX];

// Find length of longest decreasing STARTing from cur idx
int LDS_START(int index,int last,vector<int>& nums){
	if(index==nums.size())return 0;
	if(memory_lds[index][last]!=-1)return memory_lds[index][last];
	int leave_choice=LDS_START(index+1,last,nums);
	int pick_choice=0;
	if(last==nums.size() || nums[index]<nums[last])
	pick_choice=1+LDS_START(index+1,index,nums);
	return memory_lds[index][last]=max(leave_choice,pick_choice);
}
int LIS_END(int cur, vector<int> &numbers) {
	if (cur == -1)
		return 0;

	auto &ret = memory_lis[cur];
	if (ret != -1)
		return ret;

	ret = 0;
	for (int prev = cur - 1; prev >= 0; --prev)
		if (numbers[prev] < numbers[cur])
			ret = max(ret, LIS_END(prev,numbers));

	ret += 1;
	return ret;
}
class Solution {
public:
	int minimumMountainRemovals( vector<int> &nums) {
		int sz = nums.size();
        memset(memory_lds, -1, sizeof(memory_lds));
        memset(memory_lis, -1, sizeof(memory_lis));
		int longest_incerasing_decreasing = 0;
		for (int i = 0; i < sz; i++) {
			if (LIS_END(i,nums) == 1 || LDS_START(i,nums.size(),nums) == 1)
				continue;
			int cur = LIS_END(i,nums) + LDS_START(i,nums.size(),nums) - 1;
			longest_incerasing_decreasing = max(longest_incerasing_decreasing, cur);
		}
		return sz - longest_incerasing_decreasing;
	}
};
18300