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# Minimum Number of Removals to Make Mountain Array

Updated: Mar 25, 2021

You may recall that an array arr is a mountain array if and only if:

• arr.length >= 3

• There exists some index i (0-indexed) with 0 < i < arr.length - 1 such that:

• arr[0] < arr[1] < ... < arr[i - 1] < arr[i]

• arr[i] > arr[i + 1] > ... > arr[arr.length - 1]

Given an integer array nums​​​, return the minimum number of elements to remove to make nums​​​ a mountain array.

Example 1:

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

Example 2:

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

Example 3:

```Input: nums = [4,3,2,1,1,2,3,1]
Output: 4
```

Example 4:

```Input: nums = [1,2,3,4,4,3,2,1]
Output: 1
```

Constraints:

• 3 <= nums.length <= 1000

• 1 <= nums[i] <= 109

• It is guaranteed that you can make a mountain array out of nums.

Solution:

```class Solution {
public int minimumMountainRemovals(int[] nums) {
int n=nums.length;
int[] left=new int[n];
int[] right=new int[n];
int result=0;
for (int i=1;i<n;i++)
{
for (int j=0;j<i;j++)
{
if (nums[i]>nums[j])
left[i]=Math.max(left[i], left[j]+1);
}

}

for (int i=n-2; i>-1;i--)
{
for (int j=n-1;j>i;j--)
{

if (nums[i]>nums[j])
right[i]=Math.max(right[i],right[j]+1);

}

}
for (int i=1;i<n;i++)
{
// System.out.println("left["+i+"]"+left[i]);
// System.out.println("right["+i+"]"+right[i]);
if (left[i] != 0 && right[i] != 0)
result = Math.max(result, left[i] +right[i]);
}
return n - (result + 1);
}
}```