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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);
    }
}

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