• 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: DP / LIS

LIS[i] := longest increasing subsequence ends with nums[i]
LDS[i] := longest decreasing subsequence starts with nums[i]
Let nums[i] be the peak, the length of the mountain array is LIS[i] + LDS[i] – 1
Note: LIS[i] and LDS[i] must be > 1 to form a valid mountain array.
ans = min(n – (LIS[i] + LDS[i] – 1)) 0 <= i < n

Time complexity: O(n^2)
Space complexity: O(n)

// Author: Huahua
class Solution {
public:
  int minimumMountainRemovals(vector<int>& nums) {
    const int n = nums.size();
    vector<int> LIS(n, 1); // LIS[i] := Longest increasing subseq ends with nums[i]
    vector<int> LDS(n, 1); // LDS[i] := Longest decreasing subseq starts with nums[i]
    for (int i = 0; i < n; ++i)      
      for (int j = 0; j < i; ++j)
        if (nums[i] > nums[j]) LIS[i] = max(LIS[i], LIS[j] + 1);
    for (int i = n - 1; i >= 0; --i)
      for (int j = n - 1; j > i; --j)
        if (nums[i] > nums[j]) LDS[i] = max(LDS[i], LDS[j] + 1);
    int ans = INT_MAX;
    for (int i = 0; i < n; ++i) {
      if (LIS[i] < 2 || LDS[i] < 2) continue;
      ans = min(ans, n - (LIS[i] + LDS[i] - 1));
    }
    return ans;
  }
};

The post 花花酱 LeetCode 1671. Minimum Number of Removals to Make Mountain Array appeared first on Huahua's Tech Road.