Minimum Removals to Make Mountain List - Microsoft Top Interview Questions


Problem Statement :


You are given a list of integers nums. 

Return the minimum number of elements we can remove from nums such that the list becomes a mountain list.

A mountain list is a list that is first strictly increasing and then strictly decreasing. 

Each of the increasing and decreasing parts should be non-empty. You can assume that a solution exists.

Constraints

n ≤ 100,000 where n is the length of nums

Example 1

Input

nums = [1, 6, 5, 7, 4]

Output

1

Explanation

We can remove 6 to get [1, 5, 7, 4]



Solution :



                        Solution in C++ :

int solve(vector<int>& nums) {
    int n = nums.size();

    vector<int> lis;
    vector<int> dp(n);
    int idx = 0;
    for (auto i : nums) {
        auto it = lower_bound(lis.begin(), lis.end(), i);
        if (it == lis.end())
            lis.push_back(i);
        else
            *it = i;
        dp[idx++] = lis.size();
    }

    for (auto i : dp) cout << i << " ";
    cout << endl;

    int ans = INT_MAX;
    idx = 0;
    reverse(nums.begin(), nums.end());
    lis.clear();
    for (auto i : nums) {
        auto it = lower_bound(lis.begin(), lis.end(), i);
        if (it == lis.end())
            lis.push_back(i);
        else
            *it = i;

        if (dp[n - idx - 1] > 1 && lis.size() > 1) {
            ans = min(ans, n - (int)lis.size() - dp[n - idx - 1] + 1);
        }
        idx++;
    }

    return ans == INT_MAX ? -1 : ans;
}
                    


                        Solution in Python : 
                            
class Solution:
    def solve(self, nums):
        n = len(nums)

        def lis(nums):
            lengths = []
            mono_list = [math.inf]
            for num in nums:
                index = bisect_left(mono_list, num)
                if index == len(mono_list):
                    mono_list.append(num)
                else:
                    mono_list[index] = num
                lengths.append(len(mono_list) if index > 0 else -math.inf)
            return lengths

        increasing = lis(nums)
        decreasing = lis(reversed(nums))[::-1]

        return n - max(increasing[i] + decreasing[i] - 1 for i in range(1, n - 1))
                    

View More Similar Problems

Maximum Element

You have an empty sequence, and you will be given N queries. Each query is one of these three types: 1 x -Push the element x into the stack. 2 -Delete the element present at the top of the stack. 3 -Print the maximum element in the stack. Input Format The first line of input contains an integer, N . The next N lines each contain an above mentioned query. (It is guaranteed that each

View Solution →

Balanced Brackets

A bracket is considered to be any one of the following characters: (, ), {, }, [, or ]. Two brackets are considered to be a matched pair if the an opening bracket (i.e., (, [, or {) occurs to the left of a closing bracket (i.e., ), ], or }) of the exact same type. There are three types of matched pairs of brackets: [], {}, and (). A matching pair of brackets is not balanced if the set of bra

View Solution →

Equal Stacks

ou have three stacks of cylinders where each cylinder has the same diameter, but they may vary in height. You can change the height of a stack by removing and discarding its topmost cylinder any number of times. Find the maximum possible height of the stacks such that all of the stacks are exactly the same height. This means you must remove zero or more cylinders from the top of zero or more of

View Solution →

Game of Two Stacks

Alexa has two stacks of non-negative integers, stack A = [a0, a1, . . . , an-1 ] and stack B = [b0, b1, . . . , b m-1] where index 0 denotes the top of the stack. Alexa challenges Nick to play the following game: In each move, Nick can remove one integer from the top of either stack A or stack B. Nick keeps a running sum of the integers he removes from the two stacks. Nick is disqualified f

View Solution →

Largest Rectangle

Skyline Real Estate Developers is planning to demolish a number of old, unoccupied buildings and construct a shopping mall in their place. Your task is to find the largest solid area in which the mall can be constructed. There are a number of buildings in a certain two-dimensional landscape. Each building has a height, given by . If you join adjacent buildings, they will form a solid rectangle

View Solution →

Simple Text Editor

In this challenge, you must implement a simple text editor. Initially, your editor contains an empty string, S. You must perform Q operations of the following 4 types: 1. append(W) - Append W string to the end of S. 2 . delete( k ) - Delete the last k characters of S. 3 .print( k ) - Print the kth character of S. 4 . undo( ) - Undo the last (not previously undone) operation of type 1 or 2,

View Solution →