Shortest Sublist to Remove to Make Sorted List - Amazon Top Interview Questions


Problem Statement :


Given a list of integers nums, return the length of the shortest sublist that you can remove such that the resulting list is in ascending order.

Constraints

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

Example 1

Input

nums = [1, 1, 3, 5, 4, 2, 1, 9]

Output

3

Explanation

If we remove [4, 2, 1], then the list would be sorted in ascending order: [1, 1, 3, 5, 9].


Solution :



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                        Solution in C++ :

int solve(vector<int>& nums) {
    {
        bool issorted = true;
        for (int i = 1; i < nums.size() && issorted; i++) {
            issorted = nums[i] >= nums[i - 1];
        }
        if (issorted) return 0;
    }
    int prefixsize = 1;
    for (int i = 1; i < nums.size(); i++) {
        if (nums[i] < nums[i - 1]) break;
        prefixsize++;
    }
    int suffixsize = 1;
    for (int i = nums.size() - 2; i >= 0; i--) {
        if (nums[i] > nums[i + 1]) break;
        suffixsize++;
    }
    int ret = suffixsize;
    int j = 0;
    for (int i = 0; i < prefixsize; i++) {
        while (j < suffixsize && nums[nums.size() - suffixsize + j] < nums[i]) j++;
        ret = max(ret, i + 1 + suffixsize - j);
    }
    return nums.size() - ret;
}
                    

                        Solution in Java :

import java.util.*;

class Solution {
    public int solve(int[] nums) {
        final int N = nums.length;
        if (N < 2)
            return 0;
        boolean[] leftvalid = new boolean[N];
        leftvalid[0] = true;
        for (int i = 1; i != N; i++) leftvalid[i] = leftvalid[i - 1] && (nums[i] >= nums[i - 1]);
        boolean[] rightvalid = new boolean[N];
        rightvalid[N - 1] = true;
        for (int i = N - 2; i != -1; i--)
            rightvalid[i] = rightvalid[i + 1] && (nums[i] <= nums[i + 1]);
        if (rightvalid[0])
            return 0;
        int l = 1, h = N - 2;
        while (l <= h) {
            int m = (l + h) >>> 1;
            if (can(nums, leftvalid, rightvalid, m))
                h = m - 1;
            else
                l = m + 1;
        }
        return l;
    }

    private boolean can(int[] nums, boolean[] left, boolean[] right, final int K) {
        if (left[left.length - K - 1] || right[K])
            return true;
        for (int i = 1, j = K; j + 1 != left.length; i++, j++)
            if (left[i - 1] && right[j + 1] && nums[i - 1] <= nums[j + 1])
                return true;
        return false;
    }
}
                    


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