ou have a list arr of all integers in the range [1, n] sorted in a strictly increasing order. Apply the following algorithm on arr:Starting from left to right, remove the first number and every other number afterward until you reach the end of the list.Repeat the previous step again, but this time from right to left, remove the rightmost number and every other number from the remaining numbers.Keep repeating the steps again, alternating left to right and right to left, until a single number remains.Given the integer n, return the last number that remains in arr.Example 1:Input:n = 9Output:6Explanation:arr = [1, 2,3, 4,5, 6,7, 8,9] arr = [2,4, 6,8] arr = [2, 6] arr = [6]Example 2:Input:n = 1Output:1Constraints:- 1 <= n <= 109
Question
ou have a list arr of all integers in the range [1, n] sorted in a strictly increasing order. Apply the following algorithm on arr:Starting from left to right, remove the first number and every other number afterward until you reach the end of the list.Repeat the previous step again, but this time from right to left, remove the rightmost number and every other number from the remaining numbers.Keep repeating the steps again, alternating left to right and right to left, until a single number remains.Given the integer n, return the last number that remains in arr.Example 1:Input:n = 9Output:6Explanation:arr = [1, 2,3, 4,5, 6,7, 8,9] arr = [2,4, 6,8] arr = [2, 6] arr = [6]Example 2:Input:n = 1Output:1Constraints:- 1 <= n <= 109
Solution
The problem is asking to return the last number that remains after applying a certain algorithm on a list of integers from 1 to n. The algorithm is as follows:
- Starting from left to right, remove the first number and every other number afterward until you reach the end of the list.
- Repeat the previous step again, but this time from right to left, remove the rightmost number and every other number from the remaining numbers.
- Keep repeating the steps again, alternating left to right and right to left, until a single number remains.
Here is a Python solution using a deque:
from collections import deque
def lastRemaining(n):
d = deque(range(1, n+1))
left = True
while len(d) > 1:
if left:
d.popleft()
else:
d.pop()
d.rotate(-1 if left else 1)
left = not left
return d[0]
In this solution, we use a deque to efficiently remove elements from both ends of the list. We start by initializing a deque with all integers from 1 to n. Then, we use a boolean variable left to keep track of the direction. If left is True, we remove the first element of the deque, otherwise we remove the last element. After removing an element, we rotate the deque to the left if the current direction is left, and to the right otherwise. Finally, we flip the direction and repeat the process until only one element remains in the deque, which is the result.
Similar Questions
Given an array of integers nums sorted in non-decreasing order, find the starting and ending position of a given target value.If target is not found in the array, return [-1, -1].You must write an algorithm with O(log n) runtime complexity. Example 1:Input: nums = [5,7,7,8,8,10], target = 8Output: [3,4]Example 2:Input: nums = [5,7,7,8,8,10], target = 6Output: [-1,-1]Example 3:Input: nums = [], target = 0Output: [-1,-1] Constraints:0 <= nums.length <= 105-109 <= nums[i] <= 109nums is a non-decreasing array.-109 <= target <= 109
Given an unsorted array Arr[] of N integers and a Key which is present in this array. You need to write a program to find the start index( index where the element is first found from left in the array ) and end index( index where the element is first found from right in the array ).If the key does not exist in the array then return -1 for both start and end index in this case.
Write a program to implement the Selection Sort algorithm to sort an array of integers in ascending order.Input:91 3 5 7 9 2 4 6 8Output:1 2 3 4 5 6 7 8 9Explanation:Initially, the minimum element in the array is 1. It is swapped with the first element, resulting in the array [1, 3, 8, 2, 5, 4]. Next, the minimum element in the remaining unsorted part is 2. It is swapped with the second element, resulting in [1, 2, 8, 3, 5, 4]. This process continues, and the final sorted array is [1, 2, 3, 4, 5, 8].
longest consecutive elementsYou need to write a function that takes an unsorted array of integers as input and returns the length of the longest consecutive elements sequence in the array. A consecutive elements sequence is a subarray where the elements are adjacent in value, such as [1, 2, 3, 4] or [5, 6, 7, 8]. The order of the elements in the input array does not matter.For example, given the input array [100, 4, 200, 1, 3, 2], the longest consecutive elements sequence is [1, 2, 3, 4], which has a length of 4. Therefore, your function should return 4.In this case, there are no consecutive elements in the array, so the length of the longest consecutive element sequence is 1.Testcase:Input11 // no of elements of array8 10 12 14 1 2 3 4 5 6 7 // array elementsOutput:8
Given a fixed-length integer array arr, duplicate each occurrence of zero, shifting the remaining elements to the right.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.