# Posts tagged as “sort”

Given n points on a 2D plane where points[i] = [xi, yi], Return the widest vertical area between two points such that no points are inside the area.

vertical area is an area of fixed-width extending infinitely along the y-axis (i.e., infinite height). The widest vertical area is the one with the maximum width.

Note that points on the edge of a vertical area are not considered included in the area.

Example 1:

Input: points = [[8,7],[9,9],[7,4],[9,7]]
Output: 1
Explanation: Both the red and the blue area are optimal.


Example 2:

Input: points = [[3,1],[9,0],[1,0],[1,4],[5,3],[8,8]]
Output: 3


Constraints:

• n == points.length
• 2 <= n <= 105
• points[i].length == 2
• 0 <= xi, yi <= 109

## Solution: Sort by x coordinates

Time complexity: O(nlogn)
Space complexity: O(n)

## C++

Given an integer array arr, return the mean of the remaining integers after removing the smallest 5% and the largest 5% of the elements.

Answers within 10-5 of the actual answer will be considered accepted.

Example 1:

Input: arr = [1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3]
Output: 2.00000
Explanation: After erasing the minimum and the maximum values of this array, all elements are equal to 2, so the mean is 2.


Example 2:

Input: arr = [6,2,7,5,1,2,0,3,10,2,5,0,5,5,0,8,7,6,8,0]
Output: 4.00000


Example 3:

Input: arr = [6,0,7,0,7,5,7,8,3,4,0,7,8,1,6,8,1,1,2,4,8,1,9,5,4,3,8,5,10,8,6,6,1,0,6,10,8,2,3,4]
Output: 4.77778


Example 4:

Input: arr = [9,7,8,7,7,8,4,4,6,8,8,7,6,8,8,9,2,6,0,0,1,10,8,6,3,3,5,1,10,9,0,7,10,0,10,4,1,10,6,9,3,6,0,0,2,7,0,6,7,2,9,7,7,3,0,1,6,1,10,3]
Output: 5.27778


Example 5:

Input: arr = [4,8,4,10,0,7,1,3,7,8,8,3,4,1,6,2,1,1,8,0,9,8,0,3,9,10,3,10,1,10,7,3,2,1,4,9,10,7,6,4,0,8,5,1,2,1,6,2,5,0,7,10,9,10,3,7,10,5,8,5,7,6,7,6,10,9,5,10,5,5,7,2,10,7,7,8,2,0,1,1]
Output: 5.29167


Constraints:

• 20 <= arr.length <= 1000
• arr.lengthis a multiple of 20.
• 0 <= arr[i] <= 105

## Solution: Sorting

Time complexity: O(nlogn)
Space complexity: O(1)

## C++

Given the array nums consisting of n positive integers. You computed the sum of all non-empty continous subarrays from the array and then sort them in non-decreasing order, creating a new array of n * (n + 1) / 2 numbers.

Return the sum of the numbers from index left to index right (indexed from 1), inclusive, in the new array. Since the answer can be a huge number return it modulo 10^9 + 7.

Example 1:

Input: nums = [1,2,3,4], n = 4, left = 1, right = 5
Output: 13
Explanation: All subarray sums are 1, 3, 6, 10, 2, 5, 9, 3, 7, 4. After sorting them in non-decreasing order we have the new array [1, 2, 3, 3, 4, 5, 6, 7, 9, 10]. The sum of the numbers from index le = 1 to ri = 5 is 1 + 2 + 3 + 3 + 4 = 13.


Example 2:

Input: nums = [1,2,3,4], n = 4, left = 3, right = 4
Output: 6
Explanation: The given array is the same as example 1. We have the new array [1, 2, 3, 3, 4, 5, 6, 7, 9, 10]. The sum of the numbers from index le = 3 to ri = 4 is 3 + 3 = 6.


Example 3:

Input: nums = [1,2,3,4], n = 4, left = 1, right = 10
Output: 50


Constraints:

• 1 <= nums.length <= 10^3
• nums.length == n
• 1 <= nums[i] <= 100
• 1 <= left <= right <= n * (n + 1) / 2

## Solution 1: Brute Force

Find sums of all the subarrays and sort the values.

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

## Solution 2: Priority Queue/ Min Heap

For each subarray, start with one element e.g nums[i], put them into a priority queue (min heap). Each time, we have the smallest subarray sum, and extend that subarray and put the new sum back into priority queue. Thought it has the same time complexity as the brute force one in worst case, but space complexity can be reduce to O(n).

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

## Solution 3: Binary Search + Sliding Window

Use binary search to find S s.t. that there are at least k subarrys have sum <= S.

Given S, we can use sliding window to count how many subarrays have sum <= S and their total sum.

ans = sums_of_first(right) – sums_of_first(left – 1).

Time complexity: O(n * log(sum(nums))
Space complexity: O(n)

## C++

Given an array of integers arr and an integer k. Find the least number of unique integers after removing exactly k elements.

Example 1:

Input: arr = [5,5,4], k = 1
Output: 1
Explanation: Remove the single 4, only 5 is left.


Example 2:

Input: arr = [4,3,1,1,3,3,2], k = 3
Output: 2
Explanation: Remove 4, 2 and either one of the two 1s or three 3s. 1 and 3 will be left.

Constraints:

• 1 <= arr.length <= 10^5
• 1 <= arr[i] <= 10^9
• 0 <= k <= arr.length

## Solution: Greedy

Count the frequency of each unique number. Sort by frequency, remove items with lowest frequency first.

Time complexity: O(nlogn)
Space complexity: O(n)