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花花酱 LeetCode 1499. Max Value of Equation

Given an array points containing the coordinates of points on a 2D plane, sorted by the x-values, where points[i] = [xi, yi] such that xi < xj for all 1 <= i < j <= points.length. You are also given an integer k.

Find the maximum value of the equation yi + yj + |xi - xj| where |xi - xj| <= k and 1 <= i < j <= points.length. It is guaranteed that there exists at least one pair of points that satisfy the constraint |xi - xj| <= k.

Example 1:

Input: points = [[1,3],[2,0],[5,10],[6,-10]], k = 1
Output: 4
Explanation: The first two points satisfy the condition |xi - xj| <= 1 and if we calculate the equation we get 3 + 0 + |1 - 2| = 4. Third and fourth points also satisfy the condition and give a value of 10 + -10 + |5 - 6| = 1.
No other pairs satisfy the condition, so we return the max of 4 and 1.

Example 2:

Input: points = [[0,0],[3,0],[9,2]], k = 3
Output: 3
Explanation: Only the first two points have an absolute difference of 3 or less in the x-values, and give the value of 0 + 0 + |0 - 3| = 3.

Constraints:

  • 2 <= points.length <= 10^5
  • points[i].length == 2
  • -10^8 <= points[i][0], points[i][1] <= 10^8
  • 0 <= k <= 2 * 10^8
  • points[i][0] < points[j][0] for all 1 <= i < j <= points.length
  • xi form a strictly increasing sequence.

Observation

Since xj > xi, so |xi – xj| + yi + yj => xj + yj + (yi – xi)
We want to have yi – xi as large as possible while need to make sure xj – xi <= k.

Solution 1: Priority Queue / Heap

Put all the points processed so far onto the heap as (y-x, x) sorted by y-x in descending order.
Each new point (x_j, y_j), find the largest y-x such that x_j – x <= k.

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

C++

Solution 2: Monotonic Queue


Maintain a monotonic queue:
1. The queue is sorted by y – x in descending order.
2. Pop then front element when xj – x_front > k, they can’t be used anymore.
3. Record the max of {xj + yj + (y_front – x_front)}
4. Pop the back element when yj – xj > y_back – x_back, they are smaller and lefter. Won’t be useful anymore.
5. Finally, push the j-th element onto the queue.

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

C++

Java

python3

花花酱 LeetCode 1438. Longest Continuous Subarray With Absolute Diff Less Than or Equal to Limit

Given an array of integers nums and an integer limit, return the size of the longest continuous subarray such that the absolute difference between any two elements is less than or equal to limit.

In case there is no subarray satisfying the given condition return 0.

Example 1:

Input: nums = [8,2,4,7], limit = 4
Output: 2 
Explanation: All subarrays are: 
[8] with maximum absolute diff |8-8| = 0 <= 4.
[8,2] with maximum absolute diff |8-2| = 6 > 4. 
[8,2,4] with maximum absolute diff |8-2| = 6 > 4.
[8,2,4,7] with maximum absolute diff |8-2| = 6 > 4.
[2] with maximum absolute diff |2-2| = 0 <= 4.
[2,4] with maximum absolute diff |2-4| = 2 <= 4.
[2,4,7] with maximum absolute diff |2-7| = 5 > 4.
[4] with maximum absolute diff |4-4| = 0 <= 4.
[4,7] with maximum absolute diff |4-7| = 3 <= 4.
[7] with maximum absolute diff |7-7| = 0 <= 4. 
Therefore, the size of the longest subarray is 2.

Example 2:

Input: nums = [10,1,2,4,7,2], limit = 5
Output: 4 
Explanation: The subarray [2,4,7,2] is the longest since the maximum absolute diff is |2-7| = 5 <= 5.

Example 3:

Input: nums = [4,2,2,2,4,4,2,2], limit = 0
Output: 3

Constraints:

  • 1 <= nums.length <= 10^5
  • 1 <= nums[i] <= 10^9
  • 0 <= limit <= 10^9

Solution 1: Sliding Window + TreeSet

Use a treeset to maintain a range of [l, r] such that max(nums[l~r]) – min(nums[l~r]) <= limit.
Every time, we add nums[r] into the tree, and move l towards r to keep the max diff under limit.

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

C++

Solution 2: Dual Monotonic Queue

Similar to https://zxi.mytechroad.com/blog/dynamic-programming/leetcode-1425-constrained-subset-sum/

We want to maintain a range [l, r] that max(nums[l~r]) – min(nums[l~r]) <= limit, to track the max/min of a range efficiently we could use monotonic queue. One for max and one for min.

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

C++

花花酱 LeetCode 933. Number of Recent Calls

Problem

Write a class RecentCounter to count recent requests.

It has only one method: ping(int t), where t represents some time in milliseconds.

Return the number of pings that have been made from 3000 milliseconds ago until now.

Any ping with time in [t - 3000, t] will count, including the current ping.

It is guaranteed that every call to ping uses a strictly larger value of t than before.

Example 1:

Input: inputs = ["RecentCounter","ping","ping","ping","ping"], inputs = [[],[1],[100],[3001],[3002]]
Output: [null,1,2,3,3]

Note:

  1. Each test case will have at most 10000 calls to ping.
  2. Each test case will call ping with strictly increasing values of t.
  3. Each call to ping will have 1 <= t <= 10^9.

Solution: Queue

Use a FIFO queue to track all the previous pings that are within 3000 ms to current.

Time complexity: Avg O(1), Total O(n)

Space complexity: O(n)

C++