Press "Enter" to skip to content

Posts tagged as “sliding window”

花花酱 LeetCode 1456. Maximum Number of Vowels in a Substring of Given Length

Given a string s and an integer k.

Return the maximum number of vowel letters in any substring of s with length k.

Vowel letters in English are (a, e, i, o, u).

Example 1:

Input: s = "abciiidef", k = 3
Output: 3
Explanation: The substring "iii" contains 3 vowel letters.

Example 2:

Input: s = "aeiou", k = 2
Output: 2
Explanation: Any substring of length 2 contains 2 vowels.

Example 3:

Input: s = "leetcode", k = 3
Output: 2
Explanation: "lee", "eet" and "ode" contain 2 vowels.

Example 4:

Input: s = "rhythms", k = 4
Output: 0
Explanation: We can see that s doesn't have any vowel letters.

Example 5:

Input: s = "tryhard", k = 4
Output: 1

Constraints:

  • 1 <= s.length <= 10^5
  • s consists of lowercase English letters.
  • 1 <= k <= s.length

Solution: Sliding Window

Keep tracking the number of vows in a window of size k.

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

C++

花花酱 LeetCode 1425. Constrained Subset Sum

Given an integer array nums and an integer k, return the maximum sum of a non-empty subset of that array such that for every two consecutive integers in the subset, nums[i] and nums[j], where i < j, the condition j - i <= k is satisfied.

subset of an array is obtained by deleting some number of elements (can be zero) from the array, leaving the remaining elements in their original order.

Example 1:

Input: nums = [10,2,-10,5,20], k = 2
Output: 37
Explanation: The subset is [10, 2, 5, 20].

Example 2:

Input: nums = [-1,-2,-3], k = 1
Output: -1
Explanation: The subset must be non-empty, so we choose the largest number.

Example 3:

Input: nums = [10,-2,-10,-5,20], k = 2
Output: 23
Explanation: The subset is [10, -2, -5, 20].

Constraints:

  • 1 <= k <= nums.length <= 10^5
  • -10^4 <= nums[i] <= 10^4

Solution: DP / Sliding window / monotonic queue

dp[i] := max sum of a subset that include nums[i]
dp[i] := max(dp[i-1], dp[i-2], …, dp[i-k-1], 0) + nums[i]

C++

Use a monotonic queue to track the maximum of a sliding window dp[i-k-1] ~ dp[i-1].

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

C++

花花酱 LeetCode 1423. Maximum Points You Can Obtain from Cards

There are several cards arranged in a row, and each card has an associated number of points The points are given in the integer array cardPoints.

In one step, you can take one card from the beginning or from the end of the row. You have to take exactly k cards.

Your score is the sum of the points of the cards you have taken.

Given the integer array cardPoints and the integer k, return the maximum score you can obtain.

Example 1:

Input: cardPoints = [1,2,3,4,5,6,1], k = 3
Output: 12
Explanation: After the first step, your score will always be 1. However, choosing the rightmost card first will maximize your total score. The optimal strategy is to take the three cards on the right, giving a final score of 1 + 6 + 5 = 12.

Example 2:

Input: cardPoints = [2,2,2], k = 2
Output: 4
Explanation: Regardless of which two cards you take, your score will always be 4.

Example 3:

Input: cardPoints = [9,7,7,9,7,7,9], k = 7
Output: 55
Explanation: You have to take all the cards. Your score is the sum of points of all cards.

Example 4:

Input: cardPoints = [1,1000,1], k = 1
Output: 1
Explanation: You cannot take the card in the middle. Your best score is 1. 

Example 5:

Input: cardPoints = [1,79,80,1,1,1,200,1], k = 3
Output: 202

Constraints:

  • 1 <= cardPoints.length <= 10^5
  • 1 <= cardPoints[i] <= 10^4
  • 1 <= k <= cardPoints.length

Solution: Sliding Window

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

C++

花花酱 LeetCode 1383. Maximum Performance of a Team

There are n engineers numbered from 1 to n and two arrays: speed and efficiency, where speed[i] and efficiency[i] represent the speed and efficiency for the i-th engineer respectively. Return the maximum performance of a team composed of at most k engineers, since the answer can be a huge number, return this modulo 10^9 + 7.

The performance of a team is the sum of their engineers’ speeds multiplied by the minimum efficiency among their engineers. 

Example 1:

Input: n = 6, speed = [2,10,3,1,5,8], efficiency = [5,4,3,9,7,2], k = 2
Output: 60
Explanation: 
We have the maximum performance of the team by selecting engineer 2 (with speed=10 and efficiency=4) and engineer 5 (with speed=5 and efficiency=7). That is, performance = (10 + 5) * min(4, 7) = 60.

Example 2:

Input: n = 6, speed = [2,10,3,1,5,8], efficiency = [5,4,3,9,7,2], k = 3
Output: 68
Explanation:
This is the same example as the first but k = 3. We can select engineer 1, engineer 2 and engineer 5 to get the maximum performance of the team. That is, performance = (2 + 10 + 5) * min(5, 4, 7) = 68.

Example 3:

Input: n = 6, speed = [2,10,3,1,5,8], efficiency = [5,4,3,9,7,2], k = 4
Output: 72

Constraints:

  • 1 <= n <= 10^5
  • speed.length == n
  • efficiency.length == n
  • 1 <= speed[i] <= 10^5
  • 1 <= efficiency[i] <= 10^8
  • 1 <= k <= n

Solution: Greedy + Sliding Window

  1. Sort engineers by their efficiency in descending order.
  2. For each window of K engineers (we can have less than K people in the first k-1 windows), ans is sum(speed) * min(efficiency).

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

C++

Python3

花花酱 LeetCode 1343. Number of Sub-arrays of Size K and Average Greater than or Equal to Threshold

Given an array of integers arr and two integers k and threshold.

Return the number of sub-arrays of size k and average greater than or equal to threshold.

Example 1:

Input: arr = [2,2,2,2,5,5,5,8], k = 3, threshold = 4
Output: 3
Explanation: Sub-arrays [2,5,5],[5,5,5] and [5,5,8] have averages 4, 5 and 6 respectively. All other sub-arrays of size 3 have averages less than 4 (the threshold).

Example 2:

Input: arr = [1,1,1,1,1], k = 1, threshold = 0
Output: 5

Example 3:

Input: arr = [11,13,17,23,29,31,7,5,2,3], k = 3, threshold = 5
Output: 6
Explanation: The first 6 sub-arrays of size 3 have averages greater than 5. Note that averages are not integers.

Example 4:

Input: arr = [7,7,7,7,7,7,7], k = 7, threshold = 7
Output: 1

Example 5:

Input: arr = [4,4,4,4], k = 4, threshold = 1
Output: 1

Constraints:

  • 1 <= arr.length <= 10^5
  • 1 <= arr[i] <= 10^4
  • 1 <= k <= arr.length
  • 0 <= threshold <= 10^4

Solution: Sliding Window

  1. Window size = k
  2. Maintain the sum of the window
  3. Check sum >= threshold * k

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

C++