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Posts published in “Math”

花花酱 LeetCode 2373. Largest Local Values in a Matrix

You are given an n x n integer matrix grid.

Generate an integer matrix maxLocal of size (n - 2) x (n - 2) such that:

  • maxLocal[i][j] is equal to the largest value of the 3 x 3 matrix in grid centered around row i + 1 and column j + 1.

In other words, we want to find the largest value in every contiguous 3 x 3 matrix in grid.

Return the generated matrix.

Example 1:

Input: grid = [[9,9,8,1],[5,6,2,6],[8,2,6,4],[6,2,2,2]]
Output: [[9,9],[8,6]]
Explanation: The diagram above shows the original matrix and the generated matrix.
Notice that each value in the generated matrix corresponds to the largest value of a contiguous 3 x 3 matrix in grid.

Example 2:

Input: grid = [[1,1,1,1,1],[1,1,1,1,1],[1,1,2,1,1],[1,1,1,1,1],[1,1,1,1,1]]
Output: [[2,2,2],[2,2,2],[2,2,2]]
Explanation: Notice that the 2 is contained within every contiguous 3 x 3 matrix in grid.

Constraints:

  • n == grid.length == grid[i].length
  • 3 <= n <= 100
  • 1 <= grid[i][j] <= 100

Solution: Brute Force

Time complexity: O(n*n*9)
Space complexity: O(n*n)

C++

花花酱 LeetCode 2244. Minimum Rounds to Complete All Tasks

You are given a 0-indexed integer array tasks, where tasks[i] represents the difficulty level of a task. In each round, you can complete either 2 or 3 tasks of the same difficulty level.

Return the minimum rounds required to complete all the tasks, or -1 if it is not possible to complete all the tasks.

Example 1:

Input: tasks = [2,2,3,3,2,4,4,4,4,4]
Output: 4
Explanation: To complete all the tasks, a possible plan is:
- In the first round, you complete 3 tasks of difficulty level 2. 
- In the second round, you complete 2 tasks of difficulty level 3. 
- In the third round, you complete 3 tasks of difficulty level 4. 
- In the fourth round, you complete 2 tasks of difficulty level 4.  
It can be shown that all the tasks cannot be completed in fewer than 4 rounds, so the answer is 4.

Example 2:

Input: tasks = [2,3,3]
Output: -1
Explanation: There is only 1 task of difficulty level 2, but in each round, you can only complete either 2 or 3 tasks of the same difficulty level. Hence, you cannot complete all the tasks, and the answer is -1.

Constraints:

  • 1 <= tasks.length <= 105
  • 1 <= tasks[i] <= 109

Solution: Math

Count the frequency of each level. The only case that can not be finished is 1 task at some level. Otherwise we can always finish it by 2, 3 tasks at a time.

if n = 2: 2 => 1 round
if n = 3: 3 => 1 round
if n = 4: 2 + 2 => 2 rounds
if n = 5: 3 + 2 => 2 rounds

if n = 3k, n % 3 == 0 : 3 + 3 + … + 3 = k rounds
if n = 3k + 1, n % 3 == 1 : 3*(k – 1) + 2 + 2 = k + 1 rounds
if n = 3k + 2, n % 3 == 2 : 3*k + 2 = k + 1 rounds

We need (n + 2) / 3 rounds.

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

C++

花花酱 LeetCode 2240. Number of Ways to Buy Pens and Pencils

You are given an integer total indicating the amount of money you have. You are also given two integers cost1 and cost2 indicating the price of a pen and pencil respectively. You can spend part or all of your money to buy multiple quantities (or none) of each kind of writing utensil.

Return the number of distinct ways you can buy some number of pens and pencils.

Example 1:

Input: total = 20, cost1 = 10, cost2 = 5
Output: 9
Explanation: The price of a pen is 10 and the price of a pencil is 5.
- If you buy 0 pens, you can buy 0, 1, 2, 3, or 4 pencils.
- If you buy 1 pen, you can buy 0, 1, or 2 pencils.
- If you buy 2 pens, you cannot buy any pencils.
The total number of ways to buy pens and pencils is 5 + 3 + 1 = 9.

Example 2:

Input: total = 5, cost1 = 10, cost2 = 10
Output: 1
Explanation: The price of both pens and pencils are 10, which cost more than total, so you cannot buy any writing utensils. Therefore, there is only 1 way: buy 0 pens and 0 pencils.

Constraints:

  • 1 <= total, cost1, cost2 <= 106

Solution:

Enumerate all possible ways to buy k pens, e.g. 0 pen, 1 pen, …, total / cost1.
The way to buy pencils are (total – k * cost1) / cost2 + 1.
ans = sum((total – k * cost1) / cost2 + 1)) for k = 0 to total / cost1.

Time complexity: O(total / cost1)
Space complexity: O(1)

C++

花花酱 LeetCode 2235. Add Two Integers

Given two integers num1 and num2, return the sum of the two integers.

Example 1:

Input: num1 = 12, num2 = 5
Output: 17
Explanation: num1 is 12, num2 is 5, and their sum is 12 + 5 = 17, so 17 is returned.

Example 2:

Input: num1 = -10, num2 = 4
Output: -6
Explanation: num1 + num2 = -6, so -6 is returned.

Constraints:

  • -100 <= num1, num2 <= 100

Solution: Just sum them up

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

C++

花花酱 LeetCode 2177. Find Three Consecutive Integers That Sum to a Given Number

Given an integer num, return three consecutive integers (as a sorted array) that sum to num. If num cannot be expressed as the sum of three consecutive integers, return an empty array.

Example 1:

Input: num = 33
Output: [10,11,12]
Explanation: 33 can be expressed as 10 + 11 + 12 = 33.
10, 11, 12 are 3 consecutive integers, so we return [10, 11, 12].

Example 2:

Input: num = 4
Output: []
Explanation: There is no way to express 4 as the sum of 3 consecutive integers.

Constraints:

  • 0 <= num <= 1015

Solution: Math

(x / 3 – 1) + (x / 3) + (x / 3 + 1) == 3x == num, num must be divisible by 3.

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

C++