# Posts tagged as “math”

You are given a non-negative floating point number rounded to two decimal places celsius, that denotes the temperature in Celsius.

You should convert Celsius into Kelvin and Fahrenheit and return it as an array ans = [kelvin, fahrenheit].

Return the array ansAnswers within 10-5 of the actual answer will be accepted.

Note that:

• Kelvin = Celsius + 273.15
• Fahrenheit = Celsius * 1.80 + 32.00

Example 1:

Input: celsius = 36.50
Output: [309.65000,97.70000]
Explanation: Temperature at 36.50 Celsius converted in Kelvin is 309.65 and converted in Fahrenheit is 97.70.


Example 2:

Input: celsius = 122.11
Output: [395.26000,251.79800]
Explanation: Temperature at 122.11 Celsius converted in Kelvin is 395.26 and converted in Fahrenheit is 251.798.


Constraints:

• 0 <= celsius <= 1000

## Solution: Follow the formulas

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

## C++

Alice and Bob are traveling to Rome for separate business meetings.

You are given 4 strings arriveAliceleaveAlicearriveBob, and leaveBob. Alice will be in the city from the dates arriveAlice to leaveAlice (inclusive), while Bob will be in the city from the dates arriveBob to leaveBob (inclusive). Each will be a 5-character string in the format "MM-DD", corresponding to the month and day of the date.

Return the total number of days that Alice and Bob are in Rome together.

You can assume that all dates occur in the same calendar year, which is not a leap year. Note that the number of days per month can be represented as: [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31].

Example 1:

Input: arriveAlice = "08-15", leaveAlice = "08-18", arriveBob = "08-16", leaveBob = "08-19"
Output: 3
Explanation: Alice will be in Rome from August 15 to August 18. Bob will be in Rome from August 16 to August 19. They are both in Rome together on August 16th, 17th, and 18th, so the answer is 3.


Example 2:

Input: arriveAlice = "10-01", leaveAlice = "10-31", arriveBob = "11-01", leaveBob = "12-31"
Output: 0
Explanation: There is no day when Alice and Bob are in Rome together, so we return 0.


Constraints:

• All dates are provided in the format "MM-DD".
• Alice and Bob’s arrival dates are earlier than or equal to their leaving dates.
• The given dates are valid dates of a non-leap year.

## Solution: Math

Convert date to days of the year.

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

## C++

An integer n is strictly palindromic if, for every base b between 2 and n - 2 (inclusive), the string representation of the integer n in base b is palindromic.

Given an integer n, return true if n is strictly palindromic and false otherwise.

A string is palindromic if it reads the same forward and backward.

Example 1:

Input: n = 9
Output: false
Explanation: In base 2: 9 = 1001 (base 2), which is palindromic.
In base 3: 9 = 100 (base 3), which is not palindromic.
Therefore, 9 is not strictly palindromic so we return false.
Note that in bases 4, 5, 6, and 7, n = 9 is also not palindromic.


Example 2:

Input: n = 4
Output: false
Explanation: We only consider base 2: 4 = 100 (base 2), which is not palindromic.
Therefore, we return false.


Constraints:

• 4 <= n <= 105

## Solution: Just return false

No such number.

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

## C++

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++

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)