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Posts tagged as “math”

花花酱 LeetCode 1185. Day of the Week

Given a date, return the corresponding day of the week for that date.

The input is given as three integers representing the daymonth and year respectively.

Return the answer as one of the following values {"Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"}.

Example 1:

Input: day = 31, month = 8, year = 2019
Output: "Saturday"

Example 2:

Input: day = 18, month = 7, year = 1999
Output: "Sunday"

Example 3:

Input: day = 15, month = 8, year = 1993
Output: "Sunday"

Constraints:

  • The given dates are valid dates between the years 1971 and 2100.

Solution: LeapYear

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

C++

花花酱 LeetCode 1109. Corporate Flight Bookings

There are n flights, and they are labeled from 1 to n.

We have a list of flight bookings.  The i-th booking bookings[i] = [i, j, k] means that we booked kseats from flights labeled i to j inclusive.

Return an array answer of length n, representing the number of seats booked on each flight in order of their label.

Example 1:

Input: bookings = [[1,2,10],[2,3,20],[2,5,25]], n = 5
Output: [10,55,45,25,25]

Constraints:

  • 1 <= bookings.length <= 20000
  • 1 <= bookings[i][0] <= bookings[i][1] <= n <= 20000
  • 1 <= bookings[i][2] <= 10000

Solution: Marking start and end

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

C++

花花酱 LeetCode 1104. Path In Zigzag Labelled Binary Tree

In an infinite binary tree where every node has two children, the nodes are labelled in row order.

In the odd numbered rows (ie., the first, third, fifth,…), the labelling is left to right, while in the even numbered rows (second, fourth, sixth,…), the labelling is right to left.

Given the label of a node in this tree, return the labels in the path from the root of the tree to the node with that label.

Example 1:

Input: label = 14
Output: [1,3,4,14]

Example 2:

Input: label = 26
Output: [1,2,6,10,26]

Constraints:

  • 1 <= label <= 10^6

Solution: Math

Time complexity: O(logn)
Space complexity: O(logn)

C++

花花酱 LeetCode 640. Solve the Equation

Solve a given equation and return the value of x in the form of string “x=#value”. The equation contains only ‘+’, ‘-‘ operation, the variable x and its coefficient.

If there is no solution for the equation, return “No solution”.

If there are infinite solutions for the equation, return “Infinite solutions”.

If there is exactly one solution for the equation, we ensure that the value of x is an integer.

Example 1:

Input: "x+5-3+x=6+x-2"
Output: "x=2"

Example 2:

Input: "x=x"
Output: "Infinite solutions"

Example 3:

Input: "2x=x"
Output: "x=0"

Example 4:

Input: "2x+3x-6x=x+2"
Output: "x=-1"

Example 5:

Input: "x=x+2"
Output: "No solution"

Solution: Parse the equation

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

C++

花花酱 LeetCode 50. Pow(x, n)

Implement pow(xn), which calculates x raised to the power n (xn).

Example 1:

Input: 2.00000, 10
Output: 1024.00000

Example 2:

Input: 2.10000, 3
Output: 9.26100

Example 3:

Input: 2.00000, -2
Output: 0.25000
Explanation: 2-2 = 1/22 = 1/4 = 0.25

Note:

  • -100.0 < x < 100.0
  • n is a 32-bit signed integer, within the range [−231, 231 − 1]

Solution: Recursion

square x and cut n in half.
if n is negative, compute 1.0 / pow(x, |n|)

pow(x, n) := pow(x * x, n / 2) * (x if n % 2 else 1)
pow(x, 0) := 1
Example:
pow(x, 5) = pow(x^2, 2) * x
= pow(x^4, 1) * x
= pow(x^8, 0) * x^4 * x
= 1 * x^4 * x = x^5

Time complexity: O(logn)
Space complexity: O(logn)

C++