Posts published in “Math”

花花酱 LeetCode 1344. Angle Between Hands of a Clock

By zxi on February 13, 2020

Given two numbers, hour and minutes. Return the smaller angle (in sexagesimal units) formed between the hour and the minute hand.

Example 1:

Input: hour = 12, minutes = 30
Output: 165

Example 2:

Input: hour = 3, minutes = 30
Output: 75

Example 3:

Input: hour = 3, minutes = 15
Output: 7.5

Example 4:

Input: hour = 4, minutes = 50
Output: 155

Example 5:

Input: hour = 12, minutes = 0
Output: 0

Constraints:

1 <= hour <= 12
0 <= minutes <= 59
Answers within 10^-5 of the actual value will be accepted as correct.

Solution: Math

Compute the angle of the hour hand (h + m / 60.0) * 360 / 12 as a_h
Compute the angle of the minute hand m / 60.0 * 360 as a_m
ans = min(abs(a_h – a_m), 360 – abs(a_h – a_m))

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

C++

// Author: Huahua

class Solution {

public:

double angleClock(int hour, int minutes) {

double a_m = minutes * 360 / 60;

double a_h = (hour + minutes / 60.0) * 360 / 12;

return min(abs(a_m - a_h), 360 - abs(a_m - a_h));

}

};

花花酱 LeetCode 1332. Remove Palindromic Subsequences

By zxi on January 26, 2020

Given a string s consisting only of letters 'a' and 'b'. In a single step you can remove one palindromic subsequence from s.

Return the minimum number of steps to make the given string empty.

A string is a subsequence of a given string, if it is generated by deleting some characters of a given string without changing its order.

A string is called palindrome if is one that reads the same backward as well as forward.

Example 1:

Input: s = "ababa"
Output: 1
Explanation: String is already palindrome

Example 2:

Input: s = "abb"
Output: 2
Explanation: "abb" -> "bb" -> "". 
Remove palindromic subsequence "a" then "bb".

Example 3:

Input: s = "baabb"
Output: 2
Explanation: "baabb" -> "b" -> "". 
Remove palindromic subsequence "baab" then "b".

Example 4:

Input: s = ""
Output: 0

Constraints:

0 <= s.length <= 1000
s only consists of letters ‘a’ and ‘b’

Solution: Math

if s is empty => 0 step
if s is a palindrome => 1 step
Otherwise, 2 steps…
1. delete all the as
2. delete all the bs

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

C++

// Author: Huahua

class Solution {

public:

int removePalindromeSub(string s) {

if (s.empty()) return 0;

if (s == string(rbegin(s), rend(s))) return 1;

return 2;

}

};

花花酱 LeetCode 1317. Convert Integer to the Sum of Two No-Zero Integers

By zxi on January 13, 2020

Given an integer n. No-Zero integer is a positive integer which doesn’t contain any 0 in its decimal representation.

Return a list of two integers [A, B] where:

A and B are No-Zero integers.
A + B = n

It’s guarateed that there is at least one valid solution. If there are many valid solutions you can return any of them.

Example 1:

Input: n = 2

Output: [1,1]

Explanation: A = 1, B = 1. A + B = n and both A and B don't contain any 0 in their decimal representation.

Example 2:

1 2	<strong>Input:</strong> n = 11 <strong>Output:</strong> [2,9]

Example 3:

1 2	<strong>Input:</strong> n = 10000 <strong>Output:</strong> [1,9999]

Example 4:

1 2	<strong>Input:</strong> n = 69 <strong>Output:</strong> [1,68]

Example 5:

1 2	<strong>Input:</strong> n = 1010 <strong>Output:</strong> [11,999]

Constraints:

2 <= n <= 10^4

Solution: Brute Force

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

C++

// Author: Huahua

class Solution {

public:

vector<int> getNoZeroIntegers(int n) {

auto valid = [](int x) {

if (!x) return false;

while (x) {

if (x % 10 == 0) return false;

x /= 10;

}

return true;

};

for (int i = 1; i <= n / 2; ++i)

if (valid(i) && valid(n - i))

return {i, n - i};

return {};

}

};

花花酱 LeetCode 1295. Find Numbers with Even Number of Digits

By zxi on December 26, 2019

Given an array nums of integers, return how many of them contain an even number of digits.

Example 1:

Input: nums = [12,345,2,6,7896]
Output: 2
Explanation: 
12 contains 2 digits (even number of digits). 
345 contains 3 digits (odd number of digits). 
2 contains 1 digit (odd number of digits). 
6 contains 1 digit (odd number of digits). 
7896 contains 4 digits (even number of digits). 
Therefore only 12 and 7896 contain an even number of digits.

Example 2:

Input: nums = [555,901,482,1771]
Output: 1 
Explanation: 
Only 1771 contains an even number of digits.

Constraints:

1 <= nums.length <= 500
1 <= nums[i] <= 10^5

Solution: Math

Time complexity: O(n * log(max(num)))
Space complexity: O(1)

C++

// Author: Huahua

class Solution {

public:

int findNumbers(vector<int>& nums) {

return count_if(begin(nums), end(nums), [](int num) {

int d = 0;

do { ++d; } while (num /= 10);

return d % 2 == 0;

});

}

};

Python3

# Author: Huahua

class Solution:

def findNumbers(self, nums: List[int]) -> int:

return sum([len(str(x)) % 2 == 0 for x in nums])

花花酱 1276. Number of Burgers with No Waste of Ingredients

By zxi on December 1, 2019

Given two integers tomatoSlices and cheeseSlices. The ingredients of different burgers are as follows:

Jumbo Burger: 4 tomato slices and 1 cheese slice.
Small Burger: 2 Tomato slices and 1 cheese slice.

Return [total_jumbo, total_small] so that the number of remaining tomatoSlices equal to 0 and the number of remaining cheeseSlices equal to 0. If it is not possible to make the remaining tomatoSlices and cheeseSlices equal to 0 return [].

Example 1:

Input: tomatoSlices = 16, cheeseSlices = 7
Output: [1,6]
Explantion: To make one jumbo burger and 6 small burgers we need 4*1 + 2*6 = 16 tomato and 1 + 6 = 7 cheese. There will be no remaining ingredients.

Example 2:

Input: tomatoSlices = 17, cheeseSlices = 4
Output: []
Explantion: There will be no way to use all ingredients to make small and jumbo burgers.

Example 3:

Input: tomatoSlices = 4, cheeseSlices = 17
Output: []
Explantion: Making 1 jumbo burger there will be 16 cheese remaining and making 2 small burgers there will be 15 cheese remaining.

Example 4:

Input: tomatoSlices = 0, cheeseSlices = 0
Output: [0,0]

Example 5:

Input: tomatoSlices = 2, cheeseSlices = 1
Output: [0,1]

Constraints:

0 <= tomatoSlices <= 10^7
0 <= cheeseSlices <= 10^7

Solution: Math

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

C++

// Author: Huahua

class Solution {

public:

vector<int> numOfBurgers(int T, int C) {

// Jumbo = x, small = y

// 4x + 2y = T

// x + y = C

// x = (T - 2C) / 2

int x = T / 2 - C;

int y = C - x;

if (4 * x + 2 * y == T && x >= 0 && y >= 0) return {x, y};

return {};

}

};