Huahua’s Tech Road

花花酱 LeetCode 2195. Append K Integers With Minimal Sum

By zxi on March 8, 2022

You are given an integer array nums and an integer k. Append k unique positive integers that do not appear in nums to nums such that the resulting total sum is minimum.

Return the sum of the k integers appended to nums.

Example 1:

Input: nums = [1,4,25,10,25], k = 2
Output: 5
Explanation: The two unique positive integers that do not appear in nums which we append are 2 and 3.
The resulting sum of nums is 1 + 4 + 25 + 10 + 25 + 2 + 3 = 70, which is the minimum.
The sum of the two integers appended is 2 + 3 = 5, so we return 5.

Example 2:

Input: nums = [5,6], k = 6
Output: 25
Explanation: The six unique positive integers that do not appear in nums which we append are 1, 2, 3, 4, 7, and 8.
The resulting sum of nums is 5 + 6 + 1 + 2 + 3 + 4 + 7 + 8 = 36, which is the minimum. 
The sum of the six integers appended is 1 + 2 + 3 + 4 + 7 + 8 = 25, so we return 25.

Constraints:

1 <= nums.length <= 10⁵
1 <= nums[i] <= 10⁹
1 <= k <= 10⁸

Solution: Greedy + Math, fill the gap

Sort all the numbers and remove duplicated ones, and fill the gap between two neighboring numbers.
e.g. [15, 3, 8, 8] => sorted = [3, 8, 15]
fill 0->3, 1,2, sum = ((0 + 1) + (3-1)) * (3-0-1) / 2 = 3
fill 3->8, 4, 5, 6, 7, sum = ((3 + 1) + (8-1)) * (8-3-1) / 2 = 22
fill 8->15, 9, 10, …, 14, …
fill 15->inf, 16, 17, …

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

C++

// Author: Huahua

class Solution {

public:

long long minimalKSum(vector<int>& nums, int k) {

sort(begin(nums), end(nums));

long long ans = 0;

long long p = 0;

for (int c : nums) {

if (c == p) continue;

long long n = min((long long)k, c - p - 1);

ans += (p + 1 + p + n) * n / 2;

k -= n;

p = c;

}

ans += (p + 1 + p + k) * k / 2;

return ans;

}

};

花花酱 LeetCode 2194. Cells in a Range on an Excel Sheet

By zxi on March 8, 2022

A cell (r, c) of an excel sheet is represented as a string "<col><row>" where:

<col> denotes the column number c of the cell. It is represented by alphabetical letters.
- For example, the 1^st column is denoted by 'A', the 2^nd by 'B', the 3^rd by 'C', and so on.
<row> is the row number r of the cell. The r^th row is represented by the integer r.

You are given a string s in the format "<col1><row1>:<col2><row2>", where <col1> represents the column c1, <row1> represents the row r1, <col2> represents the column c2, and <row2> represents the row r2, such that r1 <= r2 and c1 <= c2.

Return the list of cells (x, y) such that r1 <= x <= r2 and c1 <= y <= c2. The cells should be represented as strings in the format mentioned above and be sorted in non-decreasing order first by columns and then by rows.

Example 1:

Input: s = "K1:L2"
Output: ["K1","K2","L1","L2"]
Explanation:
The above diagram shows the cells which should be present in the list.
The red arrows denote the order in which the cells should be presented.

Example 2:

Input: s = "A1:F1"
Output: ["A1","B1","C1","D1","E1","F1"]
Explanation:
The above diagram shows the cells which should be present in the list.
The red arrow denotes the order in which the cells should be presented.

Constraints:

s.length == 5
'A' <= s[0] <= s[3] <= 'Z'
'1' <= s[1] <= s[4] <= '9'
s consists of uppercase English letters, digits and ':'.

Solution: Brute Force

Time complexity: O((row2 – row1 + 1) * (col2 – col1 + 1))
Space complexity: O(1)

C++

// Author: Huahua

class Solution {

public:

vector<string> cellsInRange(string s) {

vector<string> ans;

for (char c = s[0]; c <= s[3]; ++c)

for (char r = s[1]; r <= s[4]; ++r)

ans.push_back(string{c, r});

return ans;

}

};

花花酱 LeetCode 2178. Maximum Split of Positive Even Integers

By zxi on March 4, 2022

You are given an integer finalSum. Split it into a sum of a maximum number of unique positive even integers.

For example, given finalSum = 12, the following splits are valid (unique positive even integers summing up to finalSum): (12), (2 + 10), (2 + 4 + 6), and (4 + 8). Among them, (2 + 4 + 6) contains the maximum number of integers. Note that finalSum cannot be split into (2 + 2 + 4 + 4) as all the numbers should be unique.

Return a list of integers that represent a valid split containing a maximum number of integers. If no valid split exists for finalSum, return an empty list. You may return the integers in any order.

Example 1:

Input: finalSum = 12
Output: [2,4,6]
Explanation: The following are valid splits: (12), (2 + 10), (2 + 4 + 6), and (4 + 8).
(2 + 4 + 6) has the maximum number of integers, which is 3. Thus, we return [2,4,6].
Note that [2,6,4], [6,2,4], etc. are also accepted.

Example 2:

Input: finalSum = 7
Output: []
Explanation: There are no valid splits for the given finalSum.
Thus, we return an empty array.

Example 3:

Input: finalSum = 28
Output: [6,8,2,12]
Explanation: The following are valid splits: (2 + 26), (6 + 8 + 2 + 12), and (4 + 24). 
(6 + 8 + 2 + 12) has the maximum number of integers, which is 4. Thus, we return [6,8,2,12].
Note that [10,2,4,12], [6,2,4,16], etc. are also accepted.

Constraints:

1 <= finalSum <= 10¹⁰

Solution: Greedy

The get the maximum number of elements, we must use the smallest numbers.

[2, 4, 6, …, 2k, x], where x > 2k
let s = 2 + 4 + … + 2k, x = num – s
since num is odd and s is also odd, so thus x = num – s.

Time complexity: O(sqrt(num)) for constructing outputs.
Space complexity: O(1)

C++

// Author: Huahua

class Solution {

public:

vector<long long> maximumEvenSplit(long long finalSum) {

if (finalSum & 1) return {};

vector<long long> ans;

long long s = 0;

for (long long i = 2; s + i <= finalSum; s += i, i += 2)

ans.push_back(i);

ans.back() += (finalSum - s);

return ans;

}

};

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

By zxi on March 4, 2022

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++

// Author: Huahua

class Solution {

public:

vector<long long> sumOfThree(long long num) {

if (num % 3) return {};

return {num / 3 - 1, num / 3, num / 3 + 1};

}

};

花花酱 LeetCode 2176. Count Equal and Divisible Pairs in an Array

By zxi on March 4, 2022

Given a 0-indexed integer array nums of length n and an integer k, return the number of pairs(i, j)where0 <= i < j < n, such thatnums[i] == nums[j]and(i * j)is divisible byk.

Example 1:

Input: nums = [3,1,2,2,2,1,3], k = 2
Output: 4
Explanation:
There are 4 pairs that meet all the requirements:
- nums[0] == nums[6], and 0 * 6 == 0, which is divisible by 2.
- nums[2] == nums[3], and 2 * 3 == 6, which is divisible by 2.
- nums[2] == nums[4], and 2 * 4 == 8, which is divisible by 2.
- nums[3] == nums[4], and 3 * 4 == 12, which is divisible by 2.

Example 2:

Input: nums = [1,2,3,4], k = 1
Output: 0
Explanation: Since no value in nums is repeated, there are no pairs (i,j) that meet all the requirements.

Constraints:

1 <= nums.length <= 100
1 <= nums[i], k <= 100

Solution: Brute Force

Time complexity: O(n²)
Space complexity: O(1)

C++

// Author: Huahua

class Solution {

public:

int countPairs(vector<int>& nums, int k) {

const int n = nums.size();

int ans = 0;

for (int i = 0; i < n; ++i)

for (int j = i + 1; j < n; ++j)

ans += (nums[i] == nums[j]) && (i * j % k == 0);

return ans;

}

};

Huahua's Tech Road

花花酱 LeetCode 2195. Append K Integers With Minimal Sum

Solution: Greedy + Math, fill the gap

C++

花花酱 LeetCode 2194. Cells in a Range on an Excel Sheet

Solution: Brute Force

C++

花花酱 LeetCode 2178. Maximum Split of Positive Even Integers

Solution: Greedy

C++

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

Solution: Math

C++

花花酱 LeetCode 2176. Count Equal and Divisible Pairs in an Array

Solution: Brute Force

C++