Posts published in “Array”

花花酱 LeetCode 2419. Longest Subarray With Maximum Bitwise AND

By zxi on September 26, 2022

You are given an integer array nums of size n.

Consider a non-empty subarray from nums that has the maximum possible bitwise AND.

In other words, let k be the maximum value of the bitwise AND of any subarray of nums. Then, only subarrays with a bitwise AND equal to k should be considered.

Return the length of the longest such subarray.

The bitwise AND of an array is the bitwise AND of all the numbers in it.

A subarray is a contiguous sequence of elements within an array.

Example 1:

Input: nums = [1,2,3,3,2,2]
Output: 2
Explanation:
The maximum possible bitwise AND of a subarray is 3.
The longest subarray with that value is [3,3], so we return 2.

Example 2:

Input: nums = [1,2,3,4]
Output: 1
Explanation:
The maximum possible bitwise AND of a subarray is 4.
The longest subarray with that value is [4], so we return 1.

Constraints:

1 <= nums.length <= 10⁵
1 <= nums[i] <= 10⁶

Solution: Find the largest number

a & b <= a
a & b <= b
if b > a, a & b < b, we choose to start a new sequence of “b” instead of continuing with “ab”

Basically, we find the largest number in the array and count the longest sequence of it. Note, there will be some tricky cases like.
b b b b a b
b a b b b b
We need to return 4 instead of 1.

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

C++

// Author: Huahua

class Solution {

public:

int longestSubarray(vector<int>& nums) {

int ans = 0;

int best = 0;

for (int i = 0, l = 0; i < nums.size(); ++i) {

if (nums[i] > best) {

best = nums[i];

ans = l = 1;

} else if (nums[i] == best) {

ans = max(ans, ++l);

} else {

l = 0;

}

return ans;

}

};

花花酱 LeetCode 2418. Sort the People

By zxi on September 26, 2022

You are given an array of strings names, and an array heights that consists of distinct positive integers. Both arrays are of length n.

For each index i, names[i] and heights[i] denote the name and height of the i^th person.

Return names sorted in descending order by the people’s heights.

Example 1:

Input: names = ["Mary","John","Emma"], heights = [180,165,170]
Output: ["Mary","Emma","John"]
Explanation: Mary is the tallest, followed by Emma and John.

Example 2:

Input: names = ["Alice","Bob","Bob"], heights = [155,185,150]
Output: ["Bob","Alice","Bob"]
Explanation: The first Bob is the tallest, followed by Alice and the second Bob.

Constraints:

n == names.length == heights.length
1 <= n <= 10³
1 <= names[i].length <= 20
1 <= heights[i] <= 10⁵
names[i] consists of lower and upper case English letters.
All the values of heights are distinct.

Solution: Zip and sort

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

C++

// Author: Huahua

class Solution {

public:

vector<string> sortPeople(vector<string>& names, vector<int>& heights) {

vector<pair<int, string*>> data;

for (int i = 0; i < names.size(); ++i)

data.emplace_back(heights[i], &names[i]);

sort(rbegin(data), rend(data));

vector<string> ans(names.size());

for (int i = 0; i < names.size(); ++i)

ans[i].swap(*data[i].second);

return ans;

}

};

花花酱 LeetCode 2395. Find Subarrays With Equal Sum

By zxi on September 7, 2022

Given a 0-indexed integer array nums, determine whether there exist two subarrays of length 2 with equal sum. Note that the two subarrays must begin at different indices.

Return true if these subarrays exist, and false otherwise.

A subarray is a contiguous non-empty sequence of elements within an array.

Example 1:

Input: nums = [4,2,4]
Output: true
Explanation: The subarrays with elements [4,2] and [2,4] have the same sum of 6.

Example 2:

Input: nums = [1,2,3,4,5]
Output: false
Explanation: No two subarrays of size 2 have the same sum.

Example 3:

Input: nums = [0,0,0]
Output: true
Explanation: The subarrays [nums[0],nums[1]] and [nums[1],nums[2]] have the same sum of 0. 
Note that even though the subarrays have the same content, the two subarrays are considered different because they are in different positions in the original array.

Constraints:

2 <= nums.length <= 1000
-10⁹ <= nums[i] <= 10⁹

Solution: Hashset

Use a hashset to track all the sums seen so far.

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

C++

// Author: Huahua

class Solution {

public:

bool findSubarrays(vector<int>& nums) {

unordered_set<int> s;

for (int i = 1; i < nums.size(); ++i)

if (!s.emplace(nums[i] + nums[i - 1]).second) return true;

return false;

}

};

花花酱 LeetCode 2303. Calculate Amount Paid in Taxes

By zxi on June 14, 2022

You are given a 0-indexed 2D integer array brackets where brackets[i] = [upper_i, percent_i] means that the i^th tax bracket has an upper bound of upper_i and is taxed at a rate of percent_i. The brackets are sorted by upper bound (i.e. upper_i-1 < upper_i for 0 < i < brackets.length).

Tax is calculated as follows:

The first upper₀ dollars earned are taxed at a rate of percent₀.
The next upper₁ - upper₀ dollars earned are taxed at a rate of percent₁.
The next upper₂ - upper₁ dollars earned are taxed at a rate of percent₂.
And so on.

You are given an integer income representing the amount of money you earned. Return the amount of money that you have to pay in taxes. Answers within 10^-5 of the actual answer will be accepted.

Example 1:

Input: brackets = [[3,50],[7,10],[12,25]], income = 10
Output: 2.65000
Explanation:
The first 3 dollars you earn are taxed at 50%. You have to pay $3 * 50% = $1.50 dollars in taxes.
The next 7 - 3 = 4 dollars you earn are taxed at 10%. You have to pay $4 * 10% = $0.40 dollars in taxes.
The final 10 - 7 = 3 dollars you earn are taxed at 25%. You have to pay $3 * 25% = $0.75 dollars in taxes.
You have to pay a total of $1.50 + $0.40 + $0.75 = $2.65 dollars in taxes.

Example 2:

Input: brackets = [[1,0],[4,25],[5,50]], income = 2
Output: 0.25000
Explanation:
The first dollar you earn is taxed at 0%. You have to pay $1 * 0% = $0 dollars in taxes.
The second dollar you earn is taxed at 25%. You have to pay $1 * 25% = $0.25 dollars in taxes.
You have to pay a total of $0 + $0.25 = $0.25 dollars in taxes.

Example 3:

Input: brackets = [[2,50]], income = 0
Output: 0.00000
Explanation:
You have no income to tax, so you have to pay a total of $0 dollars in taxes.

Constraints:

1 <= brackets.length <= 100
1 <= upper_i <= 1000
0 <= percent_i <= 100
0 <= income <= 1000
upper_i is sorted in ascending order.
All the values of upper_i are unique.
The upper bound of the last tax bracket is greater than or equal to income.

Solution: Follow the rules

“Nothing is certain except death and taxes” – Benjamin Franklin

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

C++

// Author: Huahua

class Solution {

public:

double calculateTax(vector<vector<int>>& A, int income) {

double ans = 0;

for (int i = 0; i < A.size(); ++i) {

ans += (min(income, A[i][0]) - (i ? A[i-1][0] : 0)) * A[i][1] / 100.0;

if (A[i][0] >= income) break;

}

return ans;

}

};

花花酱 LeetCode 2270. Number of Ways to Split Array

By zxi on May 15, 2022

You are given a 0-indexed integer array nums of length n.

nums contains a valid split at index i if the following are true:

The sum of the first i + 1 elements is greater than or equal to the sum of the last n - i - 1 elements.
There is at least one element to the right of i. That is, 0 <= i < n - 1.

Return the number of valid splits in nums.

Example 1:

Input: nums = [10,4,-8,7]
Output: 2
Explanation: 
There are three ways of splitting nums into two non-empty parts:
- Split nums at index 0. Then, the first part is [10], and its sum is 10. The second part is [4,-8,7], and its sum is 3. Since 10 >= 3, i = 0 is a valid split.
- Split nums at index 1. Then, the first part is [10,4], and its sum is 14. The second part is [-8,7], and its sum is -1. Since 14 >= -1, i = 1 is a valid split.
- Split nums at index 2. Then, the first part is [10,4,-8], and its sum is 6. The second part is [7], and its sum is 7. Since 6 < 7, i = 2 is not a valid split.
Thus, the number of valid splits in nums is 2.

Example 2:

Input: nums = [2,3,1,0]
Output: 2
Explanation: 
There are two valid splits in nums:
- Split nums at index 1. Then, the first part is [2,3], and its sum is 5. The second part is [1,0], and its sum is 1. Since 5 >= 1, i = 1 is a valid split. 
- Split nums at index 2. Then, the first part is [2,3,1], and its sum is 6. The second part is [0], and its sum is 0. Since 6 >= 0, i = 2 is a valid split.

Constraints:

2 <= nums.length <= 10⁵
-10⁵ <= nums[i] <= 10⁵

Solution: Prefix/Suffix Sum

Note: sum can be greater than 2^31, use long!

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

C++

// Author: Huahua

class Solution {

public:

int waysToSplitArray(vector<int>& A) {

int ans = 0;

for (long i = 0, l = 0, r = accumulate(begin(A), end(A), 0l); i < A.size() - 1; ++i)

ans += (l += A[i]) >= (r -= A[i]);

return ans;

}

};