Huahua’s Tech Road

花花酱 LeetCode 1798. Maximum Number of Consecutive Values You Can Make

By zxi on March 20, 2021

You are given an integer array coins of length n which represents the n coins that you own. The value of the i^th coin is coins[i]. You can make some value x if you can choose some of your n coins such that their values sum up to x.

Return the maximum number of consecutive integer values that you can make with your coins starting from and including 0.

Note that you may have multiple coins of the same value.

Example 1:

Input: coins = [1,3]
Output: 2
Explanation: You can make the following values:
- 0: take []
- 1: take [1]
You can make 2 consecutive integer values starting from 0.

Example 2:

Input: coins = [1,1,1,4]
Output: 8
Explanation: You can make the following values:
- 0: take []
- 1: take [1]
- 2: take [1,1]
- 3: take [1,1,1]
- 4: take [4]
- 5: take [4,1]
- 6: take [4,1,1]
- 7: take [4,1,1,1]
You can make 8 consecutive integer values starting from 0.

Example 3:

Input: nums = [1,4,10,3,1]
Output: 20

Constraints:

coins.length == n
1 <= n <= 4 * 10⁴
1 <= coins[i] <= 4 * 10⁴

Solution: Greedy + Math

We want to start with smaller values, sort input array in ascending order.

First of all, the first number has to be 1 in order to generate sum of 1.
Assuming the first i numbers can generate 0 ~ k.
Then the i+1-th number x can be used if and only if x <= k + 1, such that we can have a consecutive sum of k + 1 by adding x to a sum between [0, k] and the new maximum sum we have will be k + x.

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

C++

// Author: Huahua

class Solution {

public:

int getMaximumConsecutive(vector<int>& coins) {

sort(begin(coins), end(coins));

int ans = 0;

for (int c : coins) {

if (c > ans + 1) break;

ans += c;

}

return ans + 1;

}

};

花花酱 LeetCode 1797. Design Authentication Manager

By zxi on March 20, 2021

There is an authentication system that works with authentication tokens. For each session, the user will receive a new authentication token that will expire timeToLive seconds after the currentTime. If the token is renewed, the expiry time will be extended to expire timeToLive seconds after the (potentially different) currentTime.

Implement the AuthenticationManager class:

AuthenticationManager(int timeToLive) constructs the AuthenticationManager and sets the timeToLive.
generate(string tokenId, int currentTime) generates a new token with the given tokenId at the given currentTime in seconds.
renew(string tokenId, int currentTime) renews the unexpired token with the given tokenId at the given currentTime in seconds. If there are no unexpired tokens with the given tokenId, the request is ignored, and nothing happens.
countUnexpiredTokens(int currentTime) returns the number of unexpired tokens at the given currentTime.

Note that if a token expires at time t, and another action happens on time t (renew or countUnexpiredTokens), the expiration takes place before the other actions.

Example 1:

Input
["AuthenticationManager", "renew", "generate", "countUnexpiredTokens", "generate", "renew", "renew", "countUnexpiredTokens"]
[[5], ["aaa", 1], ["aaa", 2], [6], ["bbb", 7], ["aaa", 8], ["bbb", 10], [15]]
Output
[null, null, null, 1, null, null, null, 0]

Explanation AuthenticationManager authenticationManager = new AuthenticationManager(5); // Constructs the AuthenticationManager with timeToLive = 5 seconds. authenticationManager.renew(“aaa”, 1); // No token exists with tokenId “aaa” at time 1, so nothing happens. authenticationManager.generate(“aaa”, 2); // Generates a new token with tokenId “aaa” at time 2. authenticationManager.countUnexpiredTokens(6); // The token with tokenId “aaa” is the only unexpired one at time 6, so return 1. authenticationManager.generate(“bbb”, 7); // Generates a new token with tokenId “bbb” at time 7. authenticationManager.renew(“aaa”, 8); // The token with tokenId “aaa” expired at time 7, and 8 >= 7, so at time 8 the renew request is ignored, and nothing happens. authenticationManager.renew(“bbb”, 10); // The token with tokenId “bbb” is unexpired at time 10, so the renew request is fulfilled and now the token will expire at time 15. authenticationManager.countUnexpiredTokens(15); // The token with tokenId “bbb” expires at time 15, and the token with tokenId “aaa” expired at time 7, so currently no token is unexpired, so return 0.

Constraints:

1 <= timeToLive <= 10⁸
1 <= currentTime <= 10⁸
1 <= tokenId.length <= 5
tokenId consists only of lowercase letters.
All calls to generate will contain unique values of tokenId.
The values of currentTime across all the function calls will be strictly increasing.
At most 2000 calls will be made to all functions combined.

Solution: Hashtable

Use a hashtable to store the token and its expiration time.

Time complexity: at most O(n) per operation
Space complexity: O(n)

C++

// Author: Huahua, 160 ms, 30.1 MB

class AuthenticationManager {

public:

AuthenticationManager(int timeToLive) : ttl_(timeToLive) {}

void generate(string tokenId, int currentTime) {

clear(currentTime);

tokens_[tokenId] = currentTime + ttl_;

}

void renew(string tokenId, int currentTime) {

clear(currentTime);

if (!tokens_.count(tokenId)) return;

tokens_[tokenId] = currentTime + ttl_;

}

int countUnexpiredTokens(int currentTime) {

clear(currentTime);

return tokens_.size();

}

private:

void clear(int currentTime) {

vector<string> ids;

for (const auto& [id, t] : tokens_)

if (t <= currentTime) ids.push_back(id);

for (const string& id : ids)

tokens_.erase(id);

}

unordered_map<string, int> tokens_;

int ttl_;

};

/**

* Your AuthenticationManager object will be instantiated and called as such:

* AuthenticationManager* obj = new AuthenticationManager(timeToLive);

* obj->generate(tokenId,currentTime);

* obj->renew(tokenId,currentTime);

* int param_3 = obj->countUnexpiredTokens(currentTime);

花花酱 LeetCode 1796. Second Largest Digit in a String

By zxi on March 20, 2021

Given an alphanumeric string s, return the second largest numerical digit that appears in s, or -1 if it does not exist.

An alphanumericstring is a string consisting of lowercase English letters and digits.

Example 1:

Input: s = "dfa12321afd"
Output: 2
Explanation: The digits that appear in s are [1, 2, 3]. The second largest digit is 2.

Example 2:

Input: s = "abc1111"
Output: -1
Explanation: The digits that appear in s are [1]. There is no second largest digit.

Constraints:

1 <= s.length <= 500
s consists of only lowercase English letters and/or digits.

Solution: Hashtable

Time complexity: O(n)
Space complexity: O(10)

C++

// Author: Huahua

class Solution {

public:

int secondHighest(string s) {

vector<int> d(10);

for (char c : s)

if (c >= '0' && c <= '9')

d[c - '0'] = 1;

int order = 0;

for (int i = 9; i >= 0; --i)

if (d[i] && ++order == 2)

return i;

return -1;

}

};

花花酱 LeetCode 1793. Maximum Score of a Good Subarray

By zxi on March 18, 2021

You are given an array of integers nums (0-indexed) and an integer k.

The score of a subarray (i, j) is defined as min(nums[i], nums[i+1], ..., nums[j]) * (j - i + 1). A good subarray is a subarray where i <= k <= j.

Return the maximum possible score of a good subarray.

Example 1:

Input: nums = [1,4,3,7,4,5], k = 3
Output: 15
Explanation: The optimal subarray is (1, 5) with a score of min(4,3,7,4,5) * (5-1+1) = 3 * 5 = 15.

Example 2:

Input: nums = [5,5,4,5,4,1,1,1], k = 0
Output: 20
Explanation: The optimal subarray is (0, 4) with a score of min(5,5,4,5,4) * (4-0+1) = 4 * 5 = 20.

Constraints:

1 <= nums.length <= 10⁵
1 <= nums[i] <= 2 * 10⁴
0 <= k < nums.length

Solutions: Two Pointers

maintain a window [i, j], m = min(nums[i~j]), expend to the left if nums[i – 1] >= nums[j + 1], otherwise expend to the right.

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

C++

// Author: Huahua

class Solution {

public:

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

const int n = nums.size();

int ans = 0;

for (int i = k, j = k, m = nums[k];;) {

ans = max(ans, m * (j - i + 1));

if (j - i + 1 == n) break;

int l = i ? nums[i - 1] : -1;

int r = j + 1 < n ? nums[j + 1] : -1;

if (l >= r)

m = min(m, nums[--i]);

else

m = min(m, nums[++j]);

}

return ans;

}

};

花花酱 LeetCode 1792. Maximum Average Pass Ratio

By zxi on March 13, 2021

There is a school that has classes of students and each class will be having a final exam. You are given a 2D integer array classes, where classes[i] = [pass_i, total_i]. You know beforehand that in the i^th class, there are total_i total students, but only pass_i number of students will pass the exam.

You are also given an integer extraStudents. There are another extraStudents brilliant students that are guaranteed to pass the exam of any class they are assigned to. You want to assign each of the extraStudents students to a class in a way that maximizes the average pass ratio across all the classes.

The pass ratio of a class is equal to the number of students of the class that will pass the exam divided by the total number of students of the class. The average pass ratio is the sum of pass ratios of all the classes divided by the number of the classes.

Return the maximum possible average pass ratio after assigning the extraStudents students. Answers within 10^-5 of the actual answer will be accepted.

Example 1:

Input: classes = [[1,2],[3,5],[2,2]], extraStudents = 2
Output: 0.78333
Explanation: You can assign the two extra students to the first class. The average pass ratio will be equal to (3/4 + 3/5 + 2/2) / 3 = 0.78333.

Example 2:

Input: classes = [[2,4],[3,9],[4,5],[2,10]], extraStudents = 4
Output: 0.53485

Constraints:

1 <= classes.length <= 10⁵
classes[i].length == 2
1 <= pass_i <= total_i <= 10⁵
1 <= extraStudents <= 10⁵

Solution: Greedy + Heap

Sort by the ratio increase potential (p + 1) / (t + 1) – p / t.

Time complexity: O((m+n)logn)
Space complexity: O(n)

C++

// Author: Huahua

class Solution {

public:

double maxAverageRatio(vector<vector<int>>& classes, int extraStudents) {

const int n = classes.size();

auto ratio = [&](int i, int delta = 0) {

return static_cast<double>(classes[i][0] + delta) /

(classes[i][1] + delta);

};

priority_queue<pair<double, int>> q;

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

q.emplace(ratio(i, 1) - ratio(i), i);

while (extraStudents--) {

const auto [r, i] = q.top(); q.pop();

++classes[i][0];

++classes[i][1];

q.emplace(ratio(i, 1) - ratio(i), i);

}

double total_ratio = 0;

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

total_ratio += ratio(i);

return total_ratio / n;

}

};

Python3

# Author: Huahua

class Solution:

def maxAverageRatio(self, classes: List[List[int]], extraStudents: int) -> float:

def ratio(i, delta=0):

return (classes[i][0] + delta) / (classes[i][1] + delta)

q = []

for i, c in enumerate(classes):

heapq.heappush(q, (-(ratio(i, 1) - ratio(i)), i))

for _ in range(extraStudents):

_, i = heapq.heappop(q)

classes[i][0] += 1

classes[i][1] += 1

heapq.heappush(q, (-(ratio(i, 1) - ratio(i)), i))

return mean(ratio(i) for i, _ in enumerate(classes))

Huahua's Tech Road

花花酱 LeetCode 1798. Maximum Number of Consecutive Values You Can Make

Solution: Greedy + Math

C++

花花酱 LeetCode 1797. Design Authentication Manager

Solution: Hashtable

C++

花花酱 LeetCode 1796. Second Largest Digit in a String

Solution: Hashtable

C++

花花酱 LeetCode 1793. Maximum Score of a Good Subarray

Solutions: Two Pointers

C++

花花酱 LeetCode 1792. Maximum Average Pass Ratio

Solution: Greedy + Heap

C++

Python3