Posts published in “Simulation”

花花酱 LeetCode 1599. Maximum Profit of Operating a Centennial Wheel

By zxi on September 27, 2020

You are the operator of a Centennial Wheel that has four gondolas, and each gondola has room for up to four people. You have the ability to rotate the gondolas counterclockwise, which costs you runningCost dollars.

You are given an array customers of length n where customers[i] is the number of new customers arriving just before the i^th rotation (0-indexed). This means you must rotate the wheel i times before customers[i] arrive. Each customer pays boardingCost dollars when they board on the gondola closest to the ground and will exit once that gondola reaches the ground again.

You can stop the wheel at any time, including before serving all customers. If you decide to stop serving customers, all subsequent rotations are free in order to get all the customers down safely. Note that if there are currently more than four customers waiting at the wheel, only four will board the gondola, and the rest will wait for the next rotation.

Return the minimum number of rotations you need to perform to maximize your profit. If there is no scenario where the profit is positive, return -1.

Example 1:

Input: customers = [8,3], boardingCost = 5, runningCost = 6
Output: 3
Explanation: The numbers written on the gondolas are the number of people currently there.
1. 8 customers arrive, 4 board and 4 wait for the next gondola, the wheel rotates. Current profit is 4 * $5 - 1 * $6 = $14.
2. 3 customers arrive, the 4 waiting board the wheel and the other 3 wait, the wheel rotates. Current profit is 8 * $5 - 2 * $6 = $28.
3. The final 3 customers board the gondola, the wheel rotates. Current profit is 11 * $5 - 3 * $6 = $37.
The highest profit was $37 after rotating the wheel 3 times.

Example 2:

Input: customers = [10,9,6], boardingCost = 6, runningCost = 4
Output: 7
Explanation:
1. 10 customers arrive, 4 board and 6 wait for the next gondola, the wheel rotates. Current profit is 4 * $6 - 1 * $4 = $20.
2. 9 customers arrive, 4 board and 11 wait (2 originally waiting, 9 newly waiting), the wheel rotates. Current profit is 8 * $6 - 2 * $4 = $40.
3. The final 6 customers arrive, 4 board and 13 wait, the wheel rotates. Current profit is 12 * $6 - 3 * $4 = $60.
4. 4 board and 9 wait, the wheel rotates. Current profit is 16 * $6 - 4 * $4 = $80.
5. 4 board and 5 wait, the wheel rotates. Current profit is 20 * $6 - 5 * $4 = $100.
6. 4 board and 1 waits, the wheel rotates. Current profit is 24 * $6 - 6 * $4 = $120.
7. 1 boards, the wheel rotates. Current profit is 25 * $6 - 7 * $4 = $122.
The highest profit was $122 after rotating the wheel 7 times.

Example 3:

Input: customers = [3,4,0,5,1], boardingCost = 1, runningCost = 92
Output: -1
Explanation:
1. 3 customers arrive, 3 board and 0 wait, the wheel rotates. Current profit is 3 * $1 - 1 * $92 = -$89.
2. 4 customers arrive, 4 board and 0 wait, the wheel rotates. Current profit is 7 * $1 - 2 * $92 = -$177.
3. 0 customers arrive, 0 board and 0 wait, the wheel rotates. Current profit is 7 * $1 - 3 * $92 = -$269.
4. 5 customers arrive, 4 board and 1 waits, the wheel rotates. Current profit is 12 * $1 - 4 * $92 = -$356.
5. 1 customer arrives, 2 board and 0 wait, the wheel rotates. Current profit is 13 * $1 - 5 * $92 = -$447.
The profit was never positive, so return -1.

Example 4:

Input: customers = [10,10,6,4,7], boardingCost = 3, runningCost = 8
Output: 9
Explanation:
1. 10 customers arrive, 4 board and 6 wait, the wheel rotates. Current profit is 4 * $3 - 1 * $8 = $4.
2. 10 customers arrive, 4 board and 12 wait, the wheel rotates. Current profit is 8 * $3 - 2 * $8 = $8.
3. 6 customers arrive, 4 board and 14 wait, the wheel rotates. Current profit is 12 * $3 - 3 * $8 = $12.
4. 4 customers arrive, 4 board and 14 wait, the wheel rotates. Current profit is 16 * $3 - 4 * $8 = $16.
5. 7 customers arrive, 4 board and 17 wait, the wheel rotates. Current profit is 20 * $3 - 5 * $8 = $20.
6. 4 board and 13 wait, the wheel rotates. Current profit is 24 * $3 - 6 * $8 = $24.
7. 4 board and 9 wait, the wheel rotates. Current profit is 28 * $3 - 7 * $8 = $28.
8. 4 board and 5 wait, the wheel rotates. Current profit is 32 * $3 - 8 * $8 = $32.
9. 4 board and 1 waits, the wheel rotates. Current profit is 36 * $3 - 9 * $8 = $36.
10. 1 board and 0 wait, the wheel rotates. Current profit is 37 * $3 - 10 * $8 = $31.
The highest profit was $36 after rotating the wheel 9 times.

Constraints:

n == customers.length
1 <= n <= 10⁵
0 <= customers[i] <= 50
1 <= boardingCost, runningCost <= 100

Solution: Simulation

Process if waiting customers > 0 or i < n.

Pruning, if runningCost > 4 * boardingCost (max revenue), there is no way to make profit.

Time complexity: sum(consumers) / 4
Space complexity: O(1)

C++

class Solution {

public:

int minOperationsMaxProfit(vector<int>& customers, int boardingCost, int runningCost) {

const int n = customers.size();

constexpr int kMaxC = 4;

if (runningCost > kMaxC * boardingCost) return -1;

int c = 0;

int ans = -1;

int p = 0;

int max_p = 0;

for (int r = 0; r < n || c > 0; ++r) {

c += (r < n ? customers[r] : 0);

p += min(c, kMaxC) * boardingCost - runningCost;

c -= min(c, kMaxC);

if (p > max_p) {

max_p = p;

ans = r + 1; // 1-based

}

return ans;

}

};

花花酱 LeetCode 1598. Crawler Log Folder

By zxi on September 27, 2020

The Leetcode file system keeps a log each time some user performs a change folder operation.

The operations are described below:

"../" : Move to the parent folder of the current folder. (If you are already in the main folder, remain in the same folder).
"./" : Remain in the same folder.
"x/" : Move to the child folder named x (This folder is guaranteed to always exist).

You are given a list of strings logs where logs[i] is the operation performed by the user at the i^th step.

The file system starts in the main folder, then the operations in logs are performed.

Return the minimum number of operations needed to go back to the main folder after the change folder operations.

Example 1:

Input: logs = ["d1/","d2/","../","d21/","./"]
Output: 2
Explanation: Use this change folder operation "../" 2 times and go back to the main folder.

Example 2:

Input: logs = ["d1/","d2/","./","d3/","../","d31/"]
Output: 3

Example 3:

Input: logs = ["d1/","../","../","../"]
Output: 0

Constraints:

1 <= logs.length <= 10³
2 <= logs[i].length <= 10
logs[i] contains lowercase English letters, digits, '.', and '/'.
logs[i] follows the format described in the statement.
Folder names consist of lowercase English letters and digits.

Solution: Simulation

We only need to track the depth of current folder, and name and path can be ignored.

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

C++

// Author: Huahua

class Solution {

public:

int minOperations(vector<string>& logs) {

int ans = 0;

for (const string& log : logs) {

if (log == "../")

ans = max(ans - 1, 0);

else if (log != "./")

++ans;

}

return ans;

}

};

花花酱 LeetCode 1560. Most Visited Sector in a Circular Track

By zxi on August 23, 2020

Given an integer n and an integer array rounds. We have a circular track which consists of n sectors labeled from 1 to n. A marathon will be held on this track, the marathon consists of m rounds. The i^th round starts at sector rounds[i - 1] and ends at sector rounds[i]. For example, round 1 starts at sector rounds[0] and ends at sector rounds[1]

Return an array of the most visited sectors sorted in ascending order.

Notice that you circulate the track in ascending order of sector numbers in the counter-clockwise direction (See the first example).

Example 1:

Input: n = 4, rounds = [1,3,1,2]
Output: [1,2]
Explanation: The marathon starts at sector 1. The order of the visited sectors is as follows:
1 --> 2 --> 3 (end of round 1) --> 4 --> 1 (end of round 2) --> 2 (end of round 3 and the marathon)
We can see that both sectors 1 and 2 are visited twice and they are the most visited sectors. Sectors 3 and 4 are visited only once.

Example 2:

Input: n = 2, rounds = [2,1,2,1,2,1,2,1,2]
Output: [2]

Example 3:

Input: n = 7, rounds = [1,3,5,7]
Output: [1,2,3,4,5,6,7]

Constraints:

2 <= n <= 100
1 <= m <= 100
rounds.length == m + 1
1 <= rounds[i] <= n
rounds[i] != rounds[i + 1] for 0 <= i < m

Solution: Simulation

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

C++

class Solution {

public:

vector<int> mostVisited(int n, vector<int>& rounds) {

vector<int> counts(n);

counts[rounds[0] - 1] = 1;

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

for (int s = rounds[i - 1]; ; ++s) {

++counts[s %= n];

if (s == rounds[i] - 1) break;

}

const int max_count = *max_element(begin(counts), end(counts));

vector<int> ans;

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

if (counts[i] == max_count) ans.push_back(i + 1);

return ans;

}

};

花花酱 LeetCode 1545. Find Kth Bit in Nth Binary String

By zxi on August 10, 2020

Given two positive integers n and k, the binary string S_n is formed as follows:

S₁ = "0"
S_i = S_i-1 + "1" + reverse(invert(S_i-1)) for i > 1

Where + denotes the concatenation operation, reverse(x) returns the reversed string x, and invert(x) inverts all the bits in x (0 changes to 1 and 1 changes to 0).

For example, the first 4 strings in the above sequence are:

S₁= "0"
S₂= "011"
S₃= "0111001"
S₄ = "011100110110001"

Return the k^th bit in S_n. It is guaranteed that k is valid for the given n.

Example 1:

Input: n = 3, k = 1
Output: "0"
Explanation: S₃ is "0111001". The first bit is "0".

Example 2:

Input: n = 4, k = 11
Output: "1"
Explanation: S₄ is "011100110110001". The 11th bit is "1".

Example 3:

Input: n = 1, k = 1
Output: "0"

Example 4:

Input: n = 2, k = 3
Output: "1"

Constraints:

1 <= n <= 20
1 <= k <= 2ⁿ - 1

Solution 1: Brute Force / Simulation

Generate the string till Sn or length >= k.

Time complexity: O(2^n)
Space complexity: O(2^n)

C++

class Solution {

public:

char findKthBit(int n, int k) {

string ans = "0";

for (int i = 2; i <= n && ans.length() < k; ++i) {

string tmp(rbegin(ans), rend(ans));

for (char& c : tmp)

c = '1' - c + '0';

ans = ans + "1" + tmp;

}

return ans[k - 1];

}

};

Solution 2: Recursion

All the strings have odd length of L = (1 << n) – 1,
Let say the center m = (L + 1) / 2
if n == 1, k should be 1 and ans is “0”.
Otherwise
if k == m, we know it’s “1”.
if k < m, the answer is the same as find(n-1, K)
if k > m, we are finding a flipped and mirror char in S(n-1), thus the answer is flip(find(n-1, L – k + 1)).

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

C++

class Solution {

public:

char findKthBit(int n, int k) {

if (n == 1) return '0';

int l = (1 << n) - 1;

if (k == (l + 1) / 2) return '1';

else if (k < (l + 1) / 2)

return findKthBit(n - 1, k);

else

return '1' - findKthBit(n - 1, l - k + 1) + '0';

}

};

Java

class Solution {

public char findKthBit(int n, int k) {

if (n == 1) return '0';

int l = (1 << n) - 1;

if (k == (l + 1) / 2) return '1';

else if (k < (l + 1) / 2)

return findKthBit(n - 1, k);

else

return (char)('1' - findKthBit(n - 1, l - k + 1) + '0');

}

Python3

class Solution:

def findKthBit(self, n: int, k: int) -> str:

if n == 1: return "0"

l = (1 << n) - 1

if k == (l + 1) / 2:

return "1"

elif k < (l + 1) / 2:

return self.findKthBit(n - 1, k)

else:

return str(1 - int(self.findKthBit(n - 1, l - k + 1)))

花花酱 1528. Shuffle String

By zxi on July 25, 2020

Given a string s and an integer array indices of the same length.

The string s will be shuffled such that the character at the i^th position moves to indices[i] in the shuffled string.

Return the shuffled string.

Example 1:

Input: s = "codeleet", indices = [4,5,6,7,0,2,1,3]
Output: "leetcode"
Explanation: As shown, "codeleet" becomes "leetcode" after shuffling.

Example 2:

Input: s = "abc", indices = [0,1,2]
Output: "abc"
Explanation: After shuffling, each character remains in its position.

Example 3:

Input: s = "aiohn", indices = [3,1,4,2,0]
Output: "nihao"

Example 4:

Input: s = "aaiougrt", indices = [4,0,2,6,7,3,1,5]
Output: "arigatou"

Example 5:

Input: s = "art", indices = [1,0,2]
Output: "rat"

Constraints:

s.length == indices.length == n
1 <= n <= 100
s contains only lower-case English letters.
0 <= indices[i] < n
All values of indices are unique (i.e. indices is a permutation of the integers from 0 to n - 1).

Solution: Simulation

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

C++

// Author: Huahua

class Solution {

public:

string restoreString(string s, vector<int>& indices) {

string ans(s);

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

ans[indices[i]] = s[i];

return ans;

}

};

Java

// Author: Huahua

class Solution {

public String restoreString(String s, int[] indices) {

char[] ans = new char[s.length()];

for (int i = 0; i < s.length(); ++i)

ans[indices[i]] = s.charAt(i);

return new String(ans);

}

Pyhton3

class Solution:

def restoreString(self, s: str, indices: List[int]) -> str:

ans = [None] * len(s)

for i, idx in enumerate(indices):

ans[idx] = s[i]

return ''.join(ans)