2023-10-28
1220. Count Vowels Permutation

Topic: Dynamic Programming
Difficulty: Hard

Problem:
Given an integer n, your task is to count how many strings of length n can be formed under the following rules:

• Each character is a lower case vowel ('a', 'e', 'i', 'o', 'u')
• Each vowel 'a' may only be followed by an 'e'.
• Each vowel 'e' may only be followed by an 'a' or an 'i'.
• Each vowel 'i' may not be followed by another 'i'.
• Each vowel 'o' may only be followed by an 'i' or a 'u'.
• Each vowel 'u' may only be followed by an 'a'.

Since the answer may be too large, return it modulo 10^9 + 7.

Example 1:

Input: n = 1
Output: 5
Explanation: All possible strings are: "a", "e", "i" , "o" and "u".

Example 2:

Input: n = 2
Output: 10
Explanation: All possible strings are: "ae", "ea", "ei", "ia", "ie", "io", "iu", "oi", "ou" and "ua".

Example 3: 

Input: n = 5
Output: 68

Constraints:

• 1 <= n <= 2 * 10^4

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2023-10-30
1356. Sort Integers by The Number of 1 Bits

Topic: Array, Bit Manipulation, Sorting, Counting
Difficulty: Easy

Problem:
You are given an integer array arr. Sort the integers in the array in ascending order by the number of 1's in their binary representation and in case of two or more integers have the same number of 1's you have to sort them in ascending order.

Return the array after sorting it.

Example 1:

Input: arr = [0,1,2,3,4,5,6,7,8]
Output: [0,1,2,4,8,3,5,6,7]
Explantion: [0] is the only integer with 0 bits.
[1,2,4,8] all have 1 bit.
[3,5,6] have 2 bits.
[7] has 3 bits.
The sorted array by bits is [0,1,2,4,8,3,5,6,7]

Example 2:

Input: arr = [1024,512,256,128,64,32,16,8,4,2,1]
Output: [1,2,4,8,16,32,64,128,256,512,1024]
Explantion: All integers have 1 bit in the binary representation, you should just sort them in ascending order.

Constraints:

• 1 <= arr.length <= 500
• 0 <= arr[i] <= 10^4

2023-10-31
2433. Find The Original Array of Prefix Xor

Topic: Array, Bit Manipulation
Difficulty: Medium

Problem:
You are given an integer array pref of size n. Find and return the array arr of size n that satisfies:

• pref[i] = arr[0] ^ arr[1] ^ ... ^ arr[i].

Note that ^ denotes the bitwise-xor operation.

It can be proven that the answer is unique.

Example 1:

Input: pref = [5,2,0,3,1]
Output: [5,7,2,3,2]
Explanation: From the array [5,7,2,3,2] we have the following:
- pref[0] = 5.
- pref[1] = 5 ^ 7 = 2.
- pref[2] = 5 ^ 7 ^ 2 = 0.
- pref[3] = 5 ^ 7 ^ 2 ^ 3 = 3.
- pref[4] = 5 ^ 7 ^ 2 ^ 3 ^ 2 = 1.

Example 2:

Input: pref = [13]
Output: [13]
Explanation: We have pref[0] = arr[0] = 13.

Constraints:

• 1 <= pref.length <= 10^5
• 0 <= pref[i] <= 10^6

2023-11-01
501. Find Mode in Binary Search Tree

Topic: Tree, Depth-First Search, Binary Search Tree, Binary Tree
Difficulty: Easy

Problem:
Given the root of a binary search tree (BST) with duplicates, return all the mode(s) (i.e., the most frequently occurred element) in it.

If the tree has more than one mode, return them in any order.

Assume a BST is defined as follows:

• The left subtree of a node contains only nodes with keys less than or equal to the node's key.
• The right subtree of a node contains only nodes with keys greater than or equal to the node's key.
• Both the left and right subtrees must also be binary search trees.

Example 1:

Image: https://assets.leetcode.com/uploads/2021/03/11/mode-tree.jpg

Input: root = [1,null,2,2]
Output: [2]

Example 2:

Input: root = [0]
Output: [0]

Constraints:

• The number of nodes in the tree is in the range [1, 10^4].
• -10^5 <= Node.val <= 10^5

Follow up: Could you do that without using any extra space? (Assume that the implicit stack space incurred due to recursion does not count).

2023-11-02
2265. Count Nodes Equal to Average of Subtree

Topic: Tree, Depth-First Search, Binary Tree
Difficulty: Medium

Problem:
Given the root of a binary tree, return the number of nodes where the value of the node is equal to the average of the values in its subtree.

Note:

• The average of n elements is the sum of the n elements divided by n and rounded down to the nearest integer.
• A subtree of root is a tree consisting of root and all of its descendants.

Example 1:

Image: https://assets.leetcode.com/uploads/2022/03/15/image-20220315203925-1.png

Input: root = [4,8,5,0,1,null,6]
Output: 5
Explanation: 
For the node with value 4: The average of its subtree is (4 + 8 + 5 + 0 + 1 + 6) / 6 = 24 / 6 = 4.
For the node with value 5: The average of its subtree is (5 + 6) / 2 = 11 / 2 = 5.
For the node with value 0: The average of its subtree is 0 / 1 = 0.
For the node with value 1: The average of its subtree is 1 / 1 = 1.
For the node with value 6: The average of its subtree is 6 / 1 = 6.

Example 2:

Image: https://assets.leetcode.com/uploads/2022/03/26/image-20220326133920-1.png

Input: root = [1]
Output: 1
Explanation: For the node with value 1: The average of its subtree is 1 / 1 = 1.

Constraints:

• The number of nodes in the tree is in the range [1, 1000].
• 0 <= Node.val <= 1000

2023-11-03
1441. Build an Array With Stack Operations

Topic: Array, Stack, Simulation
Difficulty: Medium

Problem:
You are given an integer array target and an integer n.

You have an empty stack with the two following operations:

• "Push": pushes an integer to the top of the stack.
• "Pop": removes the integer on the top of the stack.

You also have a stream of the integers in the range [1, n].

Use the two stack operations to make the numbers in the stack (from the bottom to the top) equal to target. You should follow the following rules:

• If the stream of the integers is not empty, pick the next integer from the stream and push it to the top of the stack.
• If the stack is not empty, pop the integer at the top of the stack.
• If, at any moment, the elements in the stack (from the bottom to the top) are equal to target, do not read new integers from the stream and do not do more operations on the stack.

Return the stack operations needed to build target following the mentioned rules. If there are multiple valid answers, return any of them.

Example 1:

Input: target = [1,3], n = 3
Output: ["Push","Push","Pop","Push"]
Explanation: Initially the stack s is empty. The last element is the top of the stack.
Read 1 from the stream and push it to the stack. s = [1].
Read 2 from the stream and push it to the stack. s = [1,2].
Pop the integer on the top of the stack. s = [1].
Read 3 from the stream and push it to the stack. s = [1,3].

Example 2:

Input: target = [1,2,3], n = 3
Output: ["Push","Push","Push"]
Explanation: Initially the stack s is empty. The last element is the top of the stack.
Read 1 from the stream and push it to the stack. s = [1].
Read 2 from the stream and push it to the stack. s = [1,2].
Read 3 from the stream and push it to the stack. s = [1,2,3].

Example 3:

Input: target = [1,2], n = 4
Output: ["Push","Push"]
Explanation: Initially the stack s is empty. The last element is the top of the stack.
Read 1 from the stream and push it to the stack. s = [1].
Read 2 from the stream and push it to the stack. s = [1,2].
Since the stack (from the bottom to the top) is equal to target, we stop the stack operations.
The answers that read integer 3 from the stream are not accepted.

Constraints:

• 1 <= target.length <= 100
• 1 <= n <= 100
• 1 <= target[i] <= n
• target is strictly increasing.

2023-11-04
1503. Last Moment Before All Ants Fall Out of a Plank

Topic: Array, Brainteaser, Simulation
Difficulty: Medium

Problem:
We have a wooden plank of the length n units. Some ants are walking on the plank, each ant moves with a speed of 1 unit per second. Some of the ants move to the left, the other move to the right.

When two ants moving in two different directions meet at some point, they change their directions and continue moving again. Assume changing directions does not take any additional time.

When an ant reaches one end of the plank at a time t, it falls out of the plank immediately.

Given an integer n and two integer arrays left and right, the positions of the ants moving to the left and the right, return the moment when the last ant(s) fall out of the plank.

Example 1:

Image: https://assets.leetcode.com/uploads/2020/06/17/ants.jpg

Input: n = 4, left = [4,3], right = [0,1]
Output: 4
Explanation: In the image above:
-The ant at index 0 is named A and going to the right.
-The ant at index 1 is named B and going to the right.
-The ant at index 3 is named C and going to the left.
-The ant at index 4 is named D and going to the left.
The last moment when an ant was on the plank is t = 4 seconds. After that, it falls immediately out of the plank. (i.e., We can say that at t = 4.0000000001, there are no ants on the plank).

Example 2:

Image: https://assets.leetcode.com/uploads/2020/06/17/ants2.jpg

Input: n = 7, left = [], right = [0,1,2,3,4,5,6,7]
Output: 7
Explanation: All ants are going to the right, the ant at index 0 needs 7 seconds to fall.

Example 3:

Image: https://assets.leetcode.com/uploads/2020/06/17/ants3.jpg

Input: n = 7, left = [0,1,2,3,4,5,6,7], right = []
Output: 7
Explanation: All ants are going to the left, the ant at index 7 needs 7 seconds to fall.

Constraints:

• 1 <= n <= 10^4
• 0 <= left.length <= n + 1
• 0 <= left[i] <= n
• 0 <= right.length <= n + 1
• 0 <= right[i] <= n
• 1 <= left.length + right.length <= n + 1
• All values of left and right are unique, and each value can appear only in one of the two arrays.

2023-11-05
1535. Find the Winner of an Array Game

Topic: Array, Simulation
Difficulty: Medium

Problem:
Given an integer array arr of distinct integers and an integer k.

A game will be played between the first two elements of the array (i.e. arr[0] and arr[1]). In each round of the game, we compare arr[0] with arr[1], the larger integer wins and remains at position 0, and the smaller integer moves to the end of the array. The game ends when an integer wins k consecutive rounds.

Return the integer which will win the game.

It is guaranteed that there will be a winner of the game.

Example 1:

Input: arr = [2,1,3,5,4,6,7], k = 2
Output: 5
Explanation: Let's see the rounds of the game:
Round |       arr       | winner | win_count
  1   | [2,1,3,5,4,6,7] | 2      | 1
  2   | [2,3,5,4,6,7,1] | 3      | 1
  3   | [3,5,4,6,7,1,2] | 5      | 1
  4   | [5,4,6,7,1,2,3] | 5      | 2
So we can see that 4 rounds will be played and 5 is the winner because it wins 2 consecutive games.

Example 2:

Input: arr = [3,2,1], k = 10
Output: 3
Explanation: 3 will win the first 10 rounds consecutively.

Constraints:

• 2 <= arr.length <= 10^5
• 1 <= arr[i] <= 10^6
• arr contains distinct integers.
• 1 <= k <= 10^9

2023-11-06
1845. Seat Reservation Manager

Topic: Design, Heap (Priority Queue)
Difficulty: Medium

Problem:
Design a system that manages the reservation state of n seats that are numbered from 1 to n.

Implement the SeatManager class:

• SeatManager(int n) Initializes a SeatManager object that will manage n seats numbered from 1 to n. All seats are initially available.
• int reserve() Fetches the smallest-numbered unreserved seat, reserves it, and returns its number.
• void unreserve(int seatNumber) Unreserves the seat with the given seatNumber.

Example 1:

Input
["SeatManager", "reserve", "reserve", "unreserve", "reserve", "reserve", "reserve", "reserve", "unreserve"]
[[5], [], [], [2], [], [], [], [], [5]]
Output
[null, 1, 2, null, 2, 3, 4, 5, null]

Explanation
SeatManager seatManager = new SeatManager(5); // Initializes a SeatManager with 5 seats.
seatManager.reserve();    // All seats are available, so return the lowest numbered seat, which is 1.
seatManager.reserve();    // The available seats are [2,3,4,5], so return the lowest of them, which is 2.
seatManager.unreserve(2); // Unreserve seat 2, so now the available seats are [2,3,4,5].
seatManager.reserve();    // The available seats are [2,3,4,5], so return the lowest of them, which is 2.
seatManager.reserve();    // The available seats are [3,4,5], so return the lowest of them, which is 3.
seatManager.reserve();    // The available seats are [4,5], so return the lowest of them, which is 4.
seatManager.reserve();    // The only available seat is seat 5, so return 5.
seatManager.unreserve(5); // Unreserve seat 5, so now the available seats are [5].

Constraints:

• 1 <= n <= 10^5
• 1 <= seatNumber <= n
• For each call to reserve, it is guaranteed that there will be at least one unreserved seat.
• For each call to unreserve, it is guaranteed that seatNumber will be reserved.
• At most 10^5 calls in total will be made to reserve and unreserve.

2023-11-07
1921. Eliminate Maximum Number of Monsters

Topic: Array, Greedy, Sorting
Difficulty: Medium

Problem:
You are playing a video game where you are defending your city from a group of n monsters. You are given a 0-indexed integer array dist of size n, where dist[i] is the initial distance in kilometers of the i^th monster from the city.

The monsters walk toward the city at a constant speed. The speed of each monster is given to you in an integer array speed of size n, where speed[i] is the speed of the i^th monster in kilometers per minute.

You have a weapon that, once fully charged, can eliminate a single monster. However, the weapon takes one minute to charge. The weapon is fully charged at the very start.

You lose when any monster reaches your city. If a monster reaches the city at the exact moment the weapon is fully charged, it counts as a loss, and the game ends before you can use your weapon.

Return the maximum number of monsters that you can eliminate before you lose, or n if you can eliminate all the monsters before they reach the city.

Example 1:

Input: dist = [1,3,4], speed = [1,1,1]
Output: 3
Explanation:
In the beginning, the distances of the monsters are [1,3,4]. You eliminate the first monster.
After a minute, the distances of the monsters are [X,2,3]. You eliminate the second monster.
After a minute, the distances of the monsters are [X,X,2]. You eliminate the thrid monster.
All 3 monsters can be eliminated.

Example 2:

Input: dist = [1,1,2,3], speed = [1,1,1,1]
Output: 1
Explanation:
In the beginning, the distances of the monsters are [1,1,2,3]. You eliminate the first monster.
After a minute, the distances of the monsters are [X,0,1,2], so you lose.
You can only eliminate 1 monster.

Example 3:

Input: dist = [3,2,4], speed = [5,3,2]
Output: 1
Explanation:
In the beginning, the distances of the monsters are [3,2,4]. You eliminate the first monster.
After a minute, the distances of the monsters are [X,0,2], so you lose.
You can only eliminate 1 monster.

Constraints:

• n == dist.length == speed.length
• 1 <= n <= 10^5
• 1 <= dist[i], speed[i] <= 10^5

2023-11-08
2849. Determine if a Cell Is Reachable at a Given Time

Topic: Math
Difficulty: Medium

Problem:
You are given four integers sx, sy, fx, fy, and a non-negative integer t.

In an infinite 2D grid, you start at the cell (sx, sy). Each second, you must move to any of its adjacent cells.

Return true if you can reach cell (fx, fy) after exactly t seconds, or false otherwise.

A cell's adjacent cells are the 8 cells around it that share at least one corner with it. You can visit the same cell several times.

Example 1:

Image: https://assets.leetcode.com/uploads/2023/08/05/example2.svg

Input: sx = 2, sy = 4, fx = 7, fy = 7, t = 6
Output: true
Explanation: Starting at cell (2, 4), we can reach cell (7, 7) in exactly 6 seconds by going through the cells depicted in the picture above.

Example 2:

Image: https://assets.leetcode.com/uploads/2023/08/05/example1.svg

Input: sx = 3, sy = 1, fx = 7, fy = 3, t = 3
Output: false
Explanation: Starting at cell (3, 1), it takes at least 4 seconds to reach cell (7, 3) by going through the cells depicted in the picture above. Hence, we cannot reach cell (7, 3) at the third second.

Constraints:

• 1 <= sx, sy, fx, fy <= 10^9
• 0 <= t <= 10^9

2023-11-09
1759. Count Number of Homogenous Substrings

Topic: Math, String
Difficulty: Medium

Problem:
Given a string s, return the number of homogenous substrings of s. Since the answer may be too large, return it modulo 10^9 + 7.

A string is homogenous if all the characters of the string are the same.

A substring is a contiguous sequence of characters within a string.

Example 1:

Input: s = "abbcccaa"
Output: 13
Explanation: The homogenous substrings are listed as below:
"a"   appears 3 times.
"aa"  appears 1 time.
"b"   appears 2 times.
"bb"  appears 1 time.
"c"   appears 3 times.
"cc"  appears 2 times.
"ccc" appears 1 time.
3 + 1 + 2 + 1 + 3 + 2 + 1 = 13.

Example 2:

Input: s = "xy"
Output: 2
Explanation: The homogenous substrings are "x" and "y".

Example 3:

Input: s = "zzzzz"
Output: 15

Constraints:

• 1 <= s.length <= 10^5
• s consists of lowercase letters.

2023-11-10
1743. Restore the Array From Adjacent Pairs

Topic: Array, Hash Table
Difficulty: Medium

Problem:
There is an integer array nums that consists of n unique elements, but you have forgotten it. However, you do remember every pair of adjacent elements in nums.

You are given a 2D integer array adjacentPairs of size n - 1 where each adjacentPairs[i] = [u_i, v_i] indicates that the elements u_i and v_i are adjacent in nums.

It is guaranteed that every adjacent pair of elements nums[i] and nums[i+1] will exist in adjacentPairs, either as [nums[i], nums[i+1]] or [nums[i+1], nums[i]]. The pairs can appear in any order.

Return the original array nums. If there are multiple solutions, return any of them.

Example 1:

Input: adjacentPairs = [[2,1],[3,4],[3,2]]
Output: [1,2,3,4]
Explanation: This array has all its adjacent pairs in adjacentPairs.
Notice that adjacentPairs[i] may not be in left-to-right order.

Example 2:

Input: adjacentPairs = [[4,-2],[1,4],[-3,1]]
Output: [-2,4,1,-3]
Explanation: There can be negative numbers.
Another solution is [-3,1,4,-2], which would also be accepted.

Example 3:

Input: adjacentPairs = [[100000,-100000]]
Output: [100000,-100000]

Constraints:

• nums.length == n
• adjacentPairs.length == n - 1
• adjacentPairs[i].length == 2
• 2 <= n <= 10^5
• -10^5 <= nums[i], u_i, v_i <= 10^5
• There exists some nums that has adjacentPairs as its pairs.

2023-11-11
2642. Design Graph With Shortest Path Calculator

Topic: Graph, Design, Heap (Priority Queue), Shortest Path
Difficulty: Hard

Problem:
There is a directed weighted graph that consists of n nodes numbered from 0 to n - 1. The edges of the graph are initially represented by the given array edges where edges[i] = [from_i, to_i, edgeCost_i] meaning that there is an edge from from_i to to_i with the cost edgeCost_i.

Implement the Graph class:

• Graph(int n, int[][] edges) initializes the object with n nodes and the given edges.
• addEdge(int[] edge) adds an edge to the list of edges where edge = [from, to, edgeCost]. It is guaranteed that there is no edge between the two nodes before adding this one.
• int shortestPath(int node1, int node2) returns the minimum cost of a path from node1 to node2. If no path exists, return -1. The cost of a path is the sum of the costs of the edges in the path.

Example 1:

Image: https://assets.leetcode.com/uploads/2023/01/11/graph3drawio-2.png

Input
["Graph", "shortestPath", "shortestPath", "addEdge", "shortestPath"]
[[4, [[0, 2, 5], [0, 1, 2], [1, 2, 1], [3, 0, 3]]], [3, 2], [0, 3], [[1, 3, 4]], [0, 3]]
Output
[null, 6, -1, null, 6]

Explanation
Graph g = new Graph(4, [[0, 2, 5], [0, 1, 2], [1, 2, 1], [3, 0, 3]]);
g.shortestPath(3, 2); // return 6. The shortest path from 3 to 2 in the first diagram above is 3 -> 0 -> 1 -> 2 with a total cost of 3 + 2 + 1 = 6.
g.shortestPath(0, 3); // return -1. There is no path from 0 to 3.
g.addEdge([1, 3, 4]); // We add an edge from node 1 to node 3, and we get the second diagram above.
g.shortestPath(0, 3); // return 6. The shortest path from 0 to 3 now is 0 -> 1 -> 3 with a total cost of 2 + 4 = 6.

Constraints:

• 1 <= n <= 100
• 0 <= edges.length <= n * (n - 1)
• edges[i].length == edge.length == 3
• 0 <= from_i, to_i, from, to, node1, node2 <= n - 1
• 1 <= edgeCost_i, edgeCost <= 10^6
• There are no repeated edges and no self-loops in the graph at any point.
• At most 100 calls will be made for addEdge.
• At most 100 calls will be made for shortestPath.

2023-11-12
815. Bus Routes

Topic: Array, Hash Table, Breadth-First Search
Difficulty: Hard

Problem:
You are given an array routes representing bus routes where routes[i] is a bus route that the i^th bus repeats forever.

• For example, if routes[0] = [1, 5, 7], this means that the 0^th bus travels in the sequence 1 -> 5 -> 7 -> 1 -> 5 -> 7 -> 1 -> ... forever.

You will start at the bus stop source (You are not on any bus initially), and you want to go to the bus stop target. You can travel between bus stops by buses only.

Return the least number of buses you must take to travel from source to target. Return -1 if it is not possible.

Example 1:

Input: routes = [[1,2,7],[3,6,7]], source = 1, target = 6
Output: 2
Explanation: The best strategy is take the first bus to the bus stop 7, then take the second bus to the bus stop 6.

Example 2:

Input: routes = [[7,12],[4,5,15],[6],[15,19],[9,12,13]], source = 15, target = 12
Output: -1

Constraints:

• 1 <= routes.length <= 500.
• 1 <= routes[i].length <= 10^5
• All the values of routes[i] are unique.
• sum(routes[i].length) <= 10^5
• 0 <= routes[i][j] < 10^6
• 0 <= source, target < 10^6

2023-11-13
2785. Sort Vowels in a String

Topic: String, Sorting
Difficulty: Medium

Problem:
Given a 0-indexed string s, permute s to get a new string t such that:

• All consonants remain in their original places. More formally, if there is an index i with 0 <= i < s.length such that s[i] is a consonant, then t[i] = s[i].
• The vowels must be sorted in the nondecreasing order of their ASCII values. More formally, for pairs of indices i, j with 0 <= i < j < s.length such that s[i] and s[j] are vowels, then t[i] must not have a higher ASCII value than t[j].

Return the resulting string.

The vowels are 'a', 'e', 'i', 'o', and 'u', and they can appear in lowercase or uppercase. Consonants comprise all letters that are not vowels.

Example 1:

Input: s = "lEetcOde"
Output: "lEOtcede"
Explanation: 'E', 'O', and 'e' are the vowels in s; 'l', 't', 'c', and 'd' are all consonants. The vowels are sorted according to their ASCII values, and the consonants remain in the same places.

Example 2:

Input: s = "lYmpH"
Output: "lYmpH"
Explanation: There are no vowels in s (all characters in s are consonants), so we return "lYmpH".

Constraints:

• 1 <= s.length <= 10^5
• s consists only of letters of the English alphabet in uppercase and lowercase.

2023-11-14
1930. Unique Length-3 Palindromic Subsequences

Topic: Hash Table, String, Prefix Sum
Difficulty: Medium

Problem:
Given a string s, return the number of unique palindromes of length three that are a subsequence of s.

Note that even if there are multiple ways to obtain the same subsequence, it is still only counted once.

A palindrome is a string that reads the same forwards and backwards.

A subsequence of a string is a new string generated from the original string with some characters (can be none) deleted without changing the relative order of the remaining characters.

• For example, "ace" is a subsequence of "abcde".

Example 1:

Input: s = "aabca"
Output: 3
Explanation: The 3 palindromic subsequences of length 3 are:
- "aba" (subsequence of "aabca")
- "aaa" (subsequence of "aabca")
- "aca" (subsequence of "aabca")

Example 2:

Input: s = "adc"
Output: 0
Explanation: There are no palindromic subsequences of length 3 in "adc".

Example 3:

Input: s = "bbcbaba"
Output: 4
Explanation: The 4 palindromic subsequences of length 3 are:
- "bbb" (subsequence of "bbcbaba")
- "bcb" (subsequence of "bbcbaba")
- "bab" (subsequence of "bbcbaba")
- "aba" (subsequence of "bbcbaba")

Constraints:

• 3 <= s.length <= 10^5
• s consists of only lowercase English letters.

2023-11-15
1846. Maximum Element After Decreasing and Rearranging

Topic: Array, Greedy, Sorting
Difficulty: Medium

Problem:
You are given an array of positive integers arr. Perform some operations (possibly none) on arr so that it satisfies these conditions:

• The value of the first element in arr must be 1.
• The absolute difference between any 2 adjacent elements must be less than or equal to 1. In other words, abs(arr[i] - arr[i - 1]) <= 1 for each i where 1 <= i < arr.length (0-indexed). abs(x) is the absolute value of x.

There are 2 types of operations that you can perform any number of times:

• Decrease the value of any element of arr to a smaller positive integer.
• Rearrange the elements of arr to be in any order.

Return the maximum possible value of an element in arr after performing the operations to satisfy the conditions.

Example 1:

Input: arr = [2,2,1,2,1]
Output: 2
Explanation: 
We can satisfy the conditions by rearranging arr so it becomes [1,2,2,2,1].
The largest element in arr is 2.

Example 2:

Input: arr = [100,1,1000]
Output: 3
Explanation: 
One possible way to satisfy the conditions is by doing the following:
1. Rearrange arr so it becomes [1,100,1000].
2. Decrease the value of the second element to 2.
3. Decrease the value of the third element to 3.
Now arr = [1,2,3], which satisfies the conditions.
The largest element in arr is 3.

Example 3:

Input: arr = [1,2,3,4,5]
Output: 5
Explanation: The array already satisfies the conditions, and the largest element is 5.

Constraints:

• 1 <= arr.length <= 10^5
• 1 <= arr[i] <= 10^9

2023-11-16
1980. Find Unique Binary String

Topic: Array, String, Backtracking
Difficulty: Medium

Problem:
Given an array of strings nums containing n unique binary strings each of length n, return a binary string of length n that does not appear in nums. If there are multiple answers, you may return any of them.

Example 1:

Input: nums = ["01","10"]
Output: "11"
Explanation: "11" does not appear in nums. "00" would also be correct.

Example 2:

Input: nums = ["00","01"]
Output: "11"
Explanation: "11" does not appear in nums. "10" would also be correct.

Example 3:

Input: nums = ["111","011","001"]
Output: "101"
Explanation: "101" does not appear in nums. "000", "010", "100", and "110" would also be correct.

Constraints:

• n == nums.length
• 1 <= n <= 16
• nums[i].length == n
• nums[i] is either '0' or '1'.
• All the strings of nums are unique.