2025-08-17
837. New 21 Game

Topic: Math, Dynamic Programming, Sliding Window, Probability and Statistics
Difficulty: Medium

Problem:
Alice plays the following game, loosely based on the card game "21".

Alice starts with 0 points and draws numbers while she has less than k points. During each draw, she gains an integer number of points randomly from the range [1, maxPts], where maxPts is an integer. Each draw is independent and the outcomes have equal probabilities.

Alice stops drawing numbers when she gets k or more points.

Return the probability that Alice has n or fewer points.

Answers within 10^-5 of the actual answer are considered accepted.

Example 1:

Input: n = 10, k = 1, maxPts = 10
Output: 1.00000
Explanation: Alice gets a single card, then stops.

Example 2:

Input: n = 6, k = 1, maxPts = 10
Output: 0.60000
Explanation: Alice gets a single card, then stops.
In 6 out of 10 possibilities, she is at or below 6 points.

Example 3:

Input: n = 21, k = 17, maxPts = 10
Output: 0.73278

Constraints:

• 0 <= k <= n <= 10^4
• 1 <= maxPts <= 10^4

2025-08-18
679. 24 Game

Topic: Array, Math, Backtracking
Difficulty: Hard

Problem:
You are given an integer array cards of length 4. You have four cards, each containing a number in the range [1, 9]. You should arrange the numbers on these cards in a mathematical expression using the operators ['+', '-', '*', '/'] and the parentheses '(' and ')' to get the value 24.

You are restricted with the following rules:

• The division operator '/' represents real division, not integer division.
• For example, 4 / (1 - 2 / 3) = 4 / (1 / 3) = 12.
• Every operation done is between two numbers. In particular, we cannot use '-' as a unary operator.
• For example, if cards = [1, 1, 1, 1], the expression "-1 - 1 - 1 - 1" is not allowed.
• You cannot concatenate numbers together
• For example, if cards = [1, 2, 1, 2], the expression "12 + 12" is not valid.

Return true if you can get such expression that evaluates to 24, and false otherwise.

Example 1:

Input: cards = [4,1,8,7]
Output: true
Explanation: (8-4) * (7-1) = 24

Example 2:

Input: cards = [1,2,1,2]
Output: false

Constraints:

• cards.length == 4
• 1 <= cards[i] <= 9

2025-08-19
2348. Number of Zero-Filled Subarrays

Topic: Array, Math
Difficulty: Medium

Problem:
Given an integer array nums, return the number of subarrays filled with 0.

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

Example 1:

Input: nums = [1,3,0,0,2,0,0,4]
Output: 6
Explanation: 
There are 4 occurrences of [0] as a subarray.
There are 2 occurrences of [0,0] as a subarray.
There is no occurrence of a subarray with a size more than 2 filled with 0. Therefore, we return 6.

Example 2:

Input: nums = [0,0,0,2,0,0]
Output: 9
Explanation:
There are 5 occurrences of [0] as a subarray.
There are 3 occurrences of [0,0] as a subarray.
There is 1 occurrence of [0,0,0] as a subarray.
There is no occurrence of a subarray with a size more than 3 filled with 0. Therefore, we return 9.

Example 3:

Input: nums = [2,10,2019]
Output: 0
Explanation: There is no subarray filled with 0. Therefore, we return 0.

Constraints:

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

2025-08-20
1277. Count Square Submatrices with All Ones

Topic: Array, Dynamic Programming, Matrix
Difficulty: Medium

Problem:
Given a m * n matrix of ones and zeros, return how many square submatrices have all ones.

Example 1:

Input: matrix =
[
  [0,1,1,1],
  [1,1,1,1],
  [0,1,1,1]
]
Output: 15
Explanation: 
There are 10 squares of side 1.
There are 4 squares of side 2.
There is  1 square of side 3.
Total number of squares = 10 + 4 + 1 = 15.

Example 2:

Input: matrix = 
[
  [1,0,1],
  [1,1,0],
  [1,1,0]
]
Output: 7
Explanation: 
There are 6 squares of side 1.  
There is 1 square of side 2. 
Total number of squares = 6 + 1 = 7.

Constraints:

• 1 <= arr.length <= 300
• 1 <= arr[0].length <= 300
• 0 <= arr[i][j] <= 1

2025-08-21
1504. Count Submatrices With All Ones

Topic: Array, Dynamic Programming, Stack, Matrix, Monotonic Stack
Difficulty: Medium

Problem:
Given an m x n binary matrix mat, return the number of submatrices that have all ones.

Example 1:

Image: https://assets.leetcode.com/uploads/2021/10/27/ones1-grid.jpg

Input: mat = [[1,0,1],[1,1,0],[1,1,0]]
Output: 13
Explanation: 
There are 6 rectangles of side 1x1.
There are 2 rectangles of side 1x2.
There are 3 rectangles of side 2x1.
There is 1 rectangle of side 2x2. 
There is 1 rectangle of side 3x1.
Total number of rectangles = 6 + 2 + 3 + 1 + 1 = 13.

Example 2:

Image: https://assets.leetcode.com/uploads/2021/10/27/ones2-grid.jpg

Input: mat = [[0,1,1,0],[0,1,1,1],[1,1,1,0]]
Output: 24
Explanation: 
There are 8 rectangles of side 1x1.
There are 5 rectangles of side 1x2.
There are 2 rectangles of side 1x3. 
There are 4 rectangles of side 2x1.
There are 2 rectangles of side 2x2. 
There are 2 rectangles of side 3x1. 
There is 1 rectangle of side 3x2. 
Total number of rectangles = 8 + 5 + 2 + 4 + 2 + 2 + 1 = 24.

Constraints:

• 1 <= m, n <= 150
• mat[i][j] is either 0 or 1.

2025-08-22
3195. Find the Minimum Area to Cover All Ones I

Topic: Array, Matrix
Difficulty: Medium

Problem:
You are given a 2D binary array grid. Find a rectangle with horizontal and vertical sides with the smallest area, such that all the 1's in grid lie inside this rectangle.

Return the minimum possible area of the rectangle.

Example 1:

Input: grid = [0,1,0,1,0,1]

Output: 6

Explanation:

Image: https://assets.leetcode.com/uploads/2024/05/08/examplerect0.png

The smallest rectangle has a height of 2 and a width of 3, so it has an area of 2 * 3 = 6.

Example 2:

Input: grid = [1,0,0,0]

Output: 1

Explanation:

Image: https://assets.leetcode.com/uploads/2024/05/08/examplerect1.png

The smallest rectangle has both height and width 1, so its area is 1 * 1 = 1.

Constraints:

• 1 <= grid.length, grid[i].length <= 1000
• grid[i][j] is either 0 or 1.
• The input is generated such that there is at least one 1 in grid.

2025-08-23
3197. Find the Minimum Area to Cover All Ones II

Topic: Array, Matrix, Enumeration
Difficulty: Hard

Problem:
You are given a 2D binary array grid. You need to find 3 non-overlapping rectangles having non-zero areas with horizontal and vertical sides such that all the 1's in grid lie inside these rectangles.

Return the minimum possible sum of the area of these rectangles.

Note that the rectangles are allowed to touch.

Example 1:

Input: grid = [1,0,1,1,1,1]

Output: 5

Explanation:

Image: https://assets.leetcode.com/uploads/2024/05/14/example0rect21.png

• The 1's at (0, 0) and (1, 0) are covered by a rectangle of area 2.
• The 1's at (0, 2) and (1, 2) are covered by a rectangle of area 2.
• The 1 at (1, 1) is covered by a rectangle of area 1.

Example 2:

Input: grid = [1,0,1,0,0,1,0,1]

Output: 5

Explanation:

Image: https://assets.leetcode.com/uploads/2024/05/14/example1rect2.png

• The 1's at (0, 0) and (0, 2) are covered by a rectangle of area 3.
• The 1 at (1, 1) is covered by a rectangle of area 1.
• The 1 at (1, 3) is covered by a rectangle of area 1.

Constraints:

• 1 <= grid.length, grid[i].length <= 30
• grid[i][j] is either 0 or 1.
• The input is generated such that there are at least three 1's in grid.

2025-08-24
1493. Longest Subarray of 1's After Deleting One Element

Topic: Array, Dynamic Programming, Sliding Window
Difficulty: Medium

Problem:
Given a binary array nums, you should delete one element from it.

Return the size of the longest non-empty subarray containing only 1's in the resulting array. Return 0 if there is no such subarray.

Example 1:

Input: nums = [1,1,0,1]
Output: 3
Explanation: After deleting the number in position 2, [1,1,1] contains 3 numbers with value of 1's.

Example 2:

Input: nums = [0,1,1,1,0,1,1,0,1]
Output: 5
Explanation: After deleting the number in position 4, [0,1,1,1,1,1,0,1] longest subarray with value of 1's is [1,1,1,1,1].

Example 3:

Input: nums = [1,1,1]
Output: 2
Explanation: You must delete one element.

Constraints:

• 1 <= nums.length <= 10^5
• nums[i] is either 0 or 1.

2025-08-25
498. Diagonal Traverse

Topic: Array, Matrix, Simulation
Difficulty: Medium

Problem:
Given an m x n matrix mat, return an array of all the elements of the array in a diagonal order.

Example 1:

Image: https://assets.leetcode.com/uploads/2021/04/10/diag1-grid.jpg

Input: mat = [[1,2,3],[4,5,6],[7,8,9]]
Output: [1,2,4,7,5,3,6,8,9]

Example 2:

Input: mat = [[1,2],[3,4]]
Output: [1,2,3,4]

Constraints:

• m == mat.length
• n == mat[i].length
• 1 <= m, n <= 10^4
• 1 <= m * n <= 10^4
• -10^5 <= mat[i][j] <= 10^5

2025-08-26
3000. Maximum Area of Longest Diagonal Rectangle

Topic: Array
Difficulty: Easy

Problem:
You are given a 2D 0-indexed integer array dimensions.

For all indices i, 0 <= i < dimensions.length, dimensions[i][0] represents the length and dimensions[i][1] represents the width of the rectangle i.

Return the area of the rectangle having the longest diagonal. If there are multiple rectangles with the longest diagonal, return the area of the rectangle having the maximum area.

Example 1:

Input: dimensions = [[9,3],[8,6]]
Output: 48
Explanation: 
For index = 0, length = 9 and width = 3. Diagonal length = sqrt(9 * 9 + 3 * 3) = sqrt(90) ≈ 9.487.
For index = 1, length = 8 and width = 6. Diagonal length = sqrt(8 * 8 + 6 * 6) = sqrt(100) = 10.
So, the rectangle at index 1 has a greater diagonal length therefore we return area = 8 * 6 = 48.

Example 2:

Input: dimensions = [[3,4],[4,3]]
Output: 12
Explanation: Length of diagonal is the same for both which is 5, so maximum area = 12.

Constraints:

• 1 <= dimensions.length <= 100
• dimensions[i].length == 2
• 1 <= dimensions[i][0], dimensions[i][1] <= 100

2025-08-27
3459. Length of Longest V-Shaped Diagonal Segment

Topic: Array, Dynamic Programming, Memoization, Matrix
Difficulty: Hard

Problem:
You are given a 2D integer matrix grid of size n x m, where each element is either 0, 1, or 2.

A V-shaped diagonal segment is defined as:

• The segment starts with 1.
• The subsequent elements follow this infinite sequence: 2, 0, 2, 0, ....
• The segment:
• Starts along a diagonal direction (top-left to bottom-right, bottom-right to top-left, top-right to bottom-left, or bottom-left to top-right).
• Continues the sequence in the same diagonal direction.
• Makes at most one clockwise 90-degree turn to another diagonal direction while maintaining the sequence.

Image: https://assets.leetcode.com/uploads/2025/01/11/length_of_longest3.jpg

Return the length of the longest V-shaped diagonal segment. If no valid segment exists, return 0.

Example 1:

Input: grid = [2,2,1,2,2,2,0,2,2,0,2,0,1,1,0,1,0,2,2,2,2,0,0,2,2]

Output: 5

Explanation:

Image: https://assets.leetcode.com/uploads/2024/12/09/matrix_1-2.jpg

The longest V-shaped diagonal segment has a length of 5 and follows these coordinates: (0,2) → (1,3) → (2,4), takes a 90-degree clockwise turn at (2,4), and continues as (3,3) → (4,2).

Example 2:

Input: grid = [2,2,2,2,2,2,0,2,2,0,2,0,1,1,0,1,0,2,2,2,2,0,0,2,2]

Output: 4

Explanation:

Image: https://assets.leetcode.com/uploads/2024/12/09/matrix_2.jpg

The longest V-shaped diagonal segment has a length of 4 and follows these coordinates: (2,3) → (3,2), takes a 90-degree clockwise turn at (3,2), and continues as (2,1) → (1,0).

Example 3:

Input: grid = [1,2,2,2,2,2,2,2,2,0,2,0,0,0,0,0,0,2,2,2,2,0,0,2,0]

Output: 5

Explanation:

Image: https://assets.leetcode.com/uploads/2024/12/09/matrix_3.jpg

The longest V-shaped diagonal segment has a length of 5 and follows these coordinates: (0,0) → (1,1) → (2,2) → (3,3) → (4,4).

Example 4:

Input: grid = [1]

Output: 1

Explanation:

The longest V-shaped diagonal segment has a length of 1 and follows these coordinates: (0,0).

Constraints:

• n == grid.length
• m == grid[i].length
• 1 <= n, m <= 500
• grid[i][j] is either 0, 1 or 2.

2025-08-28
3446. Sort Matrix by Diagonals

Topic: Array, Sorting, Matrix
Difficulty: Medium

Problem:
You are given an n x n square matrix of integers grid. Return the matrix such that:

• The diagonals in the bottom-left triangle (including the middle diagonal) are sorted in non-increasing order.
• The diagonals in the top-right triangle are sorted in non-decreasing order.

Example 1:

Input: grid = [1,7,3,9,8,2,4,5,6]

Output: [8,2,3,9,6,7,4,5,1]

Explanation:

Image: https://assets.leetcode.com/uploads/2024/12/29/4052example1drawio.png

The diagonals with a black arrow (bottom-left triangle) should be sorted in non-increasing order:

• [1, 8, 6] becomes [8, 6, 1].
• [9, 5] and [4] remain unchanged.

The diagonals with a blue arrow (top-right triangle) should be sorted in non-decreasing order:

• [7, 2] becomes [2, 7].
• [3] remains unchanged.

Example 2:

Input: grid = [0,1,1,2]

Output: [2,1,1,0]

Explanation:

Image: https://assets.leetcode.com/uploads/2024/12/29/4052example2adrawio.png

The diagonals with a black arrow must be non-increasing, so [0, 2] is changed to [2, 0]. The other diagonals are already in the correct order.

Example 3:

Input: grid = [1]

Output: [1]

Explanation:

Diagonals with exactly one element are already in order, so no changes are needed.

Constraints:

• grid.length == grid[i].length == n
• 1 <= n <= 10
• -10^5 <= grid[i][j] <= 10^5

2025-08-29
3021. Alice and Bob Playing Flower Game

Topic: Math
Difficulty: Medium

Problem:
Alice and Bob are playing a turn-based game on a field, with two lanes of flowers between them. There are x flowers in the first lane between Alice and Bob, and y flowers in the second lane between them.

Image: https://assets.leetcode.com/uploads/2025/08/27/3021.png

The game proceeds as follows:

1. Alice takes the first turn.
2. In each turn, a player must choose either one of the lane and pick one flower from that side.
3. At the end of the turn, if there are no flowers left at all, the current player captures their opponent and wins the game.

Given two integers, n and m, the task is to compute the number of possible pairs (x, y) that satisfy the conditions:

• Alice must win the game according to the described rules.
• The number of flowers x in the first lane must be in the range [1,n].
• The number of flowers y in the second lane must be in the range [1,m].

Return the number of possible pairs (x, y) that satisfy the conditions mentioned in the statement.

Example 1:

Input: n = 3, m = 2
Output: 3
Explanation: The following pairs satisfy conditions described in the statement: (1,2), (3,2), (2,1).

Example 2:

Input: n = 1, m = 1
Output: 0
Explanation: No pairs satisfy the conditions described in the statement.

Constraints:

• 1 <= n, m <= 10^5

2025-08-30
36. Valid Sudoku

Topic: Array, Hash Table, Matrix
Difficulty: Medium

Problem:
Determine if a 9 x 9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:

1. Each row must contain the digits 1-9 without repetition.
2. Each column must contain the digits 1-9 without repetition.
3. Each of the nine 3 x 3 sub-boxes of the grid must contain the digits 1-9 without repetition.

Note:

• A Sudoku board (partially filled) could be valid but is not necessarily solvable.
• Only the filled cells need to be validated according to the mentioned rules.

Example 1:

Image: https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Sudoku-by-L2G-20050714.svg/250px-Sudoku-by-L2G-20050714.svg.png

Input: board = 
[["5","3",".",".","7",".",".",".","."]
,["6",".",".","1","9","5",".",".","."]
,[".","9","8",".",".",".",".","6","."]
,["8",".",".",".","6",".",".",".","3"]
,["4",".",".","8",".","3",".",".","1"]
,["7",".",".",".","2",".",".",".","6"]
,[".","6",".",".",".",".","2","8","."]
,[".",".",".","4","1","9",".",".","5"]
,[".",".",".",".","8",".",".","7","9"]]
Output: true

Example 2:

Input: board = 
[["8","3",".",".","7",".",".",".","."]
,["6",".",".","1","9","5",".",".","."]
,[".","9","8",".",".",".",".","6","."]
,["8",".",".",".","6",".",".",".","3"]
,["4",".",".","8",".","3",".",".","1"]
,["7",".",".",".","2",".",".",".","6"]
,[".","6",".",".",".",".","2","8","."]
,[".",".",".","4","1","9",".",".","5"]
,[".",".",".",".","8",".",".","7","9"]]
Output: false
Explanation: Same as Example 1, except with the 5 in the top left corner being modified to 8. Since there are two 8's in the top left 3x3 sub-box, it is invalid.

Constraints:

• board.length == 9
• board[i].length == 9
• board[i][j] is a digit 1-9 or '.'.

2025-08-31
37. Sudoku Solver

Topic: Array, Hash Table, Backtracking, Matrix
Difficulty: Hard

Problem:
Write a program to solve a Sudoku puzzle by filling the empty cells.

A sudoku solution must satisfy all of the following rules:

1. Each of the digits 1-9 must occur exactly once in each row.
2. Each of the digits 1-9 must occur exactly once in each column.
3. Each of the digits 1-9 must occur exactly once in each of the 9 3x3 sub-boxes of the grid.

The '.' character indicates empty cells.

Example 1:

Image: https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Sudoku-by-L2G-20050714.svg/250px-Sudoku-by-L2G-20050714.svg.png

Input: board = [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]
Output: [["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]
Explanation: The input board is shown above and the only valid solution is shown below:

Image: [https://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Sudoku-by-L2G-20050714_solution.svg/250px-Sudoku-by-L2G-20050714_solution.svg.png](https://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Sudoku-by-L2G-20050714_solution.svg/250px-Sudoku-by-L2G-20050714_solution.svg.png)

Constraints:

• board.length == 9
• board[i].length == 9
• board[i][j] is a digit or '.'.
• It is guaranteed that the input board has only one solution.

2025-09-01
1792. Maximum Average Pass Ratio

Topic: Array, Greedy, Heap (Priority Queue)
Difficulty: Medium

Problem:
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 <= 10^5
• classes[i].length == 2
• 1 <= pass_i <= total_i <= 10^5
• 1 <= extraStudents <= 10^5

2025-09-02
3025. Find the Number of Ways to Place People I

Topic: Array, Math, Geometry, Sorting, Enumeration
Difficulty: Medium

Problem:
You are given a 2D array points of size n x 2 representing integer coordinates of some points on a 2D plane, where points[i] = [x_i, y_i].

Count the number of pairs of points (A, B), where

• A is on the upper left side of B, and
• there are no other points in the rectangle (or line) they make (including the border).

Return the count.

Example 1:

Input: points = [1,1,2,2,3,3]

Output: 0

Explanation:

Image: https://assets.leetcode.com/uploads/2024/01/04/example1alicebob.png

There is no way to choose A and B so A is on the upper left side of B.

Example 2:

Input: points = [6,2,4,4,2,6]

Output: 2

Explanation:

Image: https://assets.leetcode.com/uploads/2024/06/25/t2.jpg

• The left one is the pair (points[1], points[0]), where points[1] is on the upper left side of points[0] and the rectangle is empty.
• The middle one is the pair (points[2], points[1]), same as the left one it is a valid pair.
• The right one is the pair (points[2], points[0]), where points[2] is on the upper left side of points[0], but points[1] is inside the rectangle so it's not a valid pair.

Example 3:

Input: points = [3,1,1,3,1,1]

Output: 2

Explanation:

Image: https://assets.leetcode.com/uploads/2024/06/25/t3.jpg

• The left one is the pair (points[2], points[0]), where points[2] is on the upper left side of points[0] and there are no other points on the line they form. Note that it is a valid state when the two points form a line.
• The middle one is the pair (points[1], points[2]), it is a valid pair same as the left one.
• The right one is the pair (points[1], points[0]), it is not a valid pair as points[2] is on the border of the rectangle.

Constraints:

• 2 <= n <= 50
• points[i].length == 2
• 0 <= points[i][0], points[i][1] <= 50
• All points[i] are distinct.

2025-09-03
3027. Find the Number of Ways to Place People II

Topic: Array, Math, Geometry, Sorting, Enumeration
Difficulty: Hard

Problem:
You are given a 2D array points of size n x 2 representing integer coordinates of some points on a 2D-plane, where points[i] = [x_i, y_i].

We define the right direction as positive x-axis (increasing x-coordinate) and the left direction as negative x-axis (decreasing x-coordinate). Similarly, we define the up direction as positive y-axis (increasing y-coordinate) and the down direction as negative y-axis (decreasing y-coordinate)

You have to place n people, including Alice and Bob, at these points such that there is exactly one person at every point. Alice wants to be alone with Bob, so Alice will build a rectangular fence with Alice's position as the upper left corner and Bob's position as the lower right corner of the fence (Note that the fence might not enclose any area, i.e. it can be a line). If any person other than Alice and Bob is either inside the fence or on the fence, Alice will be sad.

Return the number of pairs of points where you can place Alice and Bob, such that Alice does not become sad on building the fence.

Note that Alice can only build a fence with Alice's position as the upper left corner, and Bob's position as the lower right corner. For example, Alice cannot build either of the fences in the picture below with four corners (1, 1), (1, 3), (3, 1), and (3, 3), because:

• With Alice at (3, 3) and Bob at (1, 1), Alice's position is not the upper left corner and Bob's position is not the lower right corner of the fence.
• With Alice at (1, 3) and Bob at (1, 1), Bob's position is not the lower right corner of the fence.

Image: https://assets.leetcode.com/uploads/2024/01/04/example0alicebob-1.png

Example 1:

Image: https://assets.leetcode.com/uploads/2024/01/04/example1alicebob.png

Input: points = [[1,1],[2,2],[3,3]]
Output: 0
Explanation: There is no way to place Alice and Bob such that Alice can build a fence with Alice's position as the upper left corner and Bob's position as the lower right corner. Hence we return 0.

Example 2:

Image: https://assets.leetcode.com/uploads/2024/02/04/example2alicebob.png

Input: points = [[6,2],[4,4],[2,6]]
Output: 2
Explanation: There are two ways to place Alice and Bob such that Alice will not be sad:
- Place Alice at (4, 4) and Bob at (6, 2).
- Place Alice at (2, 6) and Bob at (4, 4).
You cannot place Alice at (2, 6) and Bob at (6, 2) because the person at (4, 4) will be inside the fence.

Example 3:

Image: https://assets.leetcode.com/uploads/2024/02/04/example4alicebob.png

Input: points = [[3,1],[1,3],[1,1]]
Output: 2
Explanation: There are two ways to place Alice and Bob such that Alice will not be sad:
- Place Alice at (1, 1) and Bob at (3, 1).
- Place Alice at (1, 3) and Bob at (1, 1).
You cannot place Alice at (1, 3) and Bob at (3, 1) because the person at (1, 1) will be on the fence.
Note that it does not matter if the fence encloses any area, the first and second fences in the image are valid.

Constraints:

• 2 <= n <= 1000
• points[i].length == 2
• -10^9 <= points[i][0], points[i][1] <= 10^9
• All points[i] are distinct.

2025-09-04
3516. Find Closest Person

Topic: Math
Difficulty: Easy

Problem:
You are given three integers x, y, and z, representing the positions of three people on a number line:

• x is the position of Person 1.
• y is the position of Person 2.
• z is the position of Person 3, who does not move.

Both Person 1 and Person 2 move toward Person 3 at the same speed.

Determine which person reaches Person 3 first:

• Return 1 if Person 1 arrives first.
• Return 2 if Person 2 arrives first.
• Return 0 if both arrive at the same time.

Return the result accordingly.

Example 1:

Input: x = 2, y = 7, z = 4

Output: 1

Explanation:

• Person 1 is at position 2 and can reach Person 3 (at position 4) in 2 steps.
• Person 2 is at position 7 and can reach Person 3 in 3 steps.

Since Person 1 reaches Person 3 first, the output is 1.

Example 2:

Input: x = 2, y = 5, z = 6

Output: 2

Explanation:

• Person 1 is at position 2 and can reach Person 3 (at position 6) in 4 steps.
• Person 2 is at position 5 and can reach Person 3 in 1 step.

Since Person 2 reaches Person 3 first, the output is 2.

Example 3:

Input: x = 1, y = 5, z = 3

Output: 0

Explanation:

• Person 1 is at position 1 and can reach Person 3 (at position 3) in 2 steps.
• Person 2 is at position 5 and can reach Person 3 in 2 steps.

Since both Person 1 and Person 2 reach Person 3 at the same time, the output is 0.

Constraints:

• 1 <= x, y, z <= 100

2025-09-05
2749. Minimum Operations to Make the Integer Zero

Topic: Bit Manipulation, Brainteaser, Enumeration
Difficulty: Medium

Problem:
You are given two integers num1 and num2.

In one operation, you can choose integer i in the range [0, 60] and subtract 2^i + num2 from num1.

Return the integer denoting the minimum number of operations needed to make num1 equal to 0.

If it is impossible to make num1 equal to 0, return -1.

Example 1:

Input: num1 = 3, num2 = -2
Output: 3
Explanation: We can make 3 equal to 0 with the following operations:
- We choose i = 2 and subtract 2^2 + (-2) from 3, 3 - (4 + (-2)) = 1.
- We choose i = 2 and subtract 2^2 + (-2) from 1, 1 - (4 + (-2)) = -1.
- We choose i = 0 and subtract 2^0 + (-2) from -1, (-1) - (1 + (-2)) = 0.
It can be proven, that 3 is the minimum number of operations that we need to perform.

Example 2:

Input: num1 = 5, num2 = 7
Output: -1
Explanation: It can be proven, that it is impossible to make 5 equal to 0 with the given operation.

Constraints:

• 1 <= num1 <= 10^9
• -10^9 <= num2 <= 10^9