LeetCode 836. Rectangle Overlap

A rectangle is represented as a list [x1, y1, x2, y2], where (x1, y1) are the coordinates of its bottom-left corner, and (x2, y2) are the coordinates of its top-right corner.

Two rectangles overlap if the area of their intersection is positive. To be clear, two rectangles that only touch at the corner or edges do not overlap.

Given two rectangles, return whether they overlap.

Example 1:

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Input: rec1 = [0,0,2,2], rec2 = [1,1,3,3]
Output: true

Example 2:

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Input: rec1 = [0,0,1,1], rec2 = [1,0,2,1]
Output: false

Notes:

  1. Both rectangles rec1 and rec2 are lists of 4 integers.
  2. All coordinates in rectangles will be between -10^9and10^9.

三门问题(蒙提霍尔问题)

三门问题,又称蒙提霍尔问题我很久以前就在网上看到过,但是一直对于网上流传的各种复杂的概率解释没什么兴趣,也一直没有想明白。昨天跟朋友突然说起这个问题,起因是虎扑的这个帖子试图用蒙特卡罗模拟来实验一下(可惜的是,这个程序写的有点小错误,不知道你发现没有),也激发了我想来用程序模拟一下的想法,没想到思考了一会之后发现从逻辑的角度来说可以非常简单的解释和理解,不需要任何概率统计的知识(或者说,小学水平?)。

LeetCode 803. Bricks Falling When Hit

We have a grid of 1s and 0s; the 1s in a cell represent bricks. A brick will not drop if and only if it is directly connected to the top of the grid, or at least one of its (4-way) adjacent bricks will not drop.

We will do some erasures sequentially. Each time we want to do the erasure at the location (i, j), the brick (if it exists) on that location will disappear, and then some other bricks may drop because of that erasure.

Return an array representing the number of bricks that will drop after each erasure in sequence.

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Example 1:
Input:
grid = [[1,0,0,0],[1,1,1,0]]
hits = [[1,0]]
Output: [2]
Explanation:
If we erase the brick at (1, 0), the brick at (1, 1) and (1, 2) will drop. So we should return 2.
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Example 2:
Input:
grid = [[1,0,0,0],[1,1,0,0]]
hits = [[1,1],[1,0]]
Output: [0,0]
Explanation:
When we erase the brick at (1, 0), the brick at (1, 1) has already disappeared due to the last move. So each erasure will cause no bricks dropping. Note that the erased brick (1, 0) will not be counted as a dropped brick.

Note:

  • The number of rows and columns in the grid will be in the range [1, 200].
  • The number of erasures will not exceed the area of the grid.
  • It is guaranteed that each erasure will be located inside the grid.
  • An erasure may refer to a location with no brick - if it does, no bricks drop.

LeetCode 802. Find Eventual Safe States

In a directed graph, we start at some node and every turn, walk along a directed edge of the graph. If we reach a node that is terminal (that is, it has no outgoing directed edges), we stop.

Now, say our starting node is *eventually safe *if and only if we must eventually walk to a terminal node. More specifically, there exists a natural number K so that for any choice of where to walk, we must have stopped at a terminal node in less than K steps.

Which nodes are eventually safe? Return them as an array in sorted order.

The directed graph has N nodes with labels 0, 1, ..., N-1, where N is the length of graph. The graph is given in the following form: graph[i] is a list of labels j such that (i, j) is a directed edge of the graph.

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Example:
Input: graph = [[1,2],[2,3],[5],[0],[5],[],[]]
Output: [2,4,5,6]
Here is a diagram of the above graph.

Illustration of graph

Note:

  • graph will have length at most 10000.
  • The number of edges in the graph will not exceed 32000.
  • Each graph[i] will be a sorted list of different integers, chosen within the range [0, graph.length - 1].

LeetCode 801. Minimum Swaps To Make Sequences Increasing

We have two integer sequences A and B of the same non-zero length.

We are allowed to swap elements A[i] and B[i]. Note that both elements are in the same index position in their respective sequences.

At the end of some number of swaps, A and B are both strictly increasing. (A sequence is strictly increasing if and only if A[0] < A[1] < A[2] < ... < A[A.length - 1].)

Given A and B, return the minimum number of swaps to make both sequences strictly increasing. It is guaranteed that the given input always makes it possible.

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Example:
Input: A = [1,3,5,4], B = [1,2,3,7]
Output: 1
Explanation:
Swap A[3] and B[3]. Then the sequences are:
A = [1, 3, 5, 7] and B = [1, 2, 3, 4]
which are both strictly increasing.

Note:

  • A, B are arrays with the same length, and that length will be in the range [1, 1000].
  • A[i], B[i] are integer values in the range [0, 2000].

LeetCode 800. Similar RGB Color

In the following, every capital letter represents some hexadecimal digit from 0 to f.

The red-green-blue color "#AABBCC" can be written as "#ABC" in shorthand. For example, "#15c" is shorthand for the color "#1155cc".

Now, say the similarity between two colors "#ABCDEF" and "#UVWXYZ" is -(AB - UV)^2 - (CD - WX)^2 - (EF - YZ)^2.

Given the color "#ABCDEF", return a 7 character color that is most similar to #ABCDEF, and has a shorthand (that is, it can be represented as some "#XYZ"

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Example 1:
Input: color = "#09f166"
Output: "#11ee66"
Explanation:
The similarity is -(0x09 - 0x11)^2 -(0xf1 - 0xee)^2 - (0x66 - 0x66)^2 = -64 -9 -0 = -73.
This is the highest among any shorthand color.

Note:

  • color is a string of length 7.
  • color is a valid RGB color: for i > 0, color[i] is a hexadecimal digit from 0 to f
  • Any answer which has the same (highest) similarity as the best answer will be accepted.
  • All inputs and outputs should use lowercase letters, and the output is 7 characters.

LeetCode 765. Couples Holding Hands

N couples sit in 2N seats arranged in a row and want to hold hands. We want to know the minimum number of swaps so that every couple is sitting side by side. A swap consists of choosing any two people, then they stand up and switch seats.

The people and seats are represented by an integer from 0 to 2N-1, the couples are numbered in order, the first couple being (0, 1), the second couple being (2, 3), and so on with the last couple being (2N-2, 2N-1).

The couples’ initial seating is given by row[i] being the value of the person who is initially sitting in the i-th seat.

Example 1:

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Input: row = [0, 2, 1, 3]
Output: 1
Explanation: We only need to swap the second (row[1]) and third (row[2]) person.

Example 2:

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Input: row = [3, 2, 0, 1]
Output: 0
Explanation: All couples are already seated side by side.

Note:

  1. len(row) is even and in the range of [4, 60].
  2. row is guaranteed to be a permutation of 0...len(row)-1.

LeetCode 764. Largest Plus Sign

In a 2D grid from (0, 0) to (N-1, N-1), every cell contains a 1, except those cells in the given list mines which are 0. What is the largest axis-aligned plus sign of 1s contained in the grid? Return the order of the plus sign. If there is none, return 0.

An “axis-aligned plus sign of 1s of order k” has some center grid[x][y] = 1 along with 4 arms of length k-1 going up, down, left, and right, and made of 1s. This is demonstrated in the diagrams below. Note that there could be 0s or 1s beyond the arms of the plus sign, only the relevant area of the plus sign is checked for 1s.

Examples of Axis-Aligned Plus Signs of Order k:

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Order 1:
000
010
000

Order 2:
00000
00100
01110
00100
00000

Order 3:
0000000
0001000
0001000
0111110
0001000
0001000
0000000

Example 1:

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Input: N = 5, mines = [[4, 2]]
Output: 2
Explanation:
11111
11111
11111
11111
11011
In the above grid, the largest plus sign can only be order 2. One of them is marked in bold.

Example 2:

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Input: N = 2, mines = []
Output: 1
Explanation:
There is no plus sign of order 2, but there is of order 1.

Example 3:

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Input: N = 1, mines = [[0, 0]]
Output: 0
Explanation:
There is no plus sign, so return 0.

Note:

  1. N will be an integer in the range [1, 500].
  2. mines will have length at most 5000.
  3. mines[i] will be length 2 and consist of integers in the range [0, N-1].
  4. (Additionally, programs submitted in C, C++, or C# will be judged with a slightly smaller time limit.)

LeetCode 763. Partition Labels

A string S of lowercase letters is given. We want to partition this string into as many parts as possible so that each letter appears in at most one part, and return a list of integers representing the size of these parts.

Example 1:

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Input: S = "ababcbacadefegdehijhklij"
Output: [9,7,8]
Explanation:
The partition is "ababcbaca", "defegde", "hijhklij".
This is a partition so that each letter appears in at most one part.
A partition like "ababcbacadefegde", "hijhklij" is incorrect, because it splits S into less parts.

Note:

  1. S will have length in range [1, 500].
  2. S will consist of lowercase letters ('a' to 'z') only.