LeetCode 839. Similar String Groups

Two strings X and Y are similar if we can swap two letters (in different positions) of X, so that it equals Y.

For example, "tars" and "rats" are similar (swapping at positions 0 and 2), and "rats" and "arts" are similar, but "star" is not similar to "tars", "rats", or "arts".

Together, these form two connected groups by similarity: {"tars", "rats", "arts"} and {"star"}. Notice that "tars" and "arts"are in the same group even though they are not similar. Formally, each group is such that a word is in the group if and only if it is similar to at least one other word in the group.

We are given a list A of unique strings. Every string in A is an anagram of every other string in A. How many groups are there?

Example 1:

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Input: ["tars","rats","arts","star"]
Output: 2

Note:

  1. A.length <= 2000
  2. A[i].length <= 1000
  3. A.length * A[i].length <= 20000
  4. All words in A consist of lowercase letters only.
  5. All words in A have the same length and are anagrams of each other.
  6. The judging time limit has been increased for this question.

LeetCode 838. Push Dominoes

There are N dominoes in a line, and we place each domino vertically upright.

In the beginning, we simultaneously push some of the dominoes either to the left or to the right.

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After each second, each domino that is falling to the left pushes the adjacent domino on the left.

Similarly, the dominoes falling to the right push their adjacent dominoes standing on the right.

When a vertical domino has dominoes falling on it from both sides, it stays still due to the balance of the forces.

For the purposes of this question, we will consider that a falling domino expends no additional force to a falling or already fallen domino.

Given a string “S” representing the initial state. S[i] = 'L', if the i-th domino has been pushed to the left; S[i] = 'R', if the i-th domino has been pushed to the right; S[i] = '.', if the i-th domino has not been pushed.

Return a string representing the final state.

Example 1:

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Input: ".L.R...LR..L.."
Output: "LL.RR.LLRRLL.."

Example 2:

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Input: "RR.L"
Output: "RR.L"
Explanation: The first domino expends no additional force on the second domino.

Note:

  1. 0 <= N <= 10^5
  2. String dominoes contains only 'L', 'R' and '.'

LeetCode 837. New 21 Game

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, W], where W is an integer. Each draw is independent and the outcomes have equal probabilities.

Alice stops drawing numbers when she gets K or more points. What is the probability that she has N or less points?

Example 1:

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Input: N = 10, K = 1, W = 10
Output: 1.00000
Explanation: Alice gets a single card, then stops.

Example 2:

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

Example 3:

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Input: N = 21, K = 17, W = 10
Output: 0.73278

Note:

  1. 0 <= K <= N <= 10000
  2. 1 <= W <= 10000
  3. Answers will be accepted as correct if they are within 10^-5 of the correct answer.
  4. The judging time limit has been reduced for this question.

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.