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花花酱 LeetCode 210. Course Schedule II

Problem

There are a total of n courses you have to take, labeled from 0 to n - 1.

Some courses may have prerequisites, for example to take course 0 you have to first take course 1, which is expressed as a pair: [0,1]

Given the total number of courses and a list of prerequisite pairs, return the ordering of courses you should take to finish all courses.

There may be multiple correct orders, you just need to return one of them. If it is impossible to finish all courses, return an empty array.

For example:

There are a total of 2 courses to take. To take course 1 you should have finished course 0. So the correct course order is [0,1]

There are a total of 4 courses to take. To take course 3 you should have finished both courses 1 and 2. Both courses 1 and 2 should be taken after you finished course 0. So one correct course order is [0,1,2,3]. Another correct ordering is[0,2,1,3].

Note:

  1. The input prerequisites is a graph represented by a list of edges, not adjacency matrices. Read more about how a graph is represented.
  2. You may assume that there are no duplicate edges in the input prerequisites.

题目大意:

给你一些课程和它的先修课程,让你输出修课顺序。如果无法修完所有课程,返回空数组。


Idea

Topological sorting

拓扑排序

Solution 1: Topological Sorting

Time complexity: O(V+E)

Space complexity: O(V+E)

C++

Java

Related Problems:

花花酱 LeetCode 742. Closest Leaf in a Binary Tree

Problem:

Given a binary tree where every node has a unique value, and a target key k, find the value of the closest leaf node to target k in the tree.

Here, closest to a leaf means the least number of edges travelled on the binary tree to reach any leaf of the tree. Also, a node is called a leaf if it has no children.

In the following examples, the input tree is represented in flattened form row by row. The actual root tree given will be a TreeNode object.

Example 1:

Example 2:

Example 3:

Note:

  1. root represents a binary tree with at least 1 node and at most 1000 nodes.
  2. Every node has a unique node.val in range [1, 1000].
  3. There exists some node in the given binary tree for which node.val == k.


题目大意:

给你一棵树,每个节点的值都不相同。

给定一个节点值,让你找到离这个节点距离最近的叶子节点的值。

Idea:

Shortest path from source to any leaf nodes in a undirected unweighted graph.

问题转换为在无向/等权重的图中找一条从起始节点到任意叶子节点最短路径。

Solution:

C++ / DFS + BFS

Time complexity: O(n)

Space complexity: O(n)

 

花花酱 LeetCode 743. Network Delay Time

There are N network nodes, labelled 1 to N.

Given times, a list of travel times as directed edges times[i] = (u, v, w), where u is the source node, v is the target node, and w is the time it takes for a signal to travel from source to target.

Now, we send a signal from a certain node K. How long will it take for all nodes to receive the signal? If it is impossible, return -1.

Note:

  1. N will be in the range [1, 100].
  2. K will be in the range [1, N].
  3. The length of times will be in the range [1, 6000].
  4. All edges times[i] = (u, v, w) will have 1 <= u, v <= N and 1 <= w <= 100.

Idea:

Construct the graph and do a shortest path from K to all other nodes.

Solution 2:

C++ / Bellman-Ford

Time complexity: O(ne)

Space complexity: O(n)

 

Solution3:

C++ / Floyd-Warshall

Time complexity: O(n^3)

Space complexity: O(n^2)

v2

花花酱 LeetCode 399. Evaluate Division

题目大意:给你一些含有变量名的分式的值,让你计算另外一些分式的值,如果不能计算返回-1。

Problem:

Equations are given in the format A / B = k, where A and B are variables represented as strings, and k is a real number (floating point number). Given some queries, return the answers. If the answer does not exist, return -1.0.

Example:
Given a / b = 2.0, b / c = 3.0.
queries are: a / c = ?, b / a = ?, a / e = ?, a / a = ?, x / x = ? .
return [6.0, 0.5, -1.0, 1.0, -1.0 ].

The input is: vector<pair<string, string>> equations, vector<double>& values, vector<pair<string, string>> queries , where equations.size() == values.size(), and the values are positive. This represents the equations. Return vector<double>.

According to the example above:

The input is always valid. You may assume that evaluating the queries will result in no division by zero and there is no contradiction.

 

Solution 1: DFS

C++

Java

Python3



Solution 2: Union Find

C++

Java

Python3

Related Problems:

花花酱 LeetCode 733. Flood Fill

Problem:

An image is represented by a 2-D array of integers, each integer representing the pixel value of the image (from 0 to 65535).

Given a coordinate (sr, sc) representing the starting pixel (row and column) of the flood fill, and a pixel value newColor, “flood fill” the image.

To perform a “flood fill”, consider the starting pixel, plus any pixels connected 4-directionally to the starting pixel of the same color as the starting pixel, plus any pixels connected 4-directionally to those pixels (also with the same color as the starting pixel), and so on. Replace the color of all of the aforementioned pixels with the newColor.

At the end, return the modified image.

Example 1:

Note:

 

  • The length of image and image[0] will be in the range [1, 50].
  • The given starting pixel will satisfy 0 <= sr < image.length and 0 <= sc < image[0].length.
  • The value of each color in image[i][j] and newColor will be an integer in [0, 65535].


Idea

DFS

Solution:

C++ / DFS

Time complexity: O(mn)

Space complexity: O(1)

Related Problems: