Data structure-graph theory

Section 1-Graph traversal

	topic	Difficulty	Accept
1	[Example question] One-stroke drawing problem		submit
2	Snow shovel		submit
3	Riding a fence		submit

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Section 2-Shortest Path

一、单源最短路: The side right cannot be negative;

1. dijkstra (朴素版)：$O(n^2)$
2. dijkstra (堆优化)：$O\left(mlogn\right)$

二、单源最短路: The side weight can be positive or negative, but there can be no negative weight loop;

1. bellman_ford：$O(nm)$
2. spfa：General $O\left(m\right)$ , the worst$O\left(nm\right)$

三、多源最短路: The side weight can be positive or negative, but there can be no negative weight loop;

1. floyd：$O(n^3)$

	topic	Difficulty	Accept
1	[Example 4.1] The shortest path problem	Simple +	submit
2	[Example 4.2] The travel of the cow	medium	submit
3	【Example 4.4】Minimum cost	medium	submit
4	[Example 4.6] Sweet butter	medium	submit
5	messenger	simple	submit
6	Optimal ride	difficult	submit
7	Shortest path	Simple +	submit
8	Heat wave	simple	submit
9	Divide candy	medium	submit
10	City road	simple	submit
11	Shortest path	simple	submit
12	SPFA (II)	unknown	No permission
13	Dijkstra (II)	unknown	No permission
14	Floyd	unknown	No permission

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Section 3-Connectivity of Graphs

	topic	Difficulty	Accept
1	Record CD		submit
2	pearl		submit

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Section 4-Consolidation

find函数：

1. 无优化: Average $O\left(logn\right)$ , the worst$O\left(n\right)$
2. 路径压缩: Average $O\left(\alpha \right(n\left)\right)$ , the worst$O\left(logn\right)$
3. 按秩合并: Average $O\left(logn\right)$ , the worst$O\left(logn\right)$
4. 路径压缩 + 按秩合并: Average $O\left(\alpha \right(n\left)\right)$， 最坏$O\left(\alpha \right(n\left)\right)$

α: Inverse Ackerman function, for the possible value n, $\alpha \left(n\right)$ are all less than 5;

	topic	Difficulty	Accept
1	[Example 4.7] Relatives	simple	submit
2	[Example 4.8] Grid game	Simple +	submit
3	Gang	Simple +	submit
4	Fight crime	medium	submit
5	Match sale	medium	submit
6	genealogy	Simple +	submit
7	relative	Simple +	submit
8	Food chain	difficult	submit

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Section 5-Minimum Spanning Tree

	topic	Difficulty	Accept
1	[Example 4.9] The construction of urban public transport network		submit
2	[Example 4.10] Optimal wiring problem		submit
3	[Example 4.11] The shortest network		submit
4	[Example 4.12] Family Tree		submit
5	local area network		submit
6	Busy city		submit
7	Liaison		submit
8	Connected grid		submit

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Section 6-Topological Sorting and Critical Path

	topic	Difficulty	Accept
1	[Example 4.13] Bonus		submit
2	Annoying slideshow		submit
3	virus		submit